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AU / Finance / FINC 3610 / comprehensive vs cumulative final exam

# comprehensive vs cumulative final exam Description

##### Description: These are the notes for the whole course for our comprehensive/cumulative final. I've included the class notes for Exams 1 and 2, and my cheat sheets for both as well as all class notes since the 2nd
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Tuesday, October 30, 2018 9:30 AM Investment Criteria - Chapter 9

## To what extent was time a factor?

Exam 2 results

- To what extent was time a factor? Low end

- Fairness? Class is split

- Difficulty? Higher end

Mean = 20.82 (69.4%)

Median = 21 (70%)

Chapter 9: Investment Criteria

- Will need to know how to calculate 7 different criteria and how to use them

○ Net Present Value

What: NPV is a measure of how much value is created or added today by undertaking an investment (the difference between an investment's market value and its cost)

 How: Estimate future cash flows. Calculate the present value of those cash flows minus the initial cost Rate of Return also known as: required rate of return, cost of capital, appropriate discount rate

Example: plan to buy machine for \$2,000 today and will produce cash flows of \$1,500 in each of next two years. Salvage value of \$0. Cost of capital is 15%. Should you buy machine?

## how to calculate 7 different criteria?

(\$1,500/1.15) + (\$1,500/(1.15*1.15)) - \$2,000 = \$438.56

OR

N = 2

I/Y = 15% PV = ???

= -\$2,438.5633

That is total, and we've already spent \$2,000, so value created by investment is \$438.5633

PMT = \$1,500

FV = 0

 Calculator Instructions

□ TI

CF (button)

2nd

Clear work

2,000

Plus/Minus button (not subtraction

Enter (must enter amount first

Down arrow

1500 Enter

Down arrow

Enter (f is frequency indicator -

keep at 1)

Down arrow

1500

NPV

15

Enter

Down arrow

Compute

□ HP

 Clear cash flow register - Orange shift and C All

Enter cash flows with CF button (so -2,000, 1,500, 1,500)

Final Exam Page 1

 Enter cash flows with CFj button (so -2,000, 1,500, 1,500)

## What is capital budgeting?

 Enter 15 using I/Y button

 Orange shift and NPV to calculate whole value of cash flows  Don't forget about the age old question of chem 1b sjsu

The Rule: an investment should be accepted if net present value is positive and rejected if it is negative

□ Assumes cash flows are reinvested at the cost of capital

 Pros

□ Uses all cash flows

□ Adjusts for Time Value of Money - timing and risk

 Cons

□ Need appropriate discount rate

□ Relatively more difficult to communicate

Final Exam Page 2

Thursday, November 1, 2018 9:30 AM More on Investment Criteria

Quiz Question Review

- True

-

Could move all amounts back to same time period or use calculator. Remember to enter initial cash outflow as   With CF calculator functions (HP)

negative amount. Enter all cash returns, the interest rate, and compute.

Announcements

- Excel Bootcamp!!! Friday, Nov. 9th

Investment Criteria

- Covered NPV on Tuesday

○ Pros

 Uses all cash flows

 Adjusts for time value of money (adjusting for risk and timing of cash flows) ○ Cons

 Need appropriate discount rate

 Relatively more difficult to communicate

- Internal Rate of Return

What: The internal rate of return is the discount rate that makes the net present value of a project equal to

zero.

How: Set NPV equal to zero and solve for "r." Calculating IRR is identical to calculating the yield to maturity  on the books.

Example: You plan to buy machine for \$2,000 today and produce cash flows of \$1,500 in each of next two  years. Salvage value = 0. Cost of capital is 15%. Don't forget about the age old question of msu d2l bozeman

 )

NPV(0) = -2,000 + (1,500 / (1 + r)1) + (1,500 / (1 + r)2 We also discuss several other topics like brooklyn study guide

 )

2,000 = (1,500 / (1 + r)1) + (1,500 / (1 + r)2

 Because this is annuity, can plug into calculator

FV = 0

N = 2

31.8729%

PV = -2,000

I/Y = ??? PMT = 1,500

□ Enter cash flows (-2,000, 1,500, 1,500)

□ Orange shift, then IRR/YR (CST button)

The Rule: an investment is acceptable if IRR exceeds the required rate of return. It should be rejected  otherwise *Assumes cash flows are reinvested at the IRR

○ Pros:

 Closely related to the NPV rule

 Relatively easier to communicate

○ Cons:

 May result in multiple answers (nonconventional cash flows)

 May result in incorrect decisions (mutually exclusive investments)

- NPV Profile

○ What is it?

 A graph showing relation between NPV of a project and various discount rates.

○ What information does it provide?

 Range of rates where NPV is positive (accept)

 Range of rates where NPV is negative (reject)

 Rate where NPV equals 0

□ Also called the IRR

 Slope of the line - sensitivity of NPV to the rate

○ Beware

 Non-conventional cash flows. (Conventional is negative first, then all positive)

□ Ex. (-252, 1431, -3035, 2850, -1000)

□ At 25% = 0

□ At 33.33% = different for different calculators/scientific notation, close to 0 □ 42.86% = .000007002 We also discuss several other topics like istudy ole miss

□ 66.67% = scientific notation/close to 0

□ The maximum # of IRR's you can have is = # times signs change on cash flows  Mutually exclusive projects

□ Example:

Final Exam Page 3

□ 42.86% = .000007002

□ 66.67% = scientific notation/close to 0

□ The maximum # of IRR's you can have is = # times signs change on cash flows  Mutually exclusive projects

□ Example:

Year

Project A

0

-350

1

50

2

100

3

150

4

200

Result

12.9082

Project B

-250

125

100

75

50

17.8047

□ Would choose B based on these results □ Crossover rate = incremental IRR (light blue line) □ Calculate difference in cash flows

A

-350

50

100

150

200

8.0683

B A - B  -250 -100  125 -75  100 0

75 75

50 150

□ Accept Project A below 8.0683, either at 8.0683, and B above 8.0683  Can happen when

□ Scale of project is different

□ When differences in timing of cash flows

Final Exam Page 4

Tuesday, November 6, 2018 9:30 AM Capital Budgeting - Chapter 10

No Recording Today! If you want to learn more check out engl 3451 class notes

Quiz Review

-

T/F - If we are evaluating mutually exclusive projects with conventional cash flows, then the net present value and internal rate of return methods always result in same decision ○ False

-

A project has a cost of capital of 12%, an initial cost of \$1,200 and cash flows of \$500 each year for 3 years. Calculate IRR Don't forget about the age old question of What is the meaning of epithelial?

N = 3

I/Y = ???

PV = -\$1,200 PMT = \$500

○ FV = 0 ○ OR: Cash flows of -\$1,200, \$500, \$500, \$500 and IRR button - Question 3 was a gimme - what will Keven dress up as for Halloween next year

Investment Criteria

- So far have covered

○ NPV and IRR

 With IRR, implicit assumption reinvestment at rate of IRR  Can result in multiple IRRs (nonconventional cash flows)

 Could be inconsistent with NPV rule

 NPV - crossover rate

- Modified Internal Rate of Return (MIRR)

○ Book talks about multiple ways to determine this

○ We focus on combination approach

What: MIRR is a calculation of IRR on modified cash flows. For the combination approach, it is the discount rate that equates the present value of all cash outflows to the future value of all cash inflows.○

How: For the combo, discount all cash outflows to time period 0 and compound all cash inflows to the end of the project. Then, calculate the discount rate that makes them equal.

Example: You plan to buy a machine that will cost \$2,000 today and produce cash flows of \$1,500, -\$500, and \$1,200 in each of the next three years. The salvage value will be zero. The cost of capital is 15%. Should you buy the machine?

 Move -\$500 back to Year 0

 Move 1,500 to Year 3

N = 3 I/Y = ???

PV = -\$2,378.07 PMT = 0 FV = \$3,183.75

R = 10.21%

Final Exam Page 5

R = 10.21%

The Rule: An investment is acceptable if the MIRR exceeds the required rate of return. It should be rejected otherwise. *Assumes cash flows are reinvested at the cost of capital

○ Pros:

 Closely related to NPV rule

 No longer possible to get multiple answers

○ Cons:

 May result in incorrect decisions (mutually exclusive investments) - The Profitability Index

What: The profitability index is the present value of an investment's future cash flows divided by its initial cost (absolute value). Also called a benefit-cost ratio.

How: Calculate the present value of the future cash flows (the PV, not the NPV) and divide by the initial cost. If a project has a positive (negative) NPV, the PI will be greater (less) than 1. ○ PI = PV of future cash flows divided by Initial Cost

○ PI = (Initial Cost + PV of future cash flows - Initial Cost) divided by Initial Cost ○ PV of future cash flows - Initial Cost = NPV

Example: You plan to buy a machine that will cost \$2,000 today and produce cash flows of \$1,500 in each of the next two years. Salvage value = 0. Cost of capital is 15%. What is its profitability index? Should you buy the machine?

PI > 1, so accept

○ Example: Must choose between 2 following mutually exclusive projects:  A - cost is \$25 and PV is \$50

 B - cost is \$100 and PV is \$150

 Which should you choose?

Criteria

A

PI

2.0

NPV

\$25

 ALWAYS CHOOSE NPV!!!!

B

1.5  \$50

○ The Rule: Only accept projects with a PI > 1, and invest in projects with the largest PI's first. ○ Pros:

 Closely related to NPV rule - frequently leads to same decision  May be useful when investment funds are limited ○ Cons:

 May result in incorrect decisions (mutually exclusive investments) - First 4 criteria are all related

- The next 3 are kinda on their own

- The Payback Rule

○ What: The payback is the length of time it takes to recover our initial investment. ○

How: Assume cash flows are received uniformly throughout the year. Calculate the number of years it will take for the future cash flows to match the initial cash outflow

Example: Cost = \$2,000 CFs of \$500, \$750, \$300, \$1,000, and \$5,000. Only accepts projects with payback of 4 years or less. Should you purchase?

Year

CFs ∑CFs

0 -2,000

Final Exam Page 6

0 -2,000

1

500

2

750

3

300

4

1,000

5

5,000

3.45 years

 ○

-1,500  -750  -450  550

5,550

The Rule: investment is acceptable if its calculated payback period is less than some pre-specified number of years

○ Pros:

 Simple/Easy to do

 Biased toward liquidity

○ Cons:

 Ignores time value of money (timing and risk of cash flows are ignored)  Ignores cash flows beyond the cutoff

 Requires an arbitrary cutoff

 Biased against long-term projects

- The Discounted Payback Rule

What: The discounted payback period is the length of time it takes for sum of discounted cash flows to equal the initial investment

How: Assume cash flows are received uniformly throughout the year. Calculate the number of years it will take for the present value of the future cash flows to match the initial cash value

○ Example: Same as above example

Year

CFs

PV of CFs∑CFs

0

-200

1

500

416.67

2

750

520.83

3

300

173.61

4

1,000

482.25

5

5,000

2,009.39

416.67

937.49

1,111.11

1,593.36

3,602.75

 Discounted payback occurs between years 4 and 5

 4+(406.64/2,009.39) = 4.2024

Final Exam Page 7

Thursday, November 8, 2018 9:30 AM More on Capital Budgeting

Quiz Question Review - False

- MIRR and NPV - so answer was B

- Draw timeline

○ Move -500 back = PV = 1,598.5969

○ Move 2,500 to the future = FV = 3636

FV = \$3636

N = 3

31.5109

I/Y = ???PV = -\$1,598.5969

PMT = 0

Announcements

- Excel bootcamp tomorrow

○ Email Mandy Harrelson at mandy@auburn.edu

Investment Criteria

- The Discounted Payback Rule

What: The discounted payback period is the length of time it takes for sum of discounted  cash flows to equal the initial investment

How: Assume cash flows are received uniformly throughout the year. Calculate the  number of years it will take for the present value of the future cash flows to match the  initial cash value

○ Example: Same as above example

Year

CFs

PV of CFs∑CFs

0

-\$200

1

\$500

\$416.67

2

\$750

\$520.83

3

\$300

\$173.61

4

\$1,000

\$482.25

5

\$5,000

\$2,009.39

\$416.67

\$937.49

\$1,111.11

\$1,593.36

\$3,602.75

 Discounted payback occurs between years 4 and 5

 4+(406.64/2,009.39) = 4.2024

Rule: An investment is acceptable if its discounted payback is less than some pre- specified number of years

○ Pros:

 Adjusts for TVM (*Does not accept negative NPV projects)

 Biased toward liquidity

○ Cons:

 Ignores cash flows beyond the cutoff (still possible to reject positive NPV projects)

 Requires an arbitrary cutoff point

 Biased against long-term projects

- The Average Accounting Return (AAR)

What: the average accounting return is the ratio of the average net income of the project  Final Exam Page 8

What: the average accounting return is the ratio of the average net income of the project  to the average book value of the investment

○ How: calculate the average net income and divide it by average book value

 Avg book value = beginning book value + Ending book value and divide that by 2

Example: buy machine that will cost \$18,000 today and produce following NI: \$500,  \$750, \$300, \$1,000, and \$5,000. machine is worthless at end of 5-year life. Only accepts  with avg return greater than 15%. Should you purchase?

Add net incomes and divide by number: [(500+750+300+1000+5000)/5] =  \$1,510.00

 Denominator: (18,000+0)/2 = 9,000

 1510/9000 = 0.1678

The Rule: investment is acceptable if its average accounting return is greater than some  pre-specified benchmark

○ Pros:

 Simple/Easy to do

○ Cons: Very Wrong

 Ignores the TVM (timing and risk)

 Requires an arbitrary benchmark

 Accounting numbers and book values

Another example: Give someone \$5, get \$1 back each year for 3 years. Return? 40%  Good Investment? HECK NO

- Suggested Problems

○ Concepts

○ Q&P

○ 2.9231 years; yes

○ 3.8663 years; no

○ 16.5866%; yes

○ 16.0122%; yes

○ 1.0357; yes

○ \$53.5107; yes

Capital Budgeting

- Corresponds with Chapter 10 (except 10.5 - we're skipping that)

- The value of anything is the present value of the future cash flows - How do we get the cash flows and then how do we determine the discount rate?

-

What is capital budgeting? The process of planning and managing the firm's long-term  investments

○ Factories, buildings, machinery, equipment

- How do we compute the value of a bond, share of stock, or a project? PV of future cash flows- Relevant Incremental Cash Flows

○ What do we include and exclude from analysis?

○ Sunk Costs?

 Money you spend that you can't get back regardless of whether you accept project

 EXCLUDE/DO NOT INCLUDE

○ Opportunity Cost?

 The value of the next best alternative

 INCLUDE

○ Side Effects

 Externalities

Product Cannibalization (effect on plain m&m's of introduction of different flavors  of m&m's)

Final Exam Page 9

of m&m's)

 INCLUDE

○ Changes in Net Working Capital

 INCLUDE

○ Taxes

 INCLUDE

○ Financing Costs

 INCLUDE in analysis; EXCLUDE from cash flows

 This impacts "r"

- Project Cash Flows

 Sales

 Subtract COGS and selling, general, & admin expenses  Subtract depreciation (reduces tax burden)

○ This gives EBIT

 For project analysis, do not subtract interest expense  Subtract taxes

○ This gives NOPAT = net operating profit after taxes

○ This gives Operating Cash Flows = OCFs

 Subtract capital expenditures (cost of buying long-term assets)  Add after-tax salvage value

 ∆ Net Working Capital

○ Project Cash Flows

- Net Working Capital

○ What is net working capital?

 Current Assets - Current Liabilities

○ Why Include it?

 Have discussed sources and uses of cash

 Impacts cash (and we're looking as cash flows of projects)

Doesn't show on income statement until sold, but we will incur costs before  goods/services are sold

○ Is it a cash inflow or a cash outflow?

 Could be either

 Increases in NWC = outflow

 Decreases in NWC = inflow

○ ***Don't forget to recover net working capital at the end of the project!!!!!  Final Exam Page 10

Tuesday, November 13, 2018 9:30 AM Capital Budgeting cont. & Risk & Return - Ch.'s 12-13

Project Cash Flows

Formula

Sales

- Costs

- Depreciation

= EBIT

- Taxes

= NOPAT

+ Depreciation

= OCFs Operating cash flows

- Capital Expenditures

+ After-tax salvage value

∆ Net Working Capital

= PROJECT CASH FLOWS

- Don't forget to recover Net Working Capital!!!!!

Salvage Value and Taxes

- How do we calculate the book value of an asset?

○ Price purchased minus accumulated depreciation ○ Accounting measure of value

- What if we sell an asset for more than book value?

○ Pay taxes on the gain

Example - In year 4, we sell a machine for \$1,000. The book value of the machine is \$800.  The tax rate is 30%. What is the after-tax salvage value?  Correct method - need to know 2 things - sell for and book value.

 \$1,000 - \$800 = \$200.00 Gain on sale

 Tax is 30% of the gain

 -\$200.00 * .3 = (\$60.0)

 After-tax salvage value is \$940 (sold-for minus tax)

- What if we sell an asset for less than book value?

○ Tax credit on the difference!

○ Example - Sell for \$1,000. Book is \$1,200. Tax rate is 30%.

 Loss on sale is \$200

 \$200 * .3 = \$60.0

 \$1,000 + \$60 = \$1,060.00

- What if sell an asset for exactly book value?

○ After-tax salvage value is equal to sales price

Depreciation

- (more than) Two different ways to calculate

Straight-line depreciation - same amount each year

Final Exam Page 11

○ Straight-line depreciation - same amount each year

 Annual depreciation expense = (purchase price - ending book value)/number of years

Purchase price includes all costs associated with getting asset ready for use  (installation, customization, etc.)

 Ending book value is usually 0 unless told otherwise  Number of depreciable years, not necessarily life of asset 

Example - bought machine for \$15,000. Depreciate to zero over 5 years. What is  annual depreciation expense if firm uses straight-line depreciation. □ Straight-line depreciation

Year

Beginning Book Value

Depreciation Ending Book Value

1

15,000

3k

12k

2

12k

3k

9k

3

9k

3k

6k

4

6k

3k

3k

5

3k

3k

0

○ MACRS - accelerated depreciation (modified accelerated cost recovery system)  Finance prefers getting more money earlier, so MACRS gives more tax benefit earlier Always depreciate to zero

Assumes asset is purchased halfway through first year (will always have extra year of  depreciation because only take half year on first year)

 Has an IRS-set table depending on class of asset

Year

3 year

5 year

1

33.33%

2

44.45%

3

14.81%

4

7.41%

5

11.52%

6

5.76%

7

8.93

8

4.46

7 year

20% 14.29

32% 24.49

19.2% 17.49

11.52% 12.49

8.93

8.92

Example - new machine for \$15,000 which is in 5-year asset class. Create a MACRS  depreciation schedule

Year

MACRS %

Depreciable Base

Depreciation Ending Book Value

1

20% 15k \$3,000

\$12,000

2

32% 15k \$4,800

\$7,200

3

19.2% 15k \$2,880

\$4,320

4

11.52% 15k \$1,728

\$2,592

5

11.52% 15k \$1,728

\$864

6

5.76% 15k \$864

\$0

Final Exam Page 12

Practice Problem Nov. 13th

Example 1

Considering new project (EasyBs), which will be on market for 5 years. Last years, spent 20k on market  study and determined appropriate price is 5/unit. Expect sales to be 10k units in year 1 and grow by 2k  units each year after. Costs expected to be 20% of sales. Marginal tax rate is 40%. Must purchase  manufacturing machine for \$100,000 (MACRS 3-year). Due to increase in inventories, net working  capital expected to increase by \$15,000. If required return is 12%, should you accept project?

- \$20k market analysis is sunk cost - do not include

0

1

2

3

45

Sales

\$50,000.00

\$60,000.00

\$70,000.00

\$80,000.00

\$90,000.00

Costs

\$10,000.00

\$12,000.00

\$14,000.00

\$16,000.00

\$18,000.00

Depreciation

\$33,330.00

\$44,450.00

\$14,810.00

\$7,410.00

\$0.00

EBIT

\$6,670.00

\$3,550.00

\$41,190.00

\$56,590.00

\$72,000.00

Taxes

(\$2,668.00)

(\$1,420.00)

(\$16,476.00)

(\$22,636.00)

(\$28,800.00)

NOPAT

\$4,002.00

\$2,130.00

\$24,714.00

\$33,954.00

\$43,200.00

Depreciation

\$33,330.00

\$44,450.00

\$14,810.00

\$7,410.00

\$0.00

OCFs

\$37,332.00

\$46,580.00

\$39,524.00

\$41,364.00

\$43,200.00

Capital Expenditures

(\$100,000.00)

After-tax salvage value

\$0.00

Change in NWC

(\$15,000.00)

\$15,000.00

Project Cash Flows

(\$115,000.00)

\$37,332.00

\$46,580.00

\$39,524.00

\$41,364.00

\$28,200.00

With above cash flows and 12% rate of return, yes, you should accept.

NPV = 72,567.4946

Practice Problem 2

Auburn Industries is evaluating the option of purchasing a fork-lift truck costing \$60,000. If purchased,  the truck will replace 4 workers, each with an average annual salary of \$15,000. However, an  experienced fork-lift operator will have to be hired at a salary of \$20,000 per year. Fuel and  maintenance expense is expected to be \$10,000 per year. At the end of its 5-year life, the truck will have a market value of \$10,000. Auburn Industries uses straightline depreciation and depreciates the asset to  \$0, assigns a 10% required rate of return for this type of investment, and has a marginal tax rate of 40%.  Should the fork-lift truck be purchased?

0

1

2

3

4

Sales

\$60,000.00

\$60,000.00

\$60,000.00

\$60,000.00

\$60,000.00

Costs

(\$30,000.00)

(\$30,000.00)

(\$30,000.00)

(\$30,000.00)

(\$30,000.00)

Depreciation

(\$12,000.00)

(\$12,000.00)

(\$12,000.00)

(\$12,000.00)

(\$12,000.00)

5

EBIT \$18,000.0 \$18,000.0 \$18,000.0 \$18,000.0 \$18,000.0 Final Exam Page 13

EBIT \$18,000.0

\$18,000.0

\$18,000.0

\$18,000.0

\$18,000.0

0

0

0

0

0

Taxes

-0.4

(\$7,200.0

(\$7,200.0

(\$7,200.0

(\$7,200.0

(\$7,200.0

NOPAT

0) \$10,800.00

0)\$10,800.00

0)

\$10,800.00

0)

\$10,800.00

0)

\$10,800.00

Depreciation

\$12,000.0

0

\$12,000.00

\$12,000.00

\$12,000.00

\$12,000.00

OCFs

\$22,800.00

\$22,800.00

\$22,800.00

\$22,800.00

\$22,800.00

Capital

Expenditures

(\$60,000.00)

After-tax

salvage value

\$6,000.00

Change in

NWCProject Cash Flows

(\$60,000.00)

\$22,800.00

\$22,800.00

\$22,800.00

\$22,800.00

\$28,800.00

1

1.1 1.21

1.331 1.4641

\$27,414.06

(\$60,000.00)

\$20,727.27

\$18,842.98

\$17,129.98

\$15,572.71

\$17,882.53

1.61051

\$30,155.

47

Final Exam Page 14

Thursday, November 15, 2018 9:30 AM More on Risk and Return

Quiz Review

- T/F Exclude interest and financing and sunk. Include opportunity costs? - True - After-tax salvage value? \$18,000

- -\$60,000

Capital Budgeting

- Company Valuation

○ How do we do it?

 PV of future cash flows

Forecast cash flows and costs, then after a set time could assume a constant growth.  Discount back to year0

○ What's the Difference?

- Risk Analysis

○ Sensitivity Analysis

 Keep everything the same and change 1 input and see what happens? ○ Scenario Analysis

 (Change multiple inputs, determine break-even points

○ Simulations

 Can change everything

 For each input, could specify probability distributions

Chapter 10 Suggested Problems

- CR

○ 1, 2, 6, 7

- Q&P

○ 1, 2, 6, 7, 8, 9, 10, 13, 14, 15, 31 (spreadsheet)

Examples

- Ex. 2

○ No associated sales

○ Cost savings of \$30,000 - (operator salary and fuel/maint costs, savings of 4 salaries) ○ Strait-line depreciation

○ Expenditure of \$60,000

○ Salvage of \$6,000

- Ex. 3

○ \$9,089.45; yes

- Ex. 4

○ -\$6,700.18; no

Risk and Return

Risk

- What determines the required rate of return on an investment? ○ The level of risk/uncertainty

- Two things to remember about risk:

There is a reward for bearing risk

Final Exam Page 15

○ There is a reward for bearing risk

○ The greater the risk, the greater the potential reward

Returns

- Cash flows for shares of stock:

○ Dividends

○ Sale price/ Capital gains (or losses)

- Example

Purchased 100 shares last year for \$50. Just received \$5 dividend Market value of stock is  now \$65. What are your dollar and percentage returns?

Dividends: \$500

Capital Gains: \$1,500

Dollar Return \$2,000

 % return = \$2,000/\$5,000 = \$0.4

 40%

 r = D1/PV0 + g

 Dividend yield is 10% and capital gains is 30%  (5/50)+((65-60)/50)=0.4

- Example

Purchased 100 shares last year for \$30/share. Just received \$1 dividend. Market is now  \$20. What are dollar and percentage returns?

Dividends

C.G

Return

  % return = (100-1000)/3000 = -0.3

\$100  -\$1,000

-\$900

 -30%

 3.33% - 33.33% = -30%

- Percentage return = (cash flows over period + change in market value)/beginning market value- What about for bonds

○ Same setup (coupon payments)

Final Exam Page 16

Tuesday, November 27, 2018 9:30 AM Market Efficiency - Chapter 12.6

Quiz Review

1. True

2. 12.22%

3. \$10,000

Risk and Return

- Determines required rate of return on the investment

- 2 things to remember

○ Reward for bearing risk

○ Greater risk, greater the potential reward

- Graphs/charts on risk and return over time for different categories - Financial History Lesson 1926-2013

Risk Premium - excess return required from an investment in a risky asset over that required from a risk-free asset

○ Even with 0 risk, still deserve a rate of return (time value of money)

Investment

Average Return

Large Company Stocks

12.1%

Small Company Stocks

16.9%

Long-Term Corporate Bonds

6.3%

Long-Term Government Bonds

5.9%

U.S. Treasury Bills = Rf

3.5%

8.6%

13.4%

2.8%

2.4%

--- (0%)

- Things which affect stock prices (just a few)

Nondiversifiable risk / market risk / systematic risk / syncratic risk

Diversifiable risk /

Tariffs

Intl war

Oil prices

Natural disaster

Unexpected change in interest rates Unexpected change in unemployment

New product announced

CEO scandal

Unexpected earnings announcementProduct recall PR issue

- Diversification and Risk

○ Nondiversifiable risk - influences a large number of assets. Also systematic, market, or syncratic○ Diversifiable risk -

Principle of Diversification - spreading investment across a number of assets will eliminate some, but not all, of the risk

○ Takes about 25 assets to eliminate diversifiable risk (ish)

- Systematic Risk and Beta

Final Exam Page 17

- Systematic Risk and Beta

Unsystematic risk is essentially eliminated by diversification, so a portfolio with many assets as almost no unsystematic risk

○ Expected return on an asset depends only on that asset's systematic risk ○

Beta coefficient β - amount of systematic risk present in a particular risky asset relative to the market portfolio (which has a beta of 1.0)

○ Risk-free asset has beta of 0

- The Capital Asset Pricing Model (CAPM)

Equilibrium asset pricing model showing that the expected return for a particular asset depends on pure time value of money plus a reward for bearing systematic risk ○ CAPM => Ri = Rf + βi (RM - Rf)

○ RM - Rf = Market risk premium =/= Return on Market

- Security Market Line

-

Example - what is expected return on share of stock whose beta is 1.15 if risk-free rate is 4% and expected return on market is 10%?

○ E(R) = .04 + 1.15*(.1-.04) = 0.109 * 100 = 10.9% ○ If beta is 2… = .04 + 2*(.1-.04) = 0.16 * 100 = 16.0%

- Suggested Problems

***Refresh yourself on how to calculate YTM before Thursday's class!!!

Market Efficiency

- What is the efficient markets hypothesis

○ The set-up

 Lots of people

 Lots of money

 Lots of time

○ Prices reflect information… quickly! (and accurately)

○ Therefore, no unusual or excess profits from trading on information - Stock Price Reaction to Good News graph

○ Lead up - stock price is level

○ Announcement - straight vertical line

○ After announcement - higher horizontal line

○ Overreaction - goes higher and comes back down over time ○ Underreaction - doesn't climb as high as it will, then slowly rises to new level - Levels of Market Efficiency

○ Three forms of market efficiency

 Weak Form

 Semi-strong form

 Strong form

Final Exam Page 18

Final Exam Page 19

Thursday, November 29, 2018 9:30 AM The Cost of Capital - Chapter 14

Quiz Question Review

1. True

2. False

3. C (8%)

4. False

- Longer quiz on Tuesday (which will likely be last quiz)

Market Efficiency

- Stock prices reflect information quickly and accurately

- 3 forms or levels of market efficiency

○ Weak Form Efficiency - reflect all past information

 Technical Analysis isn't reliable - it fails

○ Semi-strong Form Efficiency - stock prices reflect all publicly available information

 Is also weak form efficient (rectangle contains square)

○ Strong Form Efficiency - stock prices reflect all public and private information

 Contains other 2 categories

 Wouldn't need insider trading laws

- Market may be somewhere between Semi-strong and Strong - What do we know?

○ Market Reaction

○ Reporting - we hear about success, failure is hidden  Index Fund - risk over long-term is less

- Suggested Problems

The Cost of Capital

The Cost of Capital

- What are the sources of capital?

○ Stockholders (preferred and common stock, retained earnings)

○ Debt (liabilities)

- What is this cost of capital?

Cost of capital reflects the investment opportunities and alternatives in the financial market  available to suppliers of the firm's capital

 What return could these people get investing elsewhere @ same level of risk?

 Opportunity cost

○ Required rate of return

- Which cost of capital?

○ Marginal cost of capital (not historic)

- How do we calculate the cost of capital?

○ Weighted - WACC - weighted average cost of capital

The Cost of Common Stock

- There are two ways:

The Dividend Growth Model (constant growth stock)

Final Exam Page 20

○ The Dividend Growth Model (constant growth stock)

○ The Capital Asset Pricing Model (CAPM)

- Recall: P0 = D1 / (RE - g)

○ Therefore, RE = D1/P0 + g

○ RE is required rate of return on equity or cost of equity capital

-

Dividend Growth Model Example - Brian's burritos just paid \$2 dividend, which it expects to grow  at 5%/yr indefinitely. If current price of stock is \$25, what is cost of equity capital ○ We have D1 and P1, so either move dividend forward or price back.

○ 2.1/25 + .05 = 0.134 OR 2/23.8095 + .05 = 0.134

○ 13.4%

- Dividend Growth Model

Problem - we know what price of stock is today and we know what most recent dividend  was We seldom know the growth rate

○ Potential Solutions

 Historical Growth Rates

 Accounting Measure (e.g. Sustainable Growth Rate)

 Analysts' Forecasts - at least this is forward-looking rather than backward-looking

- CAPM

○ Recall: RE = Rf + βE [RM - Rf]

We know what average historical risk premium and can look up the risk-free rate (e.g. US  Treasury bills). We also can calculate or look up betas.

○ Problem

 This is just a model/theory

 Historic measure - backward-looking

The Cost of Preferred Stock

- What do we know about the dividends of preferred stock? - Recall P0 = D/RP

- Can Rearrange: RP = D/P0

The Cost of Debt

- The cost of debt is the return that the firm's creditors demand on newborrowing

- How do we get it? - look at current bonds, compare to other companies with same risk rating- Recall:

○ Coupon Rate - might reflect rate at issuance, but doesn't stay current ○ Current Yield - only reflects portion of yield, not the full return ○ Yield to Maturity - DING DING DING - takes all factors into account

The Weighted Average Cost of Capital (WACC)

- Formula

Final Exam Page 21

1. Capital gains yield is best estimate of cost of preferred stock - FALSE 3. Cost of common stock (just paid 2.00 div, 5% growth, \$25 current cost) - 13.4% - pg. 186 of notes!!! 4. WACC, it is historic cost of capital that we are interest in - FALSE, marginal cost 5. Appropriate rate for marginal cost of debt - YIELD TO MATURITY NOW

- What is cost of capital - opportunity cost

More on The Cost of Capital

Tuesday, December 4, 2018 9:30 AM

Quiz Review

2. Same expected return, same RISK

6. 8%

Review

The Cost of Capital

- Sources of capital

○ Debt

○ Preferred stock

○ Common stock

Reflects investment opportunities and alternatives in the financial market available to suppliers of the firm's  capital

- Which cost of capital? Marginal cost

Cost of Common Stock

- Dividend growth model

- Capital Asset Pricing Model (CAPM)

Cost of Preferred Stock

- Zero-growth stock

○ Next dividend / current price

Cost of Debt

- Is the return the firm's creditors demand on new borrowing

- Current yield to maturity

Logically

- Goal is to increase shareholder wealth

- Accept positive NPV project

○ Need project cash flows

○ Need rate (cost of capital)

Weighted Average Cost of Capital

- Recall from balance sheet

Assets =

Debt +

Market value

Market value

Equity

Market value

- We are also interested in after-tax cash flows

- One benefit of debt (not available to equity) is the fact that interest payments are tax deductible After-tax Cost of Debt

Firm A

Firm B

EBIT

100

100

-Interest

0

(100)

-Taxes (40%)

(40)

0

=

Net Income

60

0

Tax burden

Tax benefit of bearing debt

WACC

Final Exam Page 22

WACC

= [(E/D+E+P) * RE] + [(P/D+E+P) * RP] + [(D/D+E+P) * RD * (1 - t)]

൤൬����⎯⎯+ �� + ��൰ ∗ ��ா൨ + ൤൬ ��

⎯⎯⎯⎯⎯⎯⎯⎯⎯൰ ∗ ��௉൨ + ൤൬����⎯⎯+ �� + ��൰ ∗ ��஽ ∗ (1 − ��)൨ �� + �� + ��

- Keep in mind

○ Target Capital Structure

○ Market Values NOT Book Values

WACC Example

 Gas station risk =/= donut risk - must calculate new rate

-

BB Lean Co has 1.4 mill shares of stock outstanding. Currently sells for \$20/share. 93% of face recent quote. Total  face of \$5 mill and currently priced to yield 11%. Risk-free beta is 8% and market risk premium is 7%. You've  estimated this stock has beta of .74. If corporate tax rate is 34%, what is WACC of Lean Co.?  Project more risky - take WACC and add to it (inverse if less risky) ○ Risk-adjusted cost of capital

○ Mickey's Mullets - trying to determine WACC - have following info

More on WACC

- What does the WACC measure?

○ Discount rate for the overall firm

○ The firm's required rate of return

- If 2 things have the same risk, they should have the same required rate of return ○ If a project is more risky than average project in the firm, you have to use a higher rate ○ Conversely, if less risky, use a lower rate

- What is the WACC for a firm financed with all equity?

○ The cost of (or required return on) equity

- WACC and Company Valuation

○ Corporations live in perpetuity

- How do we estimate the appropriate discount rate for a project with a different risk than our company? ○ Mostly in this class it will be given to us

○ Own lots of gas stations, want to open donut shop

 Look as companies that just operate as donut shops

- Another WACC example

2k bonds

35k preferred

shares

100k common shares

20-year, 2 years ago, 9% coupon, annually, and 1k face. YTM of 6.5881%

5.25 annual

dividend, Dividend

yield is 7.5%

just paid a \$1.20 dividend on the common stock

yesterday, which has a beta of 0.95, and expects to

maintain a constant 7 percent growth rate in dividends.

You know the yield on short-term U.S. Treasuries is 5.3%, the historical market risk premium is 6  percent, and the firm has a marginal tax rate of 40 percent.

Final Exam Page 23

Final Exam Page 24

Thursday, December 6, 2018 9:30 AM Review for Final Exam

Review of Another WACC Example

Final Exam

- Bring scantron

- Bring financial calculator

- Bring pencil and photo ID

- Bring cheat sheet - 2 sided

2 1-sided sheets is possible, just don't tape all the way around. Must be able to see that there's only 2 sides

with info

○ Heavy paper allowed

○ INCLUDE 3-year MACRS depreciation schedule!!!!!!!!!!!!!!!!!!!!!!!!! ○ Proportions of debt and equity (debt and equity ratios)

- Study notes and book

- Do suggested problems

- Do more problems

- Be comfortable with calculator, but understand problems and the calculator setup

- Be prepared

○ What info is given

- Ask if something is not clear

- See the big picture

Content and Structure

- 41 questions given, graded out of 40

○ 20 concepts

 19 are material since exam 2 (almost all are new material)

○ 21 problems

 20/21 come from material on exam 2 and new material

- 1 roman numeral question

- 2 questions are related, 39 are independent

- Must know 3-year MACRS

Final Exam Review - Practice Problems

- P.P. 1

Final Exam Page 25

- P.P. 2 - same as 1, but with target D/E as .2753

- P.P. 3 - Should we invest?

○ NPV

 Need WACC

 Need Cash Flows

Final Exam Page 26

Final Exam Page 27

Tuesday, August 21, 2018 9:30 AM Chapter 1 - Intro to Corporate Finance

Basic Areas of Finance

- Corporate finance -> Business finance

- Investments - a whole other class devoted to this topic

- Financial Institutions

 Net Working Capital = C.A. - C.L. = \$ value of working capital

○ Mainly banks

○ Insurance companies

○ Intermediaries

- International (or Multinational or Global) Finance

What is Corporate Finance

- Focuses on 3 questions:

○ What should we invest in (as a company/firm)? - projects or assets ○ How do we finance those investments?

 Borrow money

 Use owners money

 Use internally generated money

○ How do we manage day-to-day operations of the firm?  Short-term cash flow management

- Balance Sheet Model of the Firm ○ Assets = Liabilities + Stockholders' Equity

- Capital budgeting

○ What is capital budgeting?

 The process of planning and managing the firm's long-term investments ○ How do we do it?

 Estimate cash flows (timing)

 Estimate cost of those cash flows (risk)

 Discount the cash flows (time-value of money)

- Capital Structure

○ What is capital structure?

 The mix of debt and equity describing how the firm is financed ○ Does capital structure matter?

○ How do taxes affect this decision?

○ How does this relate to the goal of the financial manager? - Short-Term Cash Flow Management

○ What does short-term cash flow management entail?

□ Measure of liquidity

 Cash Management

 Credit Management

Exam 1 Page 1

Thursday, August 23, 2018 9:30 AM Chapter 1 continued

The Firm and the Financial Markets (page 14 of textbook)

- Illustration

○ Firm decides to make/sell product

Firm

<-- Firm issues securities (A)

Financial Market

(B)

Invests in assets

Current assetsFixed assets

Cash Flow from firm (C)-->

<--Reinvested cash flows (F)

Taxes (D)|Dividends&debt payments(E)-->

Short-term debtLong-term debtEquity shares

be a

activity

cash

Ultimately, the firm must

generating

Government

The cash flows from the firm must exceed the cash flows from the financial markets.

Primary and Secondary Markets

Firms

<----Money-----

-----Stocks & Bonds-->

Primary Market

Bob --securities-->Sue

Secondary Market

Investors<--money--

-

- Debt and Equity as Contingent Claims

○ Debt is a promise to repay

○ Equity gets everything else

 A corporation has \$100 in debt

 If the value of the firm's assets is…

□ \$75, the debtholders get \$75 and stockholders get \$0 □ \$100, debtholders get \$100 and stockholders get \$0 □ \$200, debtholders get \$100 and stockholders get \$100 □ \$1,000,000, debtholders get \$100 and stockholders get \$999,900

- Sole Proprietorship - 1 owner

○ Pros

 Easy startup

 Taxed as personal income

○ Cons

 Unlimited liability

 Life limited to that of owner

 Equity limited to owner's wealth

 Difficulty in transferring ownership

- Partnership - 2 or more owners

Exam 1 Pae 2

- Partnership - 2 or more owners

○ General vs. Limited Partners

○ General

 Pros

□ Taxed as personal income

 Cons

□ Unlimited liability

□ Life limited to that of the owners

□ Equity limited to owners' combined wealth

□ Difficulty in transferring ownership

○ Limited - at least one general partner and at least one limited partner  Limited partner is just an investor - no day-to-day control of operations □ Limited liability - only what limited partner invested - Corporation

A business created as a distinct legal entity composed of one or more individuals

or entities

Must file articles of incorporation/charter - filed with Secretary of State in state

of organization (Delaware super corporation-friendly)

○ Separation of Ownership and Control

 Shareholders - own

 Directors - elected by shareholders

□ Monitor managers

□ Hire and fire managers

 Managers - run

○ Pros

 Limited liability

 Easy transfer of ownership

 Unlimited life

 Equity is not limited

○ Cons

 Difficult to start up

 Double taxation of earnings

□ Corporations earnings are taxed

□ Dividends paid to shareholders are taxed

- Other types

○ Professional Associations and Partnerships

○ LLC

○ S-Corporation (as opposed to C-Corp above)

The Goal of the Firm

- To maximize shareholder wealth!!!

- What does that mean?

○ Look for increase in price of stock

○ Dividends

○ Stock repurchases

Agency Conflicts

- What is a principal-agent relationship?

○ Principal hires agent to work on his or her behalf

 Selling home - hire real estate agent

 Athlete or entertainer - hire agent to negotiate deals

-

Agency Problem/Conflict: The possibility of conflict of interest between the  stockholders (the principal) and management (the agent) of a firm

- Agency Costs: The costs of the conflict of interest between stockholders and   Exam 1 Pae 3

-

Agency Costs: The costs of the conflict of interest between stockholders and  management.

○ Direct agency costs:

 Wasteful spending

 Monitoring and Auditing

○ Indirect agency costs

 Missed opportunities

- How do we control agency conflicts?

○ Managerial Compensation

 Stock options or shares of stock

 Cash bonus for good job performance

○ Control of the Firm

 Termination of under-performing managers

Shareholders can elect new board of directors if directors aren't managing  well - Proxy Fights

 (Hostile) Takeover

Chapter 1 suggested problems

3, 6, 7, 8

Exam 1 Pae 4

Tuesday, August 28, 2018 9:30 AM Chapter 2 - Financial Statements and Cash Flow

- Financial Statements

○ The Annual Report and Form 10-K

 Balance Sheet

 Income Statement

 Statement of Cash Flows

 Statement of Stockholders' Equity

○ EDGAR - SEC database for electronic filings

 www.sec.gov

○ Other Notes

 Financial statements are backward-looking (look at past)

□ In finance, we care more about future

 Accounting value is different from market value

□ In finance, we care about cash flows

- The Balance Sheet

○ The Balance Sheet Identity:

 Assets = Liabilities + Stockholders' Equity

 Assets are things we own

 Liabilities and Equity are how we paid for things we own ○ Liquidity

 Asset that can be converted into cash quickly (without a significant loss of value)  In the Balance Sheet

□ Cash, Accounts Receivable, Inventory - listed in order of decreasing liquidity

□ Then long-term assets, PP&E, Intangible Assets

 Pros and Cons of Liquid Assets

□ Less risky

□ Able to pay off debts

□ Does not earn any rate of return

○ Helps user to understand Capital Structure of the firm

 Proportion of debt to equity

- Home Depot Annual Report

○ In course packet and on web page

○ Item 8 - starts page 29 - is what we're looking at

○ Report from independent auditors

○ We will not be asked anything specific about HD balance sheet - just illustration of class material○ Notes begin page 36 (note 4 on page 44 for more info on long-term debt) - The Balance Sheet

○ Market Value vs. book Value

 What are market value and book value

□ Market value - Price you can buy/sell asset for today

Book value - accounting measure of value - price you paid when you bought asset minus

accumulated depreciation

□ Where on the balance sheet can we find true (market) value of the firm

 You can't

□ Equity on the balance sheet is the book value of equity

□ How do we find the true (market) value of total stockholders' equity?

 Price per share times number of shares

□ What is the goal of the firm?

 Maximize stock price/stockholders' wealth/equity

(Create market value)

Exam 1 Page 5

 (Create market value)

- The Income Statement

○ Revenues minus expenses equals income

○ The Bottom Line: Net Income or EPS (earnings per share)

○ 2 things to do with net income

 Distribute it to owners

 Reinvest in firm

○ Depreciation is a non-cash expense

○ Yost Rocks Income Statement

Revenues less costs (COGS - cost of goods sold and SGA- selling, general and administrative expenses) and depreciation equals Operating Income

 Operating Income plus Other Income = Earnings before Interest and Taxes - EBIT EBIT - Interest Expense = Pretax Income (EBT)

 EBT minus Taxes = Net Income

 Dividends are not tax-deductible

○ Home Depot Income Statement - page 32

 Note 5 (beginning on page 47) references taxes

○ GAAP

Exam 1 Page 6

Thursday, August 30, 2018 9:30 AM Chapter 2 continued

- The Income Statement

○ Revenues - Expenses = Income

○ The Bottom Line: Net Income or EPS - an accounting measure of profit ○ GAAP (U.S.) - Generally Accepted Accounting Principles

 The timing of Cash Flows

 The matching principle

□ Matching expenses and revenues to same period  Non-cash items - depreciation and amortization, etc.

- The Statement of Cash Flows

○ Cash Flow from Operating Activities

 Buying of supplies and selling of products

○ Cash Flow from Investing Activities

 Long-term assets

○ Cash Flow from Financing Activities

○ Sources and Uses of Funds

 Changes in Current Assets (all assets, not just current)

□ Anytime we increase assets, represents a use of cash □ Decrease in assets = a source of funds or cash inflow

 Changes in Current Liabilities (all liabilities and equity)

□ Opposite above

□ L&SE goes up = source of funds/cash inflow □ L&SE goes down = use of cash/outflow  Examples

□ Increase Accounts Payable

 Source of cash

□ Decrease Inventory

 Source of cash

□ Increase Accounts Receivable

 Use of cash

□ Increase Accrued Expenses

 Source of cash

○ Yost Rocks Example

 Dividends listed with Financing Activities

Interest Expense, Taxes, COGS all under Operating Activities (component of Net  Income)

- Some Things to Remember (about financial statements)

○ Depreciation is not a cash flow

○ Net income is not a cash flow

○ Financial statements are backward looking, not forward looking ○ The balance sheet shows book values, not market values

- 2015 Corporate Tax Rates (Table 2.3)

○ Will not need to memorize this. If required on exam, it will be provided. - Taxes

○ Average Tax Rate

 = taxes owed divided by taxable income

○ Marginal Tax Rate - rate we care about in Finance/this class  Tax rate that applies at the margin

 Applies to the next dollar we earn

Exam 1 Pae 7

 Applies to the next dollar we earn

○ If a corporation has \$90,000 in taxable income, how much does it owe in taxes?

 \$50,000.00*.15=\$7,500.0

 \$25,000.00*.25=\$6,250.00

 \$15,000.00*.34=\$5,100.0

 \$7,500+\$6,250+\$5,100=\$18,850.00

 18,850/90,000=0.2094%

- Suggested Problems

○ Concepts Review and Critical Thinking Questions:

 Chapter 2: 1 and 2

○ Questions and Problems:

 Chapter 2: 5, 6, 9, 13, 17, and 18

 Chapter 3: 9 and 16

Financial Statement Analysis

(do not need to memorize ratios, but need to know how to calculate them and what they tell us)

- Common-Size Financial Statements

○ Balance Sheet items as a percentage of total assets

○ Income Statement items as a percentage of total sales

- Classification of Financial Ratios

Exam 1 Pae 8

Tuesday, September 4, 2018 9:30 AM Chapter 3 - Financial Statement Analysis

Financial Statement Analysis

- Common Size Financial Statements

○ Balance Sheet items as a % of Total Assets

○ Income Statement items as a % of Total Sales

- Classification of Financial Ratios

To keep in mind - the exact method of computing these ratios can differ from place to place/textbook to textbook. Basic flavor of ratio and what it's telling us is the same Pay attention to interaction among ratios

Don't need to memorize ratios - need to know how to calculate it and what it tells us. ○ Short-term Solvency or Liquidity Ratios - measure ability to pay short-term obligations

Higher numbers indicate higher liquidity, but higher is not always better. Can pay off debts, but it isn't earning any rate of return

 Current Ratio = Current Assets/Current Liabilities

 Quick (Acid-Test) Ratio = (Current Assets - Inventories)/Current Liabilities  Cash Ratio = Cash/Current Liabilities

 Net Working Capital to Total Assets = NWC/Total Assets

□ Net working capital = Current Assets - Current Liabilities

 Interval Measure = Current Assets/Average Daily Operating Costs ○ Long-term Solvency or Financial Leverage Ratios - measure ability to pay longer term obligations Total Debt Ratio = Total Liabilities/Total Assets = (TA-Equity)/TA

 Debt-equity Ratio = Total Liabilities/Stockholders' Equity  Equity Multiplier = Total Assets/Stockholders' Equity

 Given any of these ratios, we can solve for the other two, because A=L+SE

□ Given: Total Debt Ratio = .6

 Make up numbers that work: A=100, L=60, SE=40 (100-60=40)

 Debt-equity ratio = 6/4=1.5

 Equity Multiplier = 10/4=2.5

□ Given: Debt-equity Ratio = .42

 Make up numbers that work: L=.42, E=1, A= 1+.42=1.42

 Total Debt Ratio = .42/1.42=0.2958

 Equity Multiplier = 1.42/1=1.42

□ Given: Equity Multiplier = 1.25

 Make up numbers that work: A=1.25, SE=1, L=.25

 Debt-equity Ratio = .25/1=0.25

 Total Debt Ratio = .25/1.25=0.2

 Equity Multiplier = Assets/Equity OR (Equity + Liabilities)/Equity OR 1+(Debt-equity ratio) Long-term Debt Ratio = Long-term Debt/(Long-term Debt + Equity)  Times Interest Earned (TIE) Ratio = Earnings Before Interest & Taxes/ Interest Expense

 Cash Coverage Ratio = (EBIT + Depreciation)/Interest Expense ○ Asset Management or Turnover Ratios - how efficiently are we using our assets - turnover ratios Inventory Turnover = COGS/Inventory

 Days' Sales in Inventory = 365/Inventory Turnover

 Receivables Turnover = Sales/Accounts Receivable

 Days' Sales in Receivables = 365/Receivables Turnover = also known as average collection period Net Working Capital Turnover = Sales/Net Working Capital

 Fixed Asset Turnover = Sales/Net Fixed Assets

 Total Asset Turnover = Sales/Total Assets

○ Profitability Ratios - measure ability to generate profit

 Profit Margin = Net Income/Sales

Exam 1 Pae 9

 Profit Margin = Net Income/Sales

 Return on Assets = Net Income/Total Assets

 Return on Equity = Net Income/Total Equity

○ Market Value Ratios - outside financial statements

 *Earnings per Share (EPS) = Net Income/# of shares outstanding  Price-earnings (PE) Ratio = price per share/EPS

 Price-sales Ratio = Price per share/sales per share *If company has negative Net Income

 Market-to-book Ratio = market value (price) per share/Book value of equity per share Tobin's Q = market value of assets/replacement cost of assets  Enterprise Value-EBITDA Ratio = (market value of equity + Book value of liabilities -cash)/EBITDA

Exam 1 Pae 10

Thursday, September 6, 2018 9:30 AM Chapter 3 cont. & Chapter 5 - Time Value of Money

Financial Statement Analysis

- Common Size

○ Balance sheet as % total assets

○ Income statement as % of total sales

- Classification of Financial Ratios

○ Short-term solvency

○ Long-term solvency

○ Asset management/turnover

○ Profitability

○ Market value

 EPS

 PE

 Price-Sales

 Market-to-book

 Tobin's Q

 Enterprise Value - EBITDA Ratio (Earnings before interest, taxes, depreciation, or amortization)○ Page 68 of textbook contains all ratios discussed in class

- DuPont Identity

○ Return on Equity - Net Income divided by Stockholders' Equity

 Equal to profit margin times total asset turnover times equity multiplier ○ With leverage, ROE is greater than ROA

○ Breaks ROE down into

 Profitability

- Uses and Limitations of Financial Statements

○ Uses

 Ratio Analysis

 Common Size Financial Statements

 Trend Analysis

 Cross-sectional Analysis

 The DuPont Identity

○ Limitations

 Backward-looking, not forward-looking

 Financial statements have book values, not market values

 Income Statement has accounting numbers, not actual cash flows  Benchmarking - sometimes hard to find comparable companies  Effects of Inflation - book value differs from market value  Seasonal Factors - may even out over a year, but looking at quarterly could give skewed results "Window Dressing" - making financial statements look as good/strong as possible (not fraud) Differing Operating and Accounting Practices

 The Big Picture

- Chapter 3 Suggested Problems

Exam 1 Page 11

- Chapter 3 Suggested Problems

○ Concepts Review and Critical Thinking Questions  2, 5, 7

○ Questions and Problems

 7, 12, 17, 22, 26, 27

The Time Value of Money - single most important topic we will cover this semester- Example

\$100 today

r=10%

1 year

\$100+(\$100*0.10)=\$110.00

2 years

Could be phrased as\$100*(1.10)*(1.10)=\$121.0

\$110+(\$110*0.10)=\$121.00 or \$100*(1.10)

2

3 years

\$100*(1.10)

2

\$121+(\$121*0.10)=\$133.1*(1.10)=

interest

Example -

Example -

FV Example 2 -

\$30FVt

Future Value (FV) -For example above, FV3Simple Interest -

Compound Interest -prior periods\$33.10Compounding -

Calculating Future ValueFuture Value

Future Value□

Future Value Factor -

= PVFV

0

15

* (1 + r)

t

r in decimal formula, t is number of periods Invest \$100 for 15 years at 5%

= \$100*(1+.05) (1+r)

remain constant over the two years.

15

t

= \$207.89

Year 2

???

How much will you have when you close the account in 2 years? How much compound interest did you accumulate?

for six more years at 6% per year. How much will you have in eight years?

the amount an investment is worth after one or more periods interest earned only on the original principal amount invested interest earned on both the initial principal and the interest reinvested from

the process of accumulating interest on an investment over time to earn more

You deposit \$500 into a savings account. You plan on withdrawing the money and closing the account exactly two years from today. Interest rates are 10%, compounded annually, and will

Year 0

Year 1

\$500

???

I

I

I

FV\$105

2

\$100 (\$50/year)

The effects of compoundingEffects/benefits

ncrease with time

= \$500*(1.10)

2

= \$605How much simple interest did you accumulate?

ncrease with the interest rate

ncrease with the frequency of compounding (more details on this later) you are scheduled to receive \$17,000 in two years. When you receive it, you will invest it

Year 0

Year 1

Year 2 Year 3

Year 4 Year 5 Year 6

Year 7

○ ○

○ ○

-

○ ○

○ ○

-

-

Year 8

Exam 1 Page 12

\$17,000 \$24, 114.82○ How much in year 8? - \$24,114.82

Exam 1 Page 13

Tuesday, September 11, 2018 9:30 AM Chapter 5 continued

Time Value of Money

- Calculating Future Value

FVt = PV0 x (1 + r)t ○

- Future Value: Example 3

Trying to buy \$60k car. Have \$22k today and bank pays 4% annually. How long til can afford car?

60,000 = 22,000*(1+.04)t ○

60000/22000=2.7273 = 1.04t ○

○ ln2.7273/ln1.04 = t

○ t = 25.61

- Future Value: Example 4

○ Only willing to wait 15 years in prev. example

60k=22k*(1+r)15 ○

60000/22000=2.7273 =1+r15 ○

2.72731/15 ○ = 1.0692 = 1 + r

○ 6.92% = r

- Present Value Definitions

Present Value (PV) - the current value of future cash flows discounted at the appropriate

discount rate

○ Discount - calculate the present value of some future amount

PV0=FVt/(1+r)t ○

- Figure 5.3

○ How much to invest now to have \$1 in the future

○ As interest rates rise, the Present Value is less

○ As the period of time increases, the Present Value decreases - Present Value: Still Example 1

○ Lottery - which payout would you choose?

○ Must get values to the same point on the timeline

- More examples

- Tips on Solving

○ Don't rush to get through it - setup is vital

○ Draw a timeline

○ Formulas are the same, just organized differently to provide different solutions ○ For multiple cash flows, just add up the individual present or future values ○ As time or rate increase, FV increases and PV goes down ○ There are currently only 4 components; PV, FV, t, and r

○ With any 3 components, you can solve for the 4th Cash flows always occur at end of the period ( x will happen for the next two years = end of

year 1 and end of year 2)

○ Must be consistent in unit of time

- Chapter 5 Suggested Problems

○ Concepts review and critical thinking

 1, 2, 3, 4

○ Questions and problems

 1, 2, 3, 6, 9, 13, 14, 15, 16, 18, 20

Exam 1 Pae 14

Wednesday, September 12, 2018 8:59 AM Time Value of Money Practice Problems

FINC 3610: Principles of Business Finance Time Value of Money Practice Problems

1. You are looking to purchase a home automation system when you graduate in two years. You plan to  deposit the money in an investment account earning 8 percent annually. The anticipated cost of the  system in two years is \$2,500. How much must you deposit today?

2. When you were born 21 years ago, your Aunt Burtha put \$2,000 into a saving account for you. The  account has earned an average annual return of 4 percent per year, and nothing else has been  deposited or withdrawn from the account. How much is there today?

3. Aunt Burtha also put \$2,000 into a different savings account for your brother when he was born 18  years ago. If his account has \$4,813.24 in it today, what rate of return did his account earn?

4. You decide to borrow money from Cousin Vinnie and he has agreed to a 20 percent interest rate per  year. If you borrowed \$200 last year, and know you have to pay him in full exactly \$716.64 (and make no other payments to him), how long from now until you must pay him back?

5. Five years ago, you bought a piece of art at auction for \$1.2 million. Yesterday, you sold that piece at  auction for \$2,630,937.64. You also purchased a new piece yesterday for \$300,000. If the piece you just  bought earns the same rate of return as the first one, how much will you be able to sell it for in 8 years?

6. You plan to save for a Caribbean cruise. You deposit \$500 today, \$250 in two years, and \$1,000 in  three years. If your investment account earns 9 percent per year, how much will you have in five years?

7. Which do you prefer: (1) receiving \$1,000 in five years when the interest rate is 3 percent per quarter  or (2) receiving \$1,500 in six years when the interest rate is 6 percent every six months?

8. You have won a lawsuit and the court has arranged for the defendant to pay you \$7,500 per year for  the next three years. If the appropriate discount rate is 8 percent, what is the value of your settlement  today?

9. Last year, you borrowed money from Cousin Vinnie and he agreed to a 25 percent interest rate per  year. If you borrowed \$250, and know you have to pay him in full exactly \$488.28 (and make no other  payments to him), what will be the total length of the loan?

10. An investment offers a return of 1 percent every month if you deposit a minimum of \$20,000. If you  make the minimum deposit today and do not make any additional deposits, how much will you have in  your account in 20 years?

Exam 1 Pae 15

Thursday, September 13, 2018 9:30 AM TVM Practice Problems Review

Calculator Tips and Warnings

- The operator of the calculator still needs to know what they're doing ○ Wrong inputs will generate the wrong answer

- My Calculator = HP10bII+

4 decimal places - hit orange shift button, then DISP (= button), then  hit 4

○ Set payments/year - 1, orange shift button, P/YR (PMT button) Clear TVM values - orange shift button, then clear all (C button

above on/off)

Present Value

Years Interest Rate

\$40,000

7

5%

\$6,000.06

13

9%

\$15,000

20

15%

\$25,000

9

8.0060%

- Rule of 72

Future Value  \$56,284.02

\$18,395

\$245,498

\$50,000

Not exact rule - way of estimating how long it takes to double your

money

 72/interest rate

 72/8=9

You are offered an investment that requires you to put of \$13,000

today in exchange for

○ Would you accept it if the appropriate discount rate was 8%

 Yes

○ You have the opportunity to make an investment… ○ Should you make the investment? What is the net present value?  No.

○ At 10%?

 Yes

- TVM Practice Review (Homework review)

Exam 1 Pae 16

Tuesday, September 18, 2018 9:30 AM Review for Exam 1

Review TVM Practice Problems 8 & 10

8. Lawsuit settlement

Assume payments come at the end of the year

\$7,500 in year 1

\$7,500 in year 2

\$7,500 in year 3

Calculate each year 0 value separately

[7500/1.08] + [7500/(1.082)] + [7500/(1.083)] =

10. Investment 1% return every month, how much in 20 years \$20,000*(1.01)240= \$217851.07

Review for Exam Party 1

Lowder 113A 6pm - 8pm

Do not forget scan sheet - blue full size bubble sheet

We may bring cheat sheet!

1 side of a standard 8.5x11 paper

May be printed or handwritten (put the ratios on there!)

Suggestions

Study both notes and book

Do suggested problems

Be comfortable with calculator, but understand the concepts independently! Get help if having problems

Don't!

Study solutions and not work the problems

Be careful how you use solution

Memorize all the formulas

Miss the exam

Cheat

Exam Content and Structure

31 multiple choice questions - 30 graded, 1 bonus, not specific as to bonus question

8 q's on 3 topics, 7 on 1 topic

8 quantitative/number-crunching problems and 23 conceptual

9 Roman-numeral-type multi-part conceptual questions

Topics

Chapter 1 - what is corporate finance? What is goal of firm? What are

benefits/drawbacks of diff types of business orgs? What are agency costs and how do  we mitigate them?

Chapter 2 and Section 3.1

Balance sheet - book values vs market values

Income statement - acct numbers versus cash flows

Exam 1 Pae 17

Income statement - acct numbers versus cash flows

Statement of cash flows - sources and uses of cash

Taxes - avg vs marginal tax rates

Chapter 3

Ratios - how to calculate, what they tell us, dupont identity Common size balance sheets and common size income statements Potential problems for ratio analysis

Chapter 5

Present and future values of single cash flows (and mult cash flows by adding  them up)

Calculate N, I/Y, PV, and FV

CANNOT compare cash flows across periods

Moving along timeline (PV vs FV)

Understand the concepts

Practice Problems

Exam 1 Pae 18

Thursday, September 20, 2018 9:30 AM Optional Q&A - Exam 1

Dupont Identity

ROE = NI/Equity

ROE = NI/Assets * Assets/Equity

NI/Assets provides Return on Equity

Assets/Equity provides equity multiplier

ROE = NI/Sales * Sales/Assets * Assets/Equity

NI/Sales provides profit margin (PM)

Sales/Assets provides total asset turnover (TATO)

This tells us why it went up or down. It breaks ROE into components and we can analyze the  components. It also demonstrates the relationship between the components

Common Size Financial Statements

How to calculate and why we do

Balance Sheet - based on Total Assets

Income Statement - based on Total Sales (or Total Revenues)

Compare companies of different sizes

Exam 1 Pae 19

Wednesday, September 19, 2018 11:46 AM

□ Net working capital = Current Assets - Current Liabilities  Net Working Capital to Total Assets = NWC/Total Assets

Cheat Sheet Materials

- Common Size Financial Statements

○ Balance Sheet items as a % of Total Assets

○ Income Statement items as a % of Total Sales

- Classification of Financial Ratios

○ Short-term Solvency or Liquidity Ratios - measure ability to pay short-term obligations

 Enterprise Value-EBITDA Ratio = (market value of equity + Book value of liabilities - cash)/EBITDA ○ Market Value Ratios - outside financial statements

Higher numbers indicate higher liquidity, but higher is not always better. Can pay off debts, but it isn't

earning any rate of return

 Current Ratio = Current Assets/Current Liabilities

 Quick (Acid-Test) Ratio = (Current Assets - Inventories)/Current Liabilities

 Cash Ratio = Cash/Current Liabilities

 Interval Measure = Current Assets/Average Daily Operating Costs

○ Long-term Solvency or Financial Leverage Ratios - measure ability to pay longer term obligations  Total Debt Ratio = Total Liabilities/Total Assets = (TA-Equity)/TA  Debt-equity Ratio = Total Liabilities/Stockholders' Equity

 Equity Multiplier = Total Assets/Stockholders' Equity

 Given any of these ratios, we can solve for the other two, because A=L+SE □ Given: Total Debt Ratio = .6

 Make up numbers that work: A=100, L=60, SE=40 (100-60=40)

 Debt-equity ratio = 6/4=1.5

 Equity Multiplier = 10/4=2.5

□ Given: Debt-equity Ratio = .42

 Make up numbers that work: L=.42, E=1, A= 1+.42=1.42

 Total Debt Ratio = .42/1.42=0.2958  Equity Multiplier = 1.42/1=1.42 □ Given: Equity Multiplier = 1.25  Make up numbers that work: A=1.25, SE=1, L=.25  Debt-equity Ratio = .25/1=0.25  Total Debt Ratio = .25/1.25=0.2  Equity Multiplier = Assets/Equity OR (Equity + Liabilities)/Equity OR 1+(Debt-equity ratio)  Long-term Debt Ratio = Long-term Debt/(Long-term Debt + Equity)

Asset Management or Turnover Ratios - how efficiently are we using our assets - turnover ratiosInventory Turnover = COGS/Inventory Days' Sales in Inventory = 365/Inv. Turnover Receivables Turnover = Sales/Accounts Receivable Days' Sales in Receivables = 365/Receivables Turnover = aka avg collection period

Net Working Capital Turnover = Sales/Net Working Capital

Fixed Asset Turnover = Sales/Net Fixed Assets TATO = Sales/Total Assets

Profitability Ratios - measure ability to generate profit

Profit Margin = Net Income/Sales Return on Assets = Net Income/Total Assets Return on Equity = Net Income/Total Equity Market Value Ratios - outside financial statements *Earnings per Share (EPS) = Net Income/# of shares outstanding

 Times Interest Earned (TIE) Ratio = Earnings Before Interest & Taxes/ Interest Expense

 Cash Coverage Ratio = (EBIT + Depreciation)/Interest Expense

Price-earnings (PE) Ratio = price per share/EPS

Price-sales Ratio = Price per share/sales per share *If company has negative Net Income

○ Asset Management or Turnover Ratios - how efficiently are we using our assets - turnover ratios

Market-to-book Ratio = market value (price) per share/Book value of equity per share

 Inventory Turnover = COGS/Inventory  Days' Sales in Inventory = 365/Inventory Turnover  Receivables Turnover = Sales/Accounts Receivable

Tobin's Q = market value of assets/replacement cost of assets Enterprise Value-EBITDA Ratio = (market value of equity + Book value of liabilities - cash)/EBITDADuPont Identity = (NI / Sales) * (Sales / Assets) * (Assets / Equity) = PM*TATO*EqMult Profit Margin * Total Asset Turnover = Return on Assets With leverage, ROE is greater than ROA and breaks ROE down into profitability

 Days' Sales in Receivables = 365/Receivables Turnover = also known as average collection period

Uses of Financial Statements- Ratio Analysis, Common Size Financial Statements, Trend Analysis, Cross-sectional Analysis, The DuPont Identity

 Net Working Capital Turnover = Sales/Net Working Capital

 Fixed Asset Turnover = Sales/Net Fixed Assets

 Total Asset Turnover = Sales/Total Assets

○ Profitability Ratios - measure ability to generate profit

 Profit Margin = Net Income/Sales

 Return on Assets = Net Income/Total Assets

 Return on Equity = Net Income/Total Equity

 *Earnings per Share (EPS) = Net Income/# of shares outstanding  Price-earnings (PE) Ratio = price per share/EPS  Price-sales Ratio = Price per share/sales per share *If company has negative Net Income

Limitations of Financial Statements - Backward-looking, not forward-looking, Financial statements have book values, not market values, Income Statement has accounting numbers, not actual cash flows, Benchmarking - sometimes hard to find comparable companies, Effects of Inflation -book value differs from market value, Seasonal Factors - may even out over a year, but looking at quarterly could give skewed results, "Window Dressing" -making financial statements look as good/strong as possible (not fraud), Differing Operating and Accounting Practices, The Big Picture

 Market-to-book Ratio = market value (price) per share/Book value of equity per share  Tobin's Q = market value of assets/replacement cost of assets

Exam 1 Page 20

FVt . PV0= (1 + r)t

Chapter 1

-3 questions: What should we invest in (as a company/firm)? - projects or assets /  How do we finance those investments? (Borrow money, Use owners money, Use  internally generated money) / How do we manage day-to-day operations of the  firm? - Short-term cash flow management

-Capital budgeting - The process of planning and managing the firm's long-term  investments by Estimate cash flows (timing), Estimate cost of those cash flows (risk),  Discount the cash flows (time-value of money)

-Capital Structure - The mix of debt and equity describing how the firm is financed -Short-Term Cash Flow Management - Net Working Capital = C.A. - C.L. = \$ value of  working capital

-The Goal of the Firm - To maximize shareholder wealth!!!

Corp – Pros - Limited liability,Easy transfer of ownership, Unlimited life, Equity is not  limited / Cons - Difficult to start up, Double taxation of earnings, Corporations  earnings are taxed, Dividends paid to shareholders are taxed

-Agency Problem/Conflict: The possibility of conflict of interest between the  stockholders (the principal) and management (the agent) of a firm / Agency Costs: The costs of the conflict of interest between stockholders and management. -Direct agency costs: Wasteful spending, Monitoring and Auditing, Indirect agency  costs, Missed opportunities

-How do we control agency conflicts? Managerial Compensation, Stock options or  shares of stock, Cash bonus for good job performance

-Control of the Firm - Termination of under-performing managers, Shareholders can  elect new board of directors if directors aren't managing well - Proxy Fights, (Hostile)  Takeover

Chapter 2

-The Balance Sheet - Market Value vs. book Value

-Market value - Price you can buy/sell asset for today

-Book value - accounting measure of value - price you paid when you bought asset  minus accumulated depreciation

-CAN’T find true (market) value of the firm on B.S.

Equity on the balance sheet is the book value of equity

-How do we find the true (market) value of total stockholders' equity? - Price per  share times number of shares

-The Income Statement – Rev-Exp=Income

-The Bottom Line: Net Income or EPS (earnings per share) - Distribute it to owners or  Reinvest in firm

-Depreciation is a non-cash expense

-the Statement of Cash Flows - Cash Flow from Operating Activities (Buying of  supplies and selling of products), Cash Flow from Investing Activities (Long-term  assets), Cash Flow from Financing Activities (Sources and Uses of Funds) -Changes in Current Assets (all assets, not just current) - Anytime we increase  assets, represents a use of cash / Decrease in assets = a source of funds or cash  inflow

-Changes in Current Liabilities (all liabilities and equity) - Opposite above -Some Things to Remember (about financial statements) - Depreciation & Net Income  are not cash flows / Financial statements are backward looking, not forward looking  / The balance sheet shows book values, not market values

Avg Tax Rate - taxes owed divided by taxable income / -Marginal Tax Rate – next \$

Chapter 3 - Financial Statement Analysis (Ratios)

Market Value Ratios - outside financial statements

Common Size – B.S=%TAssets, IS=%TSales

Price-earnings (PE) Ratio = price per share/EPS

Price-sales Ratio = Price per share/sales per share *If company has negative Net

Short-term Solvency or Liquidity Ratios - measure ability to pay short-term

Income

obligations

Market-to-book Ratio = market value (price) per share/Book value of equity per share

Higher numbers indicate higher liquidity, but higher is not always better. Can pay off

Tobin's Q = market value of assets/replacement cost of assets

debts, but it isn't earning any rate of return

Current Ratio = Current Assets/Current Liabilities

DuPont Identity = (NI / Sales) * (Sales / Assets) * (Assets / Equity) =

Quick (Acid-Test) Ratio = (Current Assets - Inventories)/Current Liabilities

PM*TATO*EqMult

Cash Ratio = Cash/Current Liabilities

Profit Margin * Total Asset Turnover = Return on Assets

Net Working Capital to Total Assets = NWC/Total Assets

With leverage, ROE is greater than ROA and breaks ROE down into profitability

Net working capital = Current Assets - Current Liabilities

Uses of Financial Statements- Ratio Analysis, Common Size Financial Statements,

Interval Measure = Current Assets/Average Daily Operating Costs

Trend Analysis, Cross-sectional Analysis, The DuPont Identity

Limitations of Financial Statements - Backward-looking, not forward-looking, Financial

statements have book values, not market values, Income Statement has accounting

Long-term Solvency or Financial Leverage Ratios - measure ability to pay longer

numbers, not actual cash flows, Benchmarking - sometimes hard to find comparable

term obligations

companies, Effects of Inflation - book value differs from market value, Seasonal Factors

Total Debt Ratio = Total Liabilities/Total Assets = (TA-Equity)/TA

- may even out over a year, but looking at quarterly could give skewed results, "Window

Debt-equity Ratio = Total Liabilities/Stockholders' Equity

Dressing" - making financial statements look as good/strong as possible (not fraud),

Equity Multiplier = Total Assets/Stockholders' Equity

Given any of these ratios, we can solve for the other two, because A=L+SE

Differing Operating and Accounting Practices, The Big Picture

Equity Multiplier = Assets/Equity OR (Equity + Liabilities)/Equity OR 1+(Debt-equity  ratio)

Long-term Debt Ratio = Long-term Debt/(Long-term Debt + Equity)

Times Interest Earned (TIE) Ratio = Earnings Before Interest & Taxes/ Interest  Expense

Cash Coverage Ratio = (EBIT + Depreciation)/Interest Expense

Asset Management or Turnover Ratios - how efficiently are we using our assets - turnover ratios

Inventory Turnover = COGS/Inventory Days' Sales in Inventory = 365/Inv. Turnover

Receivables Turnover = Sales/Accounts Receivable

Days' Sales in Receivables = 365/Receivables Turnover = aka avg collection period Net Working Capital Turnover = Sales/Net Working Capital

Fixed Asset Turnover = Sales/Net Fixed Assets TATO = Sales/Total Assets

Profitability Ratios - measure ability to generate profit

Profit Margin = Net Income/Sales

Return on Assets = Net Income/Total Assets

Return on Equity = Net Income/Total Equity

*Earnings per Share (EPS) = Net Income/# of shares outstanding

Chapter 5

FVt = PV0 x (1 + r)t  FVt .  PV0= (1 + r)t

-Present Value Definitions - Present Value (PV) - the current value of future cash  flows discounted at the appropriate discount rate / Discount - calculate the present  value of some future amount

As interest rates rise, the Present Value is less

As the period of time increases, the Present Value decreases

Tips on Solving

Don't rush to get through it - setup is vital

Draw a timeline

Formulas are the same, just organized differently to provide different solutions For multiple cash flows, just add up the individual present or future values As time or rate increase, FV increases and PV goes down

There are currently only 4 components; PV, FV, t, and r

With any 3 components, you can solve for the 4th

Cash flows always occur at end of the period ( x will happen for the next two years =  end of year 1 and end of year 2)

Must be consistent in unit of time

Tuesday, September 25, 2018 9:30 AM Chapter 6 - Discounted Cash Flow Valuation

Review Exam 1 and survey results

Chapter 6 - Discounted Cash Flow Valuation Future Value of Multiple Cash Flows

-

The future value of multiple cash flows is the sum of individual future values (move flows  individually to same period and then add)

FVt = CF0 x (1 + r)t + CF1 x (1 + r) ○t-1 …. CFt

○ Example on slides

Bank account today with \$500. Deposit \$1,000 at end of next 3 years. Interest rate=

5%, compounded annually. How much in 3 years

Year 0

Year 1

Year 2

Deposit

500

1000

1000

Amount

Valuing Perpetuities

Year 3  1000

- Perpetuity: a level stream of cash flows which continue forever (sometimes called consols). - Present Value of a Perpetuity: PV0 = CF1

r

-

Example: Assuming interest rates = 10%, what is value today of perpetuity paying \$500/year, w/  first payment one year from today?

PV0 = \$500/.1=\$5,000.00

Getting a payment of \$5,000 today is the same as \$500/year for forever at 10% interest

Would you be willing to pay \$6,500 for the same perpetuity if interest rates were 8%?

\$500/.08=\$6,250.0

No, I would not be willing to pay \$6,500 for something worth only \$6,250.  This doesn't take into account inflation.

Growing Perpetuities

- Present Value of a Growing Perpetuity

Exam 2 Page 1

Thursday, September 27, 2018 9:30 AM Chapter 6 - continued

Review Quiz Question

\$50/.005=\$10,000.00

.5%/month in decimal form is .005

Valuing Perpetuities

- Review definition of perpetuity and formula for present value of a perpetuity

Growing Perpetuities

- Present Value of a Growing Perpetuity: PV0 = CF1 if (only if) r > g  r - g

Rephrased: Present Value (period 0=now) equals next period's cash flow divided by  interest rate (in decimal form) minus growth rate (also in decimal form)

-

Example: Suppose you own a perpetuity that promises to pay \$1 next year, after which  payment grows at 5%/year forever. If interest=10%, what is value of perpetuity?

-

Example: Assume growing perpetuity made payment of \$120 yesterday. If cash flow  expected to grow at 5% and interest rates are still 10%, what is price of perpetuity today? Next cash flow=120*1.05=126 PV = 126/(.1-.05)=2,520

Present Value of an Annuity

- Annuity: a level stream of cash flows for a fixed period of time - Present Value of an Annuity

PV0 = ஼ிభ

⎯⎯⎯⋅ ቂ1 −

(ଵା௥)௧ ⎯⎯⎯⎯⎯ቃ

- Example: just inherited some money from Uncle Fred.

PV0 = 4000/.10 * [1-(1/(1.12))]

40000*[1-(1/1.21)] = \$6,942.1488

N=2

I/Y=10

4,000

FV=any payment above and beyond last

PV=? PMT=

payment. In annuity, FV=0

Future Value of an Annuity

- Future Value of an annuity:

FVt = CF * [(1 + r)t- 1]

○ Can be rearranged: FVt = CF * [(

- Example: What is future value (at year 2), of previous example? FV2 = 4000/.1 * [(1.12 ○ ) - 1] = \$8,400.00

N=2

I/Y=10 PV=0

PMT=4,000 FV=? PV=0 (when trying to find FV)

-

Example: books and beer expensive. You have balance of \$2,000 on visa. Interest= 2%/month. You pay \$50 minimum payment each month (starting next month) and make  no more charges on that card. How long will it take you to pay off the balance?

PV=

I/Y=2 PMT=-50

N=???

FV=0

\$2,000

We are paying, so

81.274 months

THIS IS NEGATIVE!

or 6.7728 years or 6 yrs, 9.274

mnths

Exam 2 Page 2

mnths

If you get negative N, then you

put a # in wrong (probably

payment)

- How much would you have to pay each month if you wanted to pay off in 3 years?

FV=0

PV=\$2,000

I/Y=2 PMT=???

-\$78.4657 (we pay out \$78ish per month)

N=36

Growing Annuities

- Present Value of a Growing Annuity

○ Formula given, but we will not do that in this class

Annuities Due

- So far, we've assumed cash flows occur at the end

- Annuity Due: an annuity for which the cash flows occur at the beginning of the period ○ Plugging in will give us PV of period BEFORE cash flow, or PV-1

Exam 2 Page 3

Tuesday, October 2, 2018 9:30 AM Chapter 6 - still continued

Review

- Quiz problems

- Annuities Due vs. Regular Annuities

Annuities Due

- Annuity Due: an annuity for which the cash flows occur at the beginning of the period- PV Annuity Due

○ = (PV Ordinary Annuity) x (1 + r)

-

HP 10bII+ - orange shift button + Beg/End to change when payment occurs. BAD IDEA to do this if you forget to change it back. Note the "BEG" on screen (or BGN on TI calculator(2nd + Set))

The Effect of Compounding

-

Annual Percentage Rate (APR): nominal, stated annual interest rate that ignores the effect of compound interest within the year. The APR is the periodic rate (r) times the number of compoundings per year (m)○ 12% APR is 3%/quarter

If you have a 12% APR compounded monthly is 1%/month, quarterly is 3%/quarter, semi-annually is 6%/6

months, compounded annually is 12%/year

-

Effective Annual Rage (EAR): the effective annual interest rate, which takes into account the effect of compound interest

○ Do not divide EAR by anything

○ Example: a bank loan is quoted at 10% APR, compounded semiannually. What is the EAR? 5% every 6 months

Begin with \$100

6 months will have \$105

1 year will have \$110.25

  Earned 10.25%, not 10%

 From formula below -

[1 + (.1/2)]2- 1

1.052- 1 = 1.05*1.05 - 1=0.1025 10.25%

EAR = [1 + (APR/m)]m ○ - 1

○ Example: Which loan would you choose?

Bank A = 15% compounded daily

[1+(.15/365)]365-

1

Bank B = 15.5% compounded quarterly

[1+(.155/4)]4-

1

Bank C = 16% compounded annually

[1+(.16/1)]1-1

16.18%

16.42%

16%

 Borrowing money = lowest rate = Bank C is the winner

-

HP calculator - risky to compute effective rate because it changes frequency of payments, which could mess you up on future problems

Amortization

- What is an amortized loan?

○ Same payment each month over the life of the loan ○ A portion is principal, a portion is interest

-

Example : You plan to buy a @200,000 house. You will put 10% down and finance the rest with a 30 year mortgage at 6% APR, compounded monthly. What are the monthly payments? ○ Will borrow 180k

○ Effective interest is .5%/month. = .005

180,000 = (CF1/.005) * [1 - (1/1.005360 ○ )]

CF = \$1,079.1909

Exam 2 Page 4

○ CF1 = \$1,079.1909

N

I/Y PV PMT

360

.5 180,000 ???

-1,079.1909

FV

0

○ Amortization Schedule

Month

Beginning

Balance

PMT

Portion Interest

Portion

Principal

Ending Balance

1

180,000

1,079.19

900.00 179.19

180000-179.19=179820.81

2

179,820.81

1,079.19

899.10 180.09

179820.81-180.09=

179640.72

3

179,640.72

1,079.19

898.20 180.99

179,459.73

4

179,459.73

1,079.19

897.30 181.89

179,277.84

5

179,277.84

1,079.19

898.3892 182.8008

179,095.0392

6

179,095.04

1,079.19

895.48 183.7148

178911.3244

Chapter 6 Suggested Problems

- Concepts

○ 2-8

- Questions and Problems

○ 1, 3, 4, 5, 7, 10, 12, 20, 21, 24, 26, 28, 36, 41, 43, 45, 54

Exam 2 Page 5

Thursday, October 4, 2018 9:30 AM Chapter 6 - still more on Discounted Cash Flow Valuation

My computer wasn't charged for this class, so I took notes by hand and transcribed. They may be a little more sparse than normal, but the panopto lecture capture is available.

Amortization Schedule

- This chart is in the course packet

- Calculated monthly payments - treated as annuity

N = 360

I/Y = .5

PV = 180,000 PMT = ???\$1,079.1909

FV = 0

-

- Calculator instructions!!! ○ TI Instructions

2nd (shift)

AMORT (PV button)

P1 = 4

Enter P2 = 4

Enter Up and down arrows scroll

2nd

AMORT

P1 = 1

Enter P2 = 4

Enter Up and down

○ HP instructions

 Just looking at month 4…

4

Input (below N

button)

4

(orange)

AMORT (FV

Shift

key)

"=" key will scroll through

values

 Looking at months 1 - 4

1

Input 4 Shift (orange)

AMORT

□ = = = = Scrolling takes you through PER (period), PRIN (principal portion of payment), INT (interest portion of payment),

and BAL (ending balance) - or sum of what was paid toward principal and interest if for more than one month- Chapter 6 Suggested Problems

○ Concepts Review and Critical Thinking

 2-8

○ Questions and Problems

 1,3,4,5,7,10,12,20,21,24,26,28,36,41,43,45,54

Buying new truck @ \$40,000. Putting down 10% and have 60-month loan @ 9% (APR) compounded monthlyfor the

-

balance. How much are payments?

○ If not told, safe to assume compounded monthly

○ Not the rate per month! Divide by 12

N = 60

I/Y = .75

PV = 36,000 PMT = -\$747.3008

FV = 0

- Assuming 10% interest rate, compounded annually, what is PV of \$1,000/year forever, w/ 1st payment in 1 year?○ PV0 = CF1/r = \$1,000/.1 = \$10,000.00

- What if first payment from problem above was in 5 years? ○ PV4 = CF5/r = \$10,000

N = 4

I/Y = 10

\$6,830.13

PMT = 0

PV = ???

FV = \$10,000 OR

\$10,000/(1.14) = \$10,000/(1.1*1.1*1.1*1.1) = \$6,830.13

- 10% APR, compounded annually, what is PV5 of perpetual stream of \$120 annual payments starting in 9 years?Cash flow happens every year, need EAR, which is same as APR in this case because the interest is compounded

annually. If compounded more frequently, would need to determine EAR.

○ PV8 = CF9/r = \$120/.1 = \$1,200.00

\$1,200/(1.13) = \$1,200/(1.1*1.1*1.1) = \$901.58

Exam 2 Page 6

- Maturity - specific date on which the principal amount of a bond (face/par value) is repaid

- Yield to maturity - rate required in market on the bond

\$1,200/(1.13 ○ ) = \$1,200/(1.1*1.1*1.1) = \$901.58

Pay us \$100/year for 10 years starting next year, and we will pay you and heirs \$100/year thereafter in perpetuity. At

-

what range of interest rates is this a good deal?

○ We accept when benefits > cost. Or outflows < inflows. Must compare at same point in time. ○ Cash outflow of \$100/year for 10 years = annuity - ends in year 10 (can get value at year 10) ○ Cash inflow of \$100/year forever = perpetuity - starts in year 11 (can get value at year 10)

FV10= 100/r* [(1 + r)10-

<

1] 100/r= PV10

○

○ Multiply both sides by r/100 to get rid of the fraction

(1 + r)10-

1 < 1 Both sides add 1

r)10< 2

(1 + r< 21/10

1 +  r< 1.0718 - 1 = 0.0718

r< 7.18%

○

Bonds (Everything you Wanted to Know about Bonds & Their ValueExample: Yost Rocks, Inc. issues bonds. 30 years at 12%. Pays each bondholder \$120/year and returns principal of

-

\$1,000 at end of 30 years

- Coupon - stated interest payment made on a bond

○ 12%

- Face value - aka par value - principal amount of bond to be repaid @ end of term

○ \$1,000

- Coupon rate - annual coupon divided by face value of bond (PMT)

○ \$120

○ 30 years

○ Also: yield. This is "r" and is quoted as APR - often not the same as coupon rate

Calculating the Price of a Bond

- How do we calculate the price of a bond?

- The price of a bond is equal to the present value of the bond's future cash flows. Example: Tigers, Inc. decides to issue \$1,000 bonds w/ 5 years to maturity. Coupon rate is 10% annually. YtM is also

-

10%. What is price of bond?

○ Move cash flows back to zero at yield to maturity rate

Exam 2 Page 7

Tuesday, October 9, 2018 9:30 AM Chapter 7 - Bonds and Their Value

Quiz Question Review

\$1,000 face, matures in 10y, coupon rate 8%, yield to maturity is 6%. How much does bondholder

-

receive each year in coupon payments?

- YTM not included

- Annuity

Announcements

- Tiger\$ense - Tuesday, Oct. 16th 9:30-12:15

Calculating the Price of a Bond

- How do we calculate the price of a bond?

- The price of a bond is = to the present value of the bond's future cash flows - Example

○ 100/year for 5 years + 1,000 back at end

○ PV = pmt/r * [1- 1/(1+r to the t power)] + face/(1 + r to the t power) - Coupon rate is EQUAL TO THE Yield to Maturity

 Price of the bond is equal to the face/par value of the bond -

When coupon rate is LESS THAN Yield to Maturity, the price of the bond is LESS THAN the face  value

○ Bond is trading at a discount (from its face or par value)

- When YTM=10% and pmts made semi-annually, what is price of the bond ○ Work in 6-month periods

N=10

Pmt=\$50 FV=\$1,000

Int=5%

\$1,000

PV=???

-

Just purchased a DocYost bond for \$1,050. \$1,000 face value, 8% coupon rate, paid semiannually.  Matures in 10.5 years. What is YTM?

○ Work in 6-month periods

N=21

PMT=\$40

FV=\$1,000 I/Y=???

3.6548 in 6-month period7.3097 as an APR

PV= -\$1,050

Current Yield

- Current yield: Annual coupon divided by current price - What it is: percentage of price you receive as payment - What it is not: a measure of total return ○ Same as dividend yield for stocks

-

2 \$1,000 bonds identical in every way (same risk), except coupons and prices. Both are 3 years to  maturity, and annual coupons.

1) has 8% coupon and sells for \$974.69

N= 3

9%

I/Y= ???PV= -\$974.69

PMT= \$80

FV= \$1,000

2) Has 10% coupon, if same YTM as first bond, what is its price? N= 3 I/Y= 9 PV= ??? PMT= \$100 FV= \$1,000

Exam 2 Page 8

N= 3 I/Y= 9 PV= ???

PMT= \$100 FV= \$1,000

\$1,025.3129

- What are they?

a bond that you pay for today and it does not pay coupons over time, just face value at the

end

○ No cash flows/no coupon rate

○ AKA Pure Discount Bonds

- How do I calculate their price?

○ PV = value of future cash flows

Example - what is price of a zero-coupon bond that has a face value of \$1,000 and matures in 10

-

years if the YTM is 8%?

○ PV0 = 1,000 = \$463.19

(1.08)10

You only get the face at the end (no interest/coupon payments ever, even at end). Because

there is a YTM, it means you pay less up front for the bond.

Interest Rate Risk

-

Interest Rate Risk: the risk of a change in the value of a bond because of a change in the interest  rate

○ Bond prices and market interest rates move in opposite directions All other things being equal, the longer the time to maturity, the greater the interest rate

risk

○ All other things being equal, the lower the coupon rate, the greater the interest rate risk Lower coupon, more we depend on final cash flow  Higher coupon, more dependent on earlier cash flows

Other Bond Pricing Truths

When a bond's coupon rate is greater than YTM, bond's price/market value will be greater than

-

par

- When bond's coupon is = to YTM, price=par

- When bond's coupon is less than YTM, bond's price/marker is less than par  Exam 2 Page 9

Tuesday, October 16, 2018 9:30 AM Chapters 7 & 8 - Bonds cont. and Stocks and their Value

The Term Structure of Interest Rates

- Term Structure: The relationship between interest rates and time-to-maturity of a debt security- Yield on Bonds - government and corporate (government doesn't deal with the last 3 so much)○ Real rate - flat line

○ Inflation premium - upward sloping with inflation, downward sloping with deflation

○ Interest rate risk premium - increases with time-to-maturity May be downward sloping overall depending on inflation/deflation, but the IR risk premium is always

increasing…it just may not increase as much as deflation decreases ○ Default Risk Premium

Bond Features

Indenture: the written agreement between the corporation and the lender detailing the terms of the debt issue -

-

the contract

- Terms of a Bond - maturity, par value, coupon rate, and frequency - Security - collateral

- Seniority - position for pay back relative to other lenders

- Repayment

○ Sinking Fund - requires the firm to retire a certain portion of their bonds each year - Call Provision - gives firm right to buy bonds back early

○ Call Premium - usually equal to a year's worth of coupon payments ○ Yield-to-Call

- Protective Covenants - restrictions on the actions of managers ○ Limit amount of dividends to be paid

○ Firm may not be allowed to sell off large chunks of assets

○ Maybe current ratio stays above some certain level of liquidity ○ If firm breaks a covenant, they are in technical default and could be sued

Bond Ratings

- Above BBB/Baa is investment-grade bond

- Lower ratings are higher default risk/more speculative - "junk" bonds

Corporate Bond Reporting

- Charts found in notes/online on class website

- Link to morningstar bond reporting

Will need to be able to interpret relationships and meanings from provided information- if chart provided, what

-

does it mean?

Differences between Debt and Equity

Debt

Not an ownership interest

Creditors do not have voting rights

Equity

Ownership interest

Common stockholders vote for the board of directors and other issues

Interest is considered a cost of doing business and is Dividends are not considered a cost of doing business and  Exam 2 Page 10

Interest is considered a cost of doing business and is

Dividends are not considered a cost of doing business and

tax deductible

Creditors have legal recourse if interest of principal payments are missed

are not tax deductible

Dividends are not liability of firm and stockholders

Chapter 7 Suggested Problems

- Concepts Review & Critical Thinking Questions

○ 1,3,6

- Questions and Problems

○ 2,3,4,5,6,18,20,21,22,26,29(A&B),32

○ \$604.23

○ 10%

○ \$1135.9033

○ 10%

Everything you ever wanted/needed to know about Stocks

Let's Review

- Price (value) of a share of stock is equal to the present value of the stock's future cash flows.

Stock Valuation

- Common stock cash flows

○ Dividends

○ Price we sell it for

Example - Kidd Inc stock will pay dividend in 1 year of \$1 and a dividend in 2 yrs of \$1.50. You plan to sell stock in

-

2 years right after dividend for \$27.65. If market's required return is 10%, what is price today? Exam 2 Page 11

Thursday, October 18, 2018 9:30 AM Chapter 8 - Stocks Valuation

Before-class Example:

PV0 = 1/(1.1)1+ [(1.5 + 27.65)/(1.12)] = .9091 + (29.15/1.21) = .9091 + 24.0909 = \$25.00  Everything You Wanted to Know About Stocks and Their Value

Stock Valuation

- Price is present value of future cash flows

- + ….

P0 = D1/(1 + r)1+ D2/(1 + r)2+ D3/(1 + r)3

-

Example - Kidd Inc. will pay dividend of \$1 in 1 year, and \$1.50 in two years. You will sell just after 2nd dividend for \$27.65. If market's required return on Kidd Inc. is 10%, what is price today? \$27.65 represents the value at time period 2 of all the cash flows after time period 2 (present value of future

cash flows)

○ Corporations are infinite - so this deals with perpetuities/growing perpetuities - 3 Types of Dividends

○ No growth or zero growth - same value for every dividend - perpetuity  Dividends do not increase in dollar amount

 D1 = D2 = D3…

 Dividends are paid every period forever

 Price of a share of zero growth stock is: PV0 = CF1/r

Example - Yostmeister, Inc. just paid a dividend of \$10 per share. Company expects to pay same dividend/year every year. What is price of share of stock if market's required return is 10%?□ PV0 = cash flow next period/r = \$10/.1 = \$100.00

\$10 just paid is Cash Flow0 - next period's cash flow happens to be the same as Cash Flow0for zero-growth stocks

○ Constant growth - grows at constant rate - growing perpetuity  Dividends increase at fixed rate every period

 D1 = D0 * (1 + g)

D2 = D1 * (1 + g) = D0 * (1 + g)2

D3 = D2 * (1 +g) = D0 * (1 + g)3

 Diidends are paid every period forever

 The price of a share of a constant growth stock is PV0 = CF1/(r - g) □ ONLY FOR r>g

 PVt = CFt+1/(r - g)

Example: Tigers, Inc pays dividends/share and it's growing by 5%/year. Next year's dividend is \$10 and market's required return on this stock is 8%, what is current stock price?

□ \$10/(.08-.05) = \$333.33

○ Non-constant growth - the everything else category

 Could be:

Dividends have supernormal growth for some period of time, then "slow down" and grow

□ Dividends grow erratically for a period of time then grow steadily thereafter

□ No dividends for a period of time, then…  Calculate by moving future cash flows to the present value  Steps to solving non-constant growth

□ Draw a timeline and lay out all cash flows (and growth rates)

□ Deal with the right-hand side

□ Bring it all back to zero

Exam 2 Page 12

□ Bring it all back to zero

Example: Infinite tech just paid a dividend of \$1.82. The market's required return on this stock is 16%. If company expects the dividend to grow at 30%/year for next 3 years and 10%/year thereafter, what is current price?

□ (r - g) * [PV0] = [CF1/(r - g)] * (r - g)

- The Required Rate of Return

○ Recall the dividend growth model

 Discounted Cash Flow (DCF) Model => Constant Growth  PV0 = CF1/(r - g)

 A little algebra…

□ Dividing by PV0 gives you r - g = CF1/PV0

□ r = CF1/PV0 + g

○ Dividend Yield: The dividend income portion of a stock's return ○ Capital Gains Yield: the price change portion of a stock's return

Exam 2 Page 13

Tuesday, October 23, 2018 9:30 AM Chapter 8 - continued

The Required Rate of Return

- Recall the dividend growth model (DCF Model => Constant Growth ○ PV0 = CF1

r - g

- Dividend Yield & Capital Gains Yield

○ (r-g) * PV0 = CF1

○ r-g = CF1/PV0

○ r = (CF1/PV0) + g

○ Dividend Yield: The dividend income portion of a stock's return ○ Capital Gains Yield: the price change portion of a stock's return - Constant Growth Example

Tigers, Inc.'s dividends/share expected to grow indefinitely by 5%/year. If next year's

dividend is \$10, and market's required return is 8%, what is current stock price?

 \$10.00/(.08-.05) = \$333.33

 Next year's dividend divided by (required return minus growth rate)

The Dividend Growth Rate

- PV0 = [CF0 * (1 + g)]

(r - g)

- How might we estimate the dividend growth rate?

○ Historical growth rates - what has this stock been growing at in past? Steady rate?

○ Accounting measure - e.g. sustainable growth rate

○ Analysts' Forecasts - forward-looking, maybe best choice, but not a perfect estimate

○ Take all 3 estimates into account

Market Multiples

- Pt = Benchmark PE Ratio * EPSt

Price / EPS * EPS / 1

Gives us Price / 1 > Price

Example: Suppose the median PE ratio in an industry is 20. What is your estimate of the

-

price/share of a company that has \$1.2 million in net income and 2 million shares outstanding?○ EPS = 1.2 M/2 M =

○ 20 * \$0.60 = \$12.00 (in millions)

Common Stock vs. Preferred Stock

- Common Stock

○ Voting Rights

 Majority Voting or Straight Voting

□ Majority wins every time

 Cumulative Voting

Allows minority shareholders to have a greater say in the process - encourages  participation

○ Dividends

 At the discretion of the firm - no legal obligation

○ Classes of Stock

Founder's shares - some classes have more votes/stock held - family wants to retain  voting majority

 Hershey Example - Hershey Trust owns 30% of stock, but 81.3% of all votes  Exam 2 Page 14

 Hershey Example - Hershey Trust owns 30% of stock, but 81.3% of all votes - Preferred Stock

○ Shareholders in line before common stockholders when it comes to dividends or liquidation○ Voting Rights - usually none

○ Dividends - fixed/don't change - zero-growth stock

Cumulative - if a year is missed, must double up/make up for missed dividends when  they are paid

 Non-cumulative - no need to make up for missed dividends

○ Stated/Liquidating Value

 Usually \$100

○ Preferred Stock and Debt

 Dividends are not tax-deductible

 Preferred stock is equity, not debt

Differences Between Debt and Equity

Debt

Equity

Not an ownership interest

Creditors do not have voting rights Interest is considered a cost of doing business and is tax deductibleCreditors have legal recourse if interest or principal payments are missedExcess debt can lead to financial distress and bankruptcy

Ownership interest….

Stock Markets

- Primary vs. Secondary Markets

○ Primary - firm is raising money

 IPO - Selling shares of stock to public for first time  SEO - seasoned equity - selling additional shares

 Private Placement - privately raising money

○ Secondary - buying and selling among investors

 Stock exchanges

- Dealers vs. Brokers

○ Dealers buy and sell from their own account/inventory  Bid price vs. asked price

○ Broker arranges a buyer and seller together

 Never takes posession of asset

- NYSE vs. NASDAQ

○ NYSE - physical location

○ NASDAQ - computer network, not a physical location

Looking up Stock Prices

- Issue (Stock and SYM)

- Volume

- Price (Close)

- Chg (Net Chg)

- % Chg

- Finance.yahoo.com

Chapter 8 Suggested Problems

- Concepts

○ 5, 7, 11

- Questions

Exam 2 Page 15

- Questions

Stock Valuation Examples

1. \$38.4615

2. 14.89%

3. \$4.9541

4. 8.64%

5. \$11.8400

6. \$15.3047

7. \$8.0748

Review for Exam Party 2

- Thursday at 6 pm in Lowder 113A

- Blue scantron!!!

○ Name (Last, First)

○ Calculator

○ Pencil

○ Photo ID

○ Cheat Sheet

 Same as first exam

 1 side of standard sheet of paper

- Things to Do

○ Study notes and book

○ Do (all) suggested problems

○ Be comfortable with calculator, but understand concepts (e.g. timeline) ○ Get help if having problems

○ Optional review - 2:30-3:30 in Lowder 005 on Wednesday - Don't Do

○ Study solutions and don't work problems

○ Memorize the formulas

○ Miss the exam

○ Cheat

- Content and Structure

○ 31 multiple choice questions

○ 15 problems, 16 concepts

○ 3 topics, discounted CF valuation, Bonds, Stocks

○ 3/16 Roman Numeral-type questions

○ 2 problems use same info and it's clear, other 29 are independent  Exam 2 Page 16

Wednesday, October 24, 2018 2:30 PM Finance - Bonus Session

Discounted Cash Flow Valuation

- Chap 6

- PV and FV of Single and Mult CFs

- Perpetuities and Growing

- Annuities and Due

- APR vs EAR

- Amort Schedule

Bonds

- Chapter 7

- What are they

- How do we price them

○ Zero coupon and coupon bonds

○ Find price, YTM, time-to-maturity, coupon rate, current yield - What are their characteristics

○ Callable

○ Seniority

○ Sinking fund provisions

○ Covenants

- Interest Rate Risk

- Price Reporting

Stocks

- Chapter 8

- What are they?

- How do we price them?

○ 3 types and multiples

○ Find price, dividends, discount rate, growth rate ○ Calculating dividends (just paid or will pay next year)

- What are their characteristics

○ Common vs preferred

○ Classes of stock

- Stock markets

○ Brokers vs. dealers

○ Primary vs. secondary markets

- Price Reporting

Practice Problems

1. T/F scenarios

a. F

b. F

2. C is correct

a. Less than, not greater (current yield vs coupon rate)

CY = PMT/Price <

b. Plus, not minus

c. True

d. Bonds are liability, stock is ownership

Exam 2 Page 17

d. Bonds are liability, stock is ownership

e. Lower expected YTM (lower risk)

3. C (III is not determinable at this time, market will determine in future) 4.

A (present increase, future increase) - same cash flows either way, but getting the money sooner  is more valuable

5. C (rates up means present value decreases, but future value increases) 6. \$49.7112

7. \$1.4190

8. \$29.39

9. \$1,056.5587

10. YTM = 9% - calculation gives you rate every 6 months

11. Amort table = \$214.1077 interest in the 6th month  Exam 2 Page 18

Thursday, October 25, 2018 9:30 AM Cheat Sheet Info

Future Value of Multiple Cash Flows

-

The future value of multiple cash flows is the sum of individual future values (move flows  individually to same period and then add)

FVt = CF0 x (1 + r)t + CF1 x (1 + r) ○t-1 …. CFt

Valuing Perpetuities

- Perpetuity: a level stream of cash flows which continue forever (sometimes called consols). - Present Value of a Perpetuity: PV0 = CF1

r

Growing Perpetuities

- Present Value of a Growing Perpetuity: PV0 = CF1 if (only if) r > g  r - g

Rephrased: Present Value (period 0=now) equals next period's cash flow divided by interest  rate (in decimal form) minus growth rate (also in decimal form)

Present Value of an Annuity

- Annuity: a level stream of cash flows for a fixed period of time - Present Value of an Annuity

PV0 = ஼ிభ

⎯⎯⎯⋅ ቂ1 −

(ଵା௥)௧ ⎯⎯⎯⎯⎯ቃ

������������ ���������� ���� ���� ��������������

- ������������ ���������� ���� ���� ��������������:

������ = ���� * [(1 + ��)�� − 1]

��

○ ������ ���� ��������������������: ������ = ���� * [(1 + ��)�� − 1]/��

Annuities Due

- So far, we've assumed cash flows occur at the end

- Annuity Due: an annuity for which the cash flows occur at the beginning of the period○ Plugging in will give us PV of period BEFORE cash flow, or PV-1 - PV Annuity Due

○ = (PV Ordinary Annuity) x (1 + r)

The Effect of Compounding

-

Effective Annual Rage (EAR): the effective annual interest rate, which takes into account the effect of compound interest

○ Do not divide EAR by anything

EAR = [1 + (APR/m)]m ○ - 1

- Calculator instructions!!!

○ HP instructions

 Just looking at month 4…

4 Input (below N 4 Shift AMORT (FV "=" key will scroll

Exam 2 Page 19

4 Input (below N

4 Shift

AMORT (FV

"=" key will scroll

through values□

button)

(orange)

key)

 Looking at months 1 - 4

1

Input 4 Shift (orange)

AMORT

□ = = = = ○

Scrolling takes you through PER (period), PRIN (principal portion of payment), INT (interest portion of payment), and BAL (ending balance) - or sum of what was paid toward principal and interest if  for more than one month

Bonds (Everything you Wanted to Know about Bonds & Their Value-

Example: Yost Rocks, Inc. issues bonds. 30 years at 12%. Pays each bondholder \$120/year and  returns principal of \$1,000 at end of 30 years

- Coupon - stated interest payment made on a bond ○ 12%

- Face value - aka par value - principal amount of bond to be repaid @ end of term

○ \$1,000

- Coupon rate - annual coupon divided by face value of bond (PMT)

○ \$120

- Maturity - specific date on which the principal amount of a bond (face/par value) is repaid○ 30 years

- Yield to maturity - rate required in market on the bond ○ Also: yield. This is "r" and is quoted as APR - often not the same as coupon rate

- Coupon rate is EQUAL TO THE Yield to Maturity

 Price of the bond is equal to the face/par value of the bond -

When coupon rate is LESS THAN Yield to Maturity, the price of the bond is LESS THAN the face  value

○ Bond is trading at a discount (from its face or par value)

Current Yield

- Current yield: Annual coupon divided by current price - What it is: percentage of price you receive as payment

- What it is not: a measure of total return

○ Same as dividend yield for stocks

- What are they?

a bond that you pay for today and it does not pay coupons over time, just face value at the  end

○ No cash flows/no coupon rate

○ AKA Pure Discount Bonds

- How do I calculate their price?

○ PV = value of future cash flows

-

Example - what is price of a zero-coupon bond that has a face value of \$1,000 and matures in 10  years if the YTM is 8%?

○ PV0 = 1,000 = \$463.19

(1.08)10

You only get the face at the end (no interest/coupon payments ever, even at end). Because  there is a YTM, it means you pay less up front for the bond.

Interest Rate Risk

- Interest Rate Risk: the risk of a change in the value of a bond because of a change in the interest   Exam 2 Page 20

-

Interest Rate Risk: the risk of a change in the value of a bond because of a change in the interest  rate

○ Bond prices and market interest rates move in opposite directions ○

All other things being equal, the longer the time to maturity, the greater the interest rate  risk

○ All other things being equal, the lower the coupon rate, the greater the interest rate risk Lower coupon, more we depend on final cash flow  Higher coupon, more dependent on earlier cash flows

Other Bond Pricing Truths

-

When a bond's coupon rate is greater than YTM, bond's price/market value will be greater than  par

- When bond's coupon is = to YTM, price=par

- When bond's coupon is less than YTM, bond's price/marker is less than par

The Term Structure of Interest Rates

- Term Structure: The relationship between interest rates and time-to-maturity of a debt security- Yield on Bonds - government and corporate (government doesn't deal with the last 3 so much)○ Real rate - flat line

○ Inflation premium - upward sloping with inflation, downward sloping with deflation

○ Interest rate risk premium - increases with time-to-maturity 

May be downward sloping overall depending on inflation/deflation, but the IR risk  premium is always increasing…it just may not increase as much as deflation decreases

Bond Features

-

Indenture: the written agreement between the corporation and the lender detailing the terms of  the debt issue - the contract

- Terms of a Bond - maturity, par value, coupon rate, and frequency - Security - collateral

- Seniority - position for pay back relative to other lenders

- Repayment

○ Sinking Fund - requires the firm to retire a certain portion of their bonds each year - Call Provision - gives firm right to buy bonds back early

○ Call Premium - usually equal to a year's worth of coupon payments ○ Yield-to-Call

- Protective Covenants - restrictions on the actions of managers ○ Limit amount of dividends to be paid

○ Firm may not be allowed to sell off large chunks of assets

○ Maybe current ratio stays above some certain level of liquidity ○ If firm breaks a covenant, they are in technical default and could be sued

Bond Ratings

- Above BBB/Baa is investment-grade bond

- Lower ratings are higher default risk/more speculative - "junk" bonds Differences between Debt and Equity

Debt

Not an ownership interest

Equity  Ownership interest

Exam 2 Page 21

Creditors do not have voting rights

Interest is considered a cost of doing business and is tax deductible

Creditors have legal recourse if interest of principal payments are missed

Common stockholders vote for the board of

directors and other issues

Dividends are not considered a cost of doing

business and are not tax deductible

Dividends are not liability of firm and stockholders

Stock Valuation

- Price is present value of future cash flows

- + ….

P0 = D1/(1 + r)1+ D2/(1 + r)2+ D3/(1 + r)3

- 3 Types of Dividends

○ No growth or zero growth - same value for every dividend - perpetuity  Dividends do not increase in dollar amount

 D1 = D2 = D3…

 Dividends are paid every period forever

 Price of a share of zero growth stock is: PV0 = CF1/r

○ Constant growth - grows at constant rate - growing perpetuity  Dividends increase at fixed rate every period

 D1 = D0 * (1 + g)

D2 = D1 * (1 + g) = D0 * (1 + g)2

D3 = D2 * (1 +g) = D0 * (1 + g)3

 Diidends are paid every period forever

 The price of a share of a constant growth stock is PV0 = CF1/(r - g) □ ONLY FOR r>g

 PVt = CFt+1/(r - g)

○ Non-constant growth - the everything else category

 Could be:

Dividends have supernormal growth for some period of time, then "slow down"  and grow steadily thereafter

□ Dividends grow erratically for a period of time then grow steadily thereafter

□ No dividends for a period of time, then…  Calculate by moving future cash flows to the present value  Steps to solving non-constant growth

□ Draw a timeline and lay out all cash flows (and growth rates)

□ Deal with the right-hand side

□ Bring it all back to zero

- The Required Rate of Return

○ Recall the dividend growth model

 Discounted Cash Flow (DCF) Model => Constant Growth  PV0 = CF1/(r - g)

 A little algebra…

□ (r - g) * [PV0] = [CF1/(r - g)] * (r - g)

□ Dividing by PV0 gives you r - g = CF1/PV0

□ r = (CF1/PV0) + g

□ Dividend Yield: The dividend income portion of a stock's return

□ Capital Gains Yield: the price change portion of a stock's return

The Dividend Growth Rate

- PV0 = [CF0 * (1 + g)]

(r - g)

- How might we estimate the dividend growth rate?

Exam 2 Page 22

- How might we estimate the dividend growth rate?

○ Historical growth rates - what has this stock been growing at in past? Steady rate?

○ Accounting measure - e.g. sustainable growth rate

○ Analysts' Forecasts - forward-looking, maybe best choice, but not a perfect estimate

○ Take all 3 estimates into account

Market Multiples

- Pt = Benchmark PE Ratio * EPSt

Price / EPS * EPS / 1

Gives us Price / 1 > Price

- Benchmark PE Ratio = Price/EPS

-

Example: Suppose the median PE ratio in an industry is 20. What is your estimate of the  price/share of a company that has \$1.2 million in net income and 2 million shares outstanding?○ EPS = 1.2 M/2 M = \$0.60

○ 20 * \$0.60 = \$12.00 (if trading at industry standard, price/share traded should equal this)

Common Stock vs. Preferred Stock

- Common Stock

○ Voting Rights

 Majority Voting or Straight Voting

□ Majority wins every time

 Cumulative Voting

Allows minority shareholders to have a greater say in the process - encourages  participation

○ Dividends

 At the discretion of the firm - no legal obligation

○ Classes of Stock

Founder's shares - some classes have more votes/stock held - family wants to retain voting  majority

 Hershey Example - Hershey Trust owns 30% of stock, but 81.3% of all votes - Preferred Stock

○ Shareholders in line before common stockholders when it comes to dividends or liquidation○ Voting Rights - usually none

○ Dividends - fixed/don't change - zero-growth stock

Cumulative - if a year is missed, must double up/make up for missed dividends when they  are paid

 Non-cumulative - no need to make up for missed dividends

○ Stated/Liquidating Value

 Usually \$100

○ Preferred Stock and Debt

 Dividends are not tax-deductible

 Preferred stock is equity, not debt

Stock Markets

- Primary vs. Secondary Markets

○ Primary - firm is raising money

 IPO - Selling shares of stock to public for first time

 SEO - seasoned equity - selling additional shares

 Private Placement - privately raising money

○ Secondary - buying and selling among investors

 Stock exchanges

- Dealers vs. Brokers

Dealers buy and sell from their own account/inventory

Exam 2 Page 23

○ Dealers buy and sell from their own account/inventory  Bid price vs. asked price

○ Broker arranges a buyer and seller together

 Never takes posession of asset

- NYSE vs. NASDAQ

○ NYSE - physical location

○ NASDAQ - computer network, not a physical location

Looking up Stock Prices

- Issue (Stock and SYM)

- Volume

- Price (Close)

- Chg (Net Chg)

- % Chg

Exam 2 Page 24

Wednesday, October 24, 2018 2:59 PM

TriCounty, Inc., just paid a \$2.50 dividend yesterday. Analysts anticipate dividends will grow at 16 percent for each of the next 3 years, followed by growth of 5 percent per year indefinitely. If analysts estimate the required rate of return on stocks of this risk is 12 percent, how much would you expect to pay today for a share of TriCounty, Inc.?

Granny Mae has been helping her favorite grandchild save. She has given you \$1 each year on your birthday, starting when you turned one, and taken you to deposit it in your bank account, which earns 4 percent each year. You have not deposited or withdrawn any other money. You just turned 21. However, Granny Mae is forgetful, and she forgot to give you money on your 10th and 20th birthdays. How much is in your account today?

Exam 2 Page 25

Exam 2 Page 26

Discounted Cash Flow Valuation Future Value of Multiple Cash Flows

The future value of multiple cash flows is the sum of individual  future values (move flows individually to same period and then  add)

FVt = CF0 x (1 + r)t + CF1 x (1 + r)t-1 …. CFt

Valuing Perpetuities

Perpetuity: a level stream of cash flows which continue forever  (sometimes called consols).

Present Value of a Perpetuity: PV0 = CF1

r

Growing Perpetuities

Present Value of a Growing Perpetuity:

PV0 = CF1 if (only if) r > g

r - g

Rephrased: Present Value (period 0=now) equals next  period's cash flow divided by interest rate (in decimal form)  minus growth rate (also in decimal form)

Present Value of an Annuity

Annuity: a level stream of cash flows for a fixed period of time Present Value of an Annuity

PV0 = ����1

��⋅ [1 −1

(1+��)��]

Future Value of an Annuity

Future Value of an annuity:

FVt = CF * [(1 + r)t- 1]

r

Can be rearranged: FVt = CF * [(1+r)t-1]/r

Annuities Due

So far, we've assumed cash flows occur at the end

Annuity Due: an annuity for which the cash flows occur at the  beginning of the period

Plugging in will give us PV of period BEFORE cash flow, or PV-1 PV Annuity Due

= (PV Ordinary Annuity) x (1 + r)

The Effect of Compounding

Effective Annual Rage (EAR): the effective annual interest rate,  which takes into account the effect of compound interest Do not divide EAR by anything

EAR = [1 + (APR/m)]m - 1

Calculator instructions!!!

HP instructions

Just looking at month 4…

4 Input

4 Shift

AMORT

"=" key will

(below N

(orange)

(FV key)

scroll

button)

Looking at months 1 - 4

1 Input 4 Shift (orange) AMORT = =  = =

Scrolling takes you through PER (period), PRIN (principal portion of  payment), INT (interest portion of payment), and BAL (ending balance) - or sum of what was paid toward principal and interest if for more than  one month

Differences between Debt and Equity

Debt Equity

Not an ownership interest Ownership interest

Creditors do not have voting

Common stockholders vote for

rights

the board of directors and other

issues

Interest is considered a cost

Dividends are not considered a

of doing business and is tax

cost of doing business and are

deductible

not tax deductible

Creditors have legal recourse

Dividends are not liability of firm

if interest of principal

and stockholders

payments are missed

***IF changing interest rate for shorter period (semi annual/monthly), MAKE SURE TO CHANGE BACK TO APR  IF NECESSARY!!!

Bond Valuation

Example: Yost Rocks, Inc. issues bonds. 30 years at 12%. Pays each  bondholder \$120/year and returns principal of \$1,000 at end of 30 years Coupon - stated interest payment made on a bond

12%

Face value - aka par value - principal amount of bond to be repaid @  end of term

\$1,000

Coupon rate - annual coupon divided by face value of bond (PMT) \$120

Maturity - specific date on which the principal amount of a bond  (face/par value) is repaid

30 years

Yield to maturity - rate required in market on the bond

Also: yield. This is "r" and is quoted as APR - often not the same as  coupon rate

Coupon rate is EQUAL TO THE Yield to Maturity

Price of the bond is equal to the face/par value of the bond When coupon rate is LESS THAN Yield to Maturity, the price of the  bond is LESS THAN the face value

Bond is trading at a discount (from its face or par value)

Current Yield

Current yield: Annual coupon divided by current price

What it is: percentage of price you receive as payment

What it is not: a measure of total return

Same as dividend yield for stocks

Zero-coupon bonds?

What are they?

a bond that you pay for today and it does not pay coupons over time,  just face value at the end

No cash flows/no coupon rate

AKA Pure Discount Bonds

How do I calculate their price?

PV = value of future cash flows

Example - what is price of a zero-coupon bond that has a face value of  \$1,000 and matures in 10 years if the YTM is 8%?

PV0 = 1,000 = \$463.19

(1.08)10

You only get the face at the end (no interest/coupon payments ever,  even at end). Because there is a YTM, it means you pay less up front  for the bond.

Interest Rate Risk

Interest Rate Risk: the risk of a change in the value of a bond because  of a change in the interest rate

Bond prices and market interest rates move in opposite directions All other things being equal, the longer the time to maturity, the greater  the interest rate risk

All other things being equal, the lower the coupon rate, the greater the interest rate risk

Lower coupon, more we depend on final cash flow

Higher coupon, more dependent on earlier cash flows

Other Bond Pricing Truths

When a bond's coupon rate is greater than YTM, bond's price/market  value will be greater than par

When bond's coupon is = to YTM, price=par

When bond's coupon is less than YTM, bond's price/marker is less than  par

The Term Structure of Interest Rates

Term Structure: The relationship between interest rates and time-to maturity of a debt security

Yield on Bonds - government and corporate (government doesn't deal  with the last 3 so much)

Real rate - flat line

Inflation premium - upward sloping with inflation, downward sloping with  deflation

Interest rate risk premium - increases with time-to-maturity May be downward sloping overall depending on inflation/deflation, but the IR risk premium is always increasing…it just may not increase as  much as deflation decreases

Bond Features

Indenture: the written agreement between the corporation and the  lender detailing the terms of the debt issue - the contract

Terms of a Bond - maturity, par value, coupon rate, and frequency Security – collateral; Seniority - position for pay back relative to other  lenders;

Repayment - Sinking Fund - requires the firm to retire a certain portion  of their bonds each year

Call Provision - gives firm right to buy bonds back early

Call Premium - usually equal to a year's worth of coupon payments Yield-to-Call

Protective Covenants - restrictions on the actions of managers Limit amount of dividends to be paid

Firm may not be allowed to sell off large chunks of assets

Maybe current ratio stays above some certain level of liquidity If firm breaks a covenant, they are in technical default and could be  sued

Bond Ratings

Lower ratings are higher default risk/more speculative - "junk" bonds

Stock Valuation

Stock Valuation

Price is present value of future cash flows

P0 = D1/(1 + r)1 + D2/(1 + r)2 + D3/(1 + r)3 + ….

No growth or zero growth - same value for every dividend - perpetuity  Price of a share of zero growth stock is: PV0 = CF1/r

Constant growth - grows at constant rate - growing perpetuity  Dividends increase at fixed rate every period

D1 = D0 * (1 + g)

The price of a share of a constant growth stock is PV0 = CF1/(r - g) ONLY FOR r>g

PVt = CFt+1/(r - g)

Non-constant growth - the everything else category

Draw a timeline and lay out all cash flows (and growth rates) Deal with the right-hand side

Bring it all back to zero

The Required Rate of Return

Recall the dividend growth model

Discounted Cash Flow (DCF) Model => Constant Growth

PV0 = CF1/(r - g)

A little algebra…

(r - g) * [PV0] = [CF1/(r - g)] * (r - g)

Dividing by PV0 gives you r - g = CF1/PV0

r = (CF1/PV0) + g

Dividend Yield: The dividend income portion of a stock's return Capital Gains Yield: the price change portion of a stock's return The Dividend Growth Rate

PV0 = [CF0 * (1 + g)]

(r - g)

How might we estimate the dividend growth rate?

Historical growth rates - what has this stock been growing at in past?  Steady rate?

Accounting measure - e.g. sustainable growth rate

Analysts' Forecasts - forward-looking, maybe best choice, but not a  perfect estimate

Take all 3 estimates into account

Market Multiples

Pt = Benchmark PE Ratio * EPSt

Price / EPS * EPS / 1 Gives us Price / 1 > Price

Benchmark PE Ratio = Price/EPS

Example: Suppose the median PE ratio in an industry is 20. What is  your estimate of the price/share of a company that has \$1.2 million in  net income and 2 million shares outstanding?

EPS = 1.2 M/2 M = \$0.60

20 * \$0.60 = \$12.00 (if trading at industry standard, price/share traded  should equal this)

Common Stock vs. Preferred Stock

Common Stock

Voting Rights - Majority Voting or Straight Voting

Majority wins every time

Cumulative Voting

Allows minority shareholders to have > say   encourages participation

Dividends - At the discretion of the firm - no legal obligation Classes of Stock - Founder's shares - some classes have more  votes/stock held - family wants to retain voting majority

Hershey Example - Hershey Trust owns 30% of stock, but 81.3% of all  votes

Preferred Stock - Shareholders in line before common stockholders  when it comes to dividends or liquidation

Voting Rights - usually none

Dividends - fixed/don't change - zero-growth stock

Cumulative - if a year is missed, must double up/make up for  missed dividends when they are paid

Non-cumulative - no need to make up for missed dividends  Stated/Liquidating Value - Usually \$100

Preferred Stock and Debt - Dividends are not tax-deductible - Preferred  stock is equity, not debt

Stock Markets

Primary vs. Secondary Markets

Primary - firm is raising money

IPO - Selling shares of stock to public for first time

SEO - seasoned equity - selling additional shares

Private Placement - privately raising money

Secondary - buying and selling among investors

Stock exchanges

Dealers vs. Brokers

Dealers buy and sell from their own account/inventory  Bid price vs. asked price

Broker arranges a buyer and seller together

Never takes posession of asset

NYSE vs. NASDAQ

NYSE - physical location

NASDAQ - computer network, not a physical location Looking up Stock Prices

Issue (Stock and SYM); Volume; Price (Close); Chg (Net Chg); % Chg

o

o

o

∙ o

o o

∙ o

o

Future Value of Multiple Cash Flows

∙ The future value of multiple cash flows is the sum of individual future values (move flows individually to same period and then add) o FVt = CF0 x (1 + r)t + CF1 x (1 + r)t-1 …. CFt

Valuing Perpetuities

∙ Perpetuity: a level stream of cash flows which continue forever (sometimes called consols).

∙ Present Value of a Perpetuity: PV0 = CF1

r

Growing Perpetuities

∙ Present Value of a Growing Perpetuity:

PV0 = CF1 if (only if) r > g

r - g

o Rephrased: Present Value (period 0=now) equals next period's cash flow divided by interest rate (in decimal form) minus growth rate (also in decimal form) Present Value of an Annuity

∙ Annuity: a level stream of cash flows for a fixed period of time

∙ Present Value of an Annuity

PV0 = ����1

��⋅ [1 −1

(1+��)��]

Future Value of an Annuity

∙ Future Value of an annuity:

FVt = CF * [(1 + r)t- 1]

r

o Can be rearranged: FVt = CF * [(1+r)t-1]/r

Annuities Due

So far, we've assumed cash flows occur at the end

Annuity Due: an annuity for which the cash flows occur at the beginning of the period

Plugging in will give us PV of period BEFORE cash flow, or PV-1

PV Annuity Due

= (PV Ordinary Annuity) x (1 + r)

The Effect of Compounding

Effective Annual Rage (EAR): the effective annual interest rate, which takes into account the effect of compound interest

Do not divide EAR by anything

EAR = [1 + (APR/m)]m - 1

Calculator instructions!!!

HP instructions

Just looking at month 4…

4

Input (below N button)

4

Shift (orange)

AMORT (FV key)

"=" key will scroll through values

Looking at months 1 - 4

1

Input

4

Shift (orange)

AMORT

= = = =

Scrolling takes you through PER (period), PRIN (principal portion of payment), INT (interest portion of payment), and BAL (ending balance) - or sum of what was paid toward principal and interest if for  more than one month

Bonds (Everything you Wanted to Know about Bonds & Their Value

Example: Yost Rocks, Inc. issues bonds. 30 years at 12%. Pays each bondholder \$120/year and returns principal of \$1,000 at end of 30 years

Coupon - stated interest payment made on a bond

12%

Face value - aka par value - principal amount of bond to be repaid @ end of term

\$1,000

Coupon rate - annual coupon divided by face value of bond (PMT)

\$120

Maturity - specific date on which the principal amount of a bond (face/par value) is repaid

30 years

Yield to maturity - rate required in market on the bond

Also: yield. This is "r" and is quoted as APR - often not the same as coupon rate

Coupon rate is EQUAL TO THE Yield to Maturity

Price of the bond is equal to the face/par value of the bond

When coupon rate is LESS THAN Yield to Maturity, the price of the bond is LESS THAN the face value

Bond is trading at a discount (from its face or par value)

Current Yield

Current yield: Annual coupon divided by current price

What it is: percentage of price you receive as payment

What it is not: a measure of total return

Same as dividend yield for stocks

What are they?

a bond that you pay for today and it does not pay coupons over time, just face value at the end

No cash flows/no coupon rate

AKA Pure Discount Bonds

How do I calculate their price?

PV = value of future cash flows

Example - what is price of a zero-coupon bond that has a face value of \$1,000 and matures in 10 years if the YTM is 8%?

PV0 = 1,000 = \$463.19

(1.08)10

You only get the face at the end (no interest/coupon payments ever, even at end). Because there is a YTM, it means you pay less up front for the bond.

Interest Rate Risk

Interest Rate Risk: the risk of a change in the value of a bond because of a change in the interest rate

Bond prices and market interest rates move in opposite directions

All other things being equal, the longer the time to maturity, the greater the interest rate risk

All other things being equal, the lower the coupon rate, the greater the interest rate risk

Lower coupon, more we depend on final cash flow

Higher coupon, more dependent on earlier cash flows

Other Bond Pricing Truths

When a bond's coupon rate is greater than YTM, bond's price/market value will be greater than par

When bond's coupon is = to YTM, price=par

When bond's coupon is less than YTM, bond's price/marker is less than par

The Term Structure of Interest Rates

Term Structure: The relationship between interest rates and time-to-maturity of a debt security

Yield on Bonds - government and corporate (government doesn't deal with the last 3 so much)

Real rate - flat line

Inflation premium - upward sloping with inflation, downward sloping with deflation

Interest rate risk premium - increases with time-to-maturity

May be downward sloping overall depending on inflation/deflation, but the IR risk premium is always increasing…it just may not increase as much as deflation decreases Default Risk Premium

Bond Features

Indenture: the written agreement between the corporation and the lender detailing the terms of the debt issue - the contract

Terms of a Bond - maturity, par value, coupon rate, and frequency

Security - collateral

Seniority - position for pay back relative to other lenders

Repayment

Sinking Fund - requires the firm to retire a certain portion of their bonds each year

Call Provision - gives firm right to buy bonds back early

Call Premium - usually equal to a year's worth of coupon payments

Yield-to-Call

Protective Covenants - restrictions on the actions of managers

Limit amount of dividends to be paid

Firm may not be allowed to sell off large chunks of assets

Maybe current ratio stays above some certain level of liquidity

If firm breaks a covenant, they are in technical default and could be sued

Bond Ratings

Lower ratings are higher default risk/more speculative - "junk" bonds

Differences between Debt and Equity

Debt

Equity

Not an ownership interest

Ownership interest

Creditors do not have voting rights

Common stockholders vote for the board of directors and  other issues

Interest is considered a cost of doing business and is  tax deductible

Dividends are not considered a cost of doing business and  are not tax deductible

Creditors have legal recourse if interest of principal  payments are missed

Dividends are not liability of firm and stockholders

Stock Valuation

Price is present value of future cash flows

P0 = D1/(1 + r)1 + D2/(1 + r)2 + D3/(1 + r)3 + ….

3 Types of Dividends

No growth or zero growth - same value for every dividend - perpetuity

Dividends do not increase in dollar amount

D1 = D2 = D3…

Dividends are paid every period forever

Price of a share of zero growth stock is: PV0 = CF1/r

Constant growth - grows at constant rate - growing perpetuity

Dividends increase at fixed rate every period

D1 = D0 * (1 + g)

D2 = D1 * (1 + g) = D0 * (1 + g)2

D3 = D2 * (1 +g) = D0 * (1 + g)3

Diidends are paid every period forever

The price of a share of a constant growth stock is PV0 = CF1/(r - g)

ONLY FOR r>g

PVt = CFt+1/(r - g)

Non-constant growth - the everything else category

Could be:

Dividends have supernormal growth for some period of time, then "slow down" and grow steadily thereafter

Dividends grow erratically for a period of time then grow steadily thereafter

No dividends for a period of time, then…

Calculate by moving future cash flows to the present value

Steps to solving non-constant growth

Draw a timeline and lay out all cash flows (and growth rates)

Deal with the right-hand side

Bring it all back to zero

The Required Rate of Return

Recall the dividend growth model

Discounted Cash Flow (DCF) Model => Constant Growth

PV0 = CF1/(r - g)

A little algebra…

(r - g) * [PV0] = [CF1/(r - g)] * (r - g)

Dividing by PV0 gives you r - g = CF1/PV0

r = (CF1/PV0) + g

Dividend Yield: The dividend income portion of a stock's return

Capital Gains Yield: the price change portion of a stock's return

The Dividend Growth Rate

PV0 = [CF0 * (1 + g)]

(r - g)

How might we estimate the dividend growth rate?

Historical growth rates - what has this stock been growing at in past? Steady rate?

Accounting measure - e.g. sustainable growth rate

Analysts' Forecasts - forward-looking, maybe best choice, but not a perfect estimate

Take all 3 estimates into account

Market Multiples

Pt = Benchmark PE Ratio * EPSt

Price / EPS * EPS / 1

Gives us Price / 1 > Price

Benchmark PE Ratio = Price/EPS

Example: Suppose the median PE ratio in an industry is 20. What is your estimate of the price/share of a company that has \$1.2 million in net income and 2 million shares outstanding? EPS = 1.2 M/2 M = \$0.60

20 * \$0.60 = \$12.00 (if trading at industry standard, price/share traded should equal this)

Common Stock vs. Preferred Stock

Common Stock

Voting Rights

Majority Voting or Straight Voting

Majority wins every time

Cumulative Voting

Allows minority shareholders to have a greater say in the process - encourages participation

Dividends

At the discretion of the firm - no legal obligation

Classes of Stock

Founder's shares - some classes have more votes/stock held - family wants to retain voting majority

Hershey Example - Hershey Trust owns 30% of stock, but 81.3% of all votes

Preferred Stock

Shareholders in line before common stockholders when it comes to dividends or liquidation

Voting Rights - usually none

Dividends - fixed/don't change - zero-growth stock

Cumulative - if a year is missed, must double up/make up for missed dividends when they are paid

Non-cumulative - no need to make up for missed dividends

Stated/Liquidating Value

Usually \$100

Preferred Stock and Debt

Dividends are not tax-deductible

Preferred stock is equity, not debt

Stock Markets

Primary vs. Secondary Markets

Primary - firm is raising money

IPO - Selling shares of stock to public for first time

SEO - seasoned equity - selling additional shares

Private Placement - privately raising money

Secondary - buying and selling among investors

Stock exchanges

Dealers vs. Brokers

Dealers buy and sell from their own account/inventory

Broker arranges a buyer and seller together

Never takes posession of asset

NYSE vs. NASDAQ

NYSE - physical location

NASDAQ - computer network, not a physical location

Looking up Stock Prices Issue (Stock and SYM) Volume

Price (Close)

Chg (Net Chg)

% Chg

Will need to know how to calculate 7 different criteria and how to use them

Net Present Value - measure of how much value is created by undertaking an investment (the difference between an investment's market value  and its cost)

How: Estimate future cash flows. Calculate the present value of those cash flows minus the initial cost

The Rule: an investment should be accepted if net present value is positive and rejected if it is negative Assumes cash flows are reinvested at the  cost of capital

Pros - Uses all cash flows, and adjusts for Time Value of Money - timing and risk

Cons - Need appropriate discount rate, and relatively more difficult to communicate

Internal Rate of Return - the discount rate that makes the NPV = 0

How: Set NPV = 0 & solve for "r." Calculating IRR is identical to calculating the YTM

Example: You plan to buy machine for \$2,000 today and produce cash flows of \$1,500 in each of next two years. Salvage value = 0. Cost of capital  is 15%.

NPV(0) = -2,000 + (1,500 / (1 + r)1) + (1,500 / (1 + r)2)

Because this is annuity, can plug into calculator

With CF calculator functions (HP)

Enter cash flows (-2,000, 1,500, 1,500)

Orange shift, then IRR/YR (CST button)

The Rule: is acceptable if IRR > required rate of return. It should be rejected otherwise *Assumes cash flows are reinvested at the IRR Pros: Closely related to the NPV rule & Relatively easier to communicate

Cons: May result in multiple answers (nonconventional cash flows) & May result in incorrect decisions (mutually exclusive investments) NPV Profile - A graph showing relation between NPV of a project and various discount rates.

What information does it provide?

Range where NPV is + (accept), Range where NPV is - (reject), Rate where NPV equals 0 - Also called the IRR

Slope of line - sensitivity of NPV to the rate

Beware: Non-conventional cash flows. (Conventional is negative first, then all positive)

The maximum # of IRR's you can have is = # times signs change on cash flows

Mutually exclusive projects

Might choose one project overall, but there may be crossover rate below which other project is preferable

Can happen when: Scale of project is different & When differences in timing of cash flows

Modified Internal Rate of Return (MIRR) - (combo approach): calculation of IRR on modified cash flows. For combo approach, is discount rate that  equates the present value of all cash outflows to the future value of all cash inflows.

How: For the combo, discount all cash outflows to time period 0 and compound all cash inflows to the end of the project. Then, calculate the  discount rate that makes them equal.

Example: You plan to buy a machine that will cost \$2,000 today and produce cash flows of \$1,500, -\$500, and \$1,200 in each of the next three  years. The salvage value will be zero. The cost of capital is 15%. Should you buy the machine?

Move -\$500 back to Year 0, & Move 1,500 to Year 3

N=time, I/Y=?, PV=-CFs, PMT=0, FV=+CFs

The Rule: acceptable if the MIRR > required rate of return. It should be rejected otherwise. *Assumes cash flows are reinvested at the cost of  capital

Pros: Closely related to NPV rule & No longer possible to get multiple answers

Cons: May result in incorrect decisions (mutually exclusive investments)

The Profitability Index - the present value of an investment's future cash flows divided by its initial cost (absolute value). Also called a benefit-cost  ratio.

How: Calculate the present value of the future cash flows (the PV, not the NPV) and divide by the initial cost. If a project has a positive (negative)  NPV, the PI will be greater (less) than 1.

PI = PV of future cash flows divided by Initial Cost

PI = (Initial Cost + PV of future cash flows - Initial Cost) divided by Initial Cost

PV of future cash flows - Initial Cost = NPV

Example: You plan to buy a machine that will cost \$2,000 today and produce cash flows of \$1,500 in each of the next two years. Salvage value = 0.  Cost of capital is 15%. What is its profitability index? Should you buy the machine? PI > 1, so accept

Example: Must choose between 2 following mutually exclusive projects:

A - cost is \$25 and PV is \$50, B - cost is \$100 and PV is \$150

Which should you choose? PI says A, NPV says B

ALWAYS CHOOSE NPV!!!!

The Rule: Only accept projects with a PI > 1, and invest in projects with the largest PI's first.

Pros: Closely related to NPV rule - frequently leads to same decision & May be useful when investment funds are limited Cons: May result in incorrect decisions (mutually exclusive investments)

The Payback Rule - the length of time it takes to recover our initial investment.

How: Assume cash flows are received uniformly throughout the year. Calculate the number of years it will take for the future cash flows to match  the initial cash outflow

Example: Cost = \$2,000, CFs of \$500, \$750, \$300, \$1,000, and \$5,000. Only accepts projects with payback of 4 years or less. Should you purchase? Pays off between 3 and 4

The Rule: investment is acceptable if its calculated payback period is less than some pre-specified number of years Pros: Simple/Easy to do & Biased toward liquidity

Cons: Ignores TVM, Ignores cash flows beyond the cutoff, Requires an arbitrary cutoff, Biased against long-term projects

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