Description
Tuesday, October 30, 2018 9:30 AM Investment Criteria  Chapter 9
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?
($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)
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
 Financial Leadership
 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
Nonconventional 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 benefitcost 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 prespecified 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 longterm 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
Adjusts for TVM
○
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
Adjusts for TVM
○
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 longterm 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 5year 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 prespecified 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
 Additional Practice
○ 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 longterm 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
○ Start with Income Statement
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
Add depreciation back in
○ This gives Operating Cash Flows = OCFs
Subtract capital expenditures (cost of buying longterm assets) Add aftertax 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 1213
Project Cash Flows
Formula
Sales
 Costs
 Depreciation
= EBIT
 Taxes
= NOPAT
+ Depreciation
= OCFs Operating cash flows
 Capital Expenditures
+ Aftertax 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 aftertax 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)
Aftertax salvage value is $940 (soldfor 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?
○ Aftertax salvage value is equal to sales price
Depreciation
 (more than) Two different ways to calculate
Straightline depreciation  same amount each year
Final Exam Page 11
○ Straightline 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 straightline depreciation. □ Straightline 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 IRSset 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 5year 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 3year). 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)
Aftertax 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 forklift truck costing $60,000. If purchased, the truck will replace 4 workers, each with an average annual salary of $15,000. However, an experienced forklift 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 5year 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 forklift 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)
Aftertax
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  Aftertax 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 breakeven 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) ○ Straitline 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)+((6560)/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 = (1001000)/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 19262013
○
Risk Premium  excess return required from an investment in a risky asset over that required from a riskfree 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%
LongTerm Corporate Bonds
6.3%
LongTerm Government Bonds
5.9%
U.S. Treasury Bills = Rf
3.5%
○
Risk Premium
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)
○ Riskfree 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 riskfree 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 setup
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
Semistrong 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
○ Semistrong 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 Semistrong and Strong  What do we know?
○ Market Reaction
○ Reporting  we hear about success, failure is hidden Index Fund  risk over longterm 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 forwardlooking rather than backwardlooking
 CAPM
○ Recall: RE = Rf + βE [RM  Rf]
○
We know what average historical risk premium and can look up the riskfree rate (e.g. US Treasury bills). We also can calculate or look up betas.
○ Problem
This is just a model/theory
Historic measure  backwardlooking
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
 Zerogrowth 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 aftertax cash flows
 One benefit of debt (not available to equity) is the fact that interest payments are tax deductible Aftertax 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%. Riskfree 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) ○ Riskadjusted 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
20year, 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 shortterm 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
 7.7901% (watch video for more info or see previous page of notes for more info)
Final Exam
 Bring scantron
 Bring financial calculator
 Bring pencil and photo ID
 Bring cheat sheet  2 sided
2 1sided 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 3year 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
 Read questions carefully
○ What info is given
○ What is being asked
 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 3year 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 daytoday operations of the firm? Shortterm 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 longterm investments ○ How do we do it?
Estimate cash flows (timing)
Estimate cost of those cash flows (risk)
Discount the cash flows (timevalue 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?  ShortTerm Cash Flow Management
○ What does shortterm 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)>
Shortterm debtLongterm 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
□ Easy startup  business license and partnership agreement
□ 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 daytoday 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 corporationfriendly)
○ 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
○ SCorporation (as opposed to CCorp 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 principalagent 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 underperforming 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 10K
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 backwardlooking (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 longterm 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 longterm 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 noncash 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 taxdeductible
○ 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 Noncash 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
Longterm 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)
 CommonSize 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. ○ Shortterm Solvency or Liquidity Ratios  measure ability to pay shortterm 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 (AcidTest) 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 ○ Longterm Solvency or Financial Leverage Ratios  measure ability to pay longer term obligations Total Debt Ratio = Total Liabilities/Total Assets = (TAEquity)/TA
Debtequity 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 (10060=40)
Debtequity ratio = 6/4=1.5
Equity Multiplier = 10/4=2.5
□ Given: Debtequity 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
Debtequity Ratio = .25/1=0.25
Total Debt Ratio = .25/1.25=0.2
Equity Multiplier = Assets/Equity OR (Equity + Liabilities)/Equity OR 1+(Debtequity ratio) Longterm Debt Ratio = Longterm Debt/(Longterm 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 Priceearnings (PE) Ratio = price per share/EPS
Pricesales Ratio = Price per share/sales per share *If company has negative Net Income
Markettobook Ratio = market value (price) per share/Book value of equity per share Tobin's Q = market value of assets/replacement cost of assets Enterprise ValueEBITDA 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
○ Shortterm solvency
○ Longterm solvency
○ Asset management/turnover
○ Profitability
○ Market value
EPS
PE
PriceSales
Markettobook
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
Crosssectional Analysis
The DuPont Identity
○ Limitations
Backwardlooking, not forwardlooking
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)
Additional Practice
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
 Additional Practice
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
Forget your calculator
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/numbercrunching problems and 23 conceptual
9 Romannumeraltype multipart 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
○ Shortterm Solvency or Liquidity Ratios  measure ability to pay shortterm obligations
Enterprise ValueEBITDA 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 (AcidTest) Ratio = (Current Assets  Inventories)/Current Liabilities
Cash Ratio = Cash/Current Liabilities
Interval Measure = Current Assets/Average Daily Operating Costs
○ Longterm Solvency or Financial Leverage Ratios  measure ability to pay longer term obligations Total Debt Ratio = Total Liabilities/Total Assets = (TAEquity)/TA Debtequity 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 (10060=40)
Debtequity ratio = 6/4=1.5
Equity Multiplier = 10/4=2.5
□ Given: Debtequity 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 Debtequity Ratio = .25/1=0.25 Total Debt Ratio = .25/1.25=0.2 Equity Multiplier = Assets/Equity OR (Equity + Liabilities)/Equity OR 1+(Debtequity ratio) Longterm Debt Ratio = Longterm Debt/(Longterm 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
Priceearnings (PE) Ratio = price per share/EPS
Pricesales 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
Markettobook 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 ValueEBITDA 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, Crosssectional 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 Priceearnings (PE) Ratio = price per share/EPS Pricesales Ratio = Price per share/sales per share *If company has negative Net Income
Limitations of Financial Statements  Backwardlooking, not forwardlooking, 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
Markettobook 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 daytoday operations of the firm?  Shortterm cash flow management
Capital budgeting  The process of planning and managing the firm's longterm investments by Estimate cash flows (timing), Estimate cost of those cash flows (risk), Discount the cash flows (timevalue of money)
Capital Structure  The mix of debt and equity describing how the firm is financed ShortTerm 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 underperforming 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 – RevExp=Income
The Bottom Line: Net Income or EPS (earnings per share)  Distribute it to owners or Reinvest in firm
Depreciation is a noncash expense
the Statement of Cash Flows  Cash Flow from Operating Activities (Buying of supplies and selling of products), Cash Flow from Investing Activities (Longterm 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
Priceearnings (PE) Ratio = price per share/EPS
Pricesales Ratio = Price per share/sales per share *If company has negative Net
Shortterm Solvency or Liquidity Ratios  measure ability to pay shortterm
Income
obligations
Markettobook 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 (AcidTest) 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, Crosssectional Analysis, The DuPont Identity
Limitations of Financial Statements  Backwardlooking, not forwardlooking, Financial
statements have book values, not market values, Income Statement has accounting
Longterm 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 = (TAEquity)/TA
 may even out over a year, but looking at quarterly could give skewed results, "Window
Debtequity 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+(Debtequity ratio)
Longterm Debt Ratio = Longterm Debt/(Longterm 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) ○t1 …. 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
ଵ
⎯⎯⎯⋅ 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 PV1
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, semiannually 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)]11
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
180000179.19=179820.81
2
179,820.81
1,079.19
899.10 180.09
179820.81180.09=
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
○ 28
 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
28
○ Questions and Problems
1,3,4,5,7,10,12,20,21,24,26,28,36,41,43,45,54
Additional Practice
Buying new truck @ $40,000. Putting down 10% and have 60month 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 9:3012:15
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 semiannually, what is price of the bond ○ Work in 6month 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 6month periods
○
N=21
PMT=$40
FV=$1,000 I/Y=???
3.6548 in 6month 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 about zerocoupon 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 zerocoupon 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 timetomaturity 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 timetomaturity 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
○ Liquidity/Marketability Premium ○ Taxability 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 ○ YieldtoCall
 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 investmentgrade 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
 Examples  Answers
○ $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
Beforeclass 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 zerogrowth 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
○ Nonconstant 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 nonconstant growth
□ Draw a timeline and lay out all cash flows (and growth rates)
□ Deal with the righthand 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
○ (rg) * PV0 = CF1
○ rg = 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  forwardlooking, 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  zerogrowth stock
Cumulative  if a year is missed, must double up/make up for missed dividends when they are paid
Noncumulative  no need to make up for missed dividends
○ Stated/Liquidating Value
Usually $100
○ Preferred Stock and Debt
Dividends are not taxdeductible
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  2:303:30 in Lowder 005 on Wednesday  Don't Do
○ Study solutions and don't work problems
○ Memorize the formulas
○ Miss the exam
○ Forget your calculator
○ Cheat
 Content and Structure
○ 31 multiple choice questions
○ Graded out of 30
○ 15 problems, 16 concepts
○ 3 topics, discounted CF valuation, Bonds, Stocks
○ 3/16 Roman Numeraltype 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, timetomaturity, 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) ○t1 …. 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
ଵ
⎯⎯⎯⋅ 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 PV1  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 about zerocoupon 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 zerocoupon 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 timetomaturity 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 timetomaturity
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
○ Liquidity/Marketability Premium ○ Taxability 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 ○ YieldtoCall
 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 investmentgrade 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)
○ Nonconstant 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 nonconstant growth
□ Draw a timeline and lay out all cash flows (and growth rates)
□ Deal with the righthand 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  forwardlooking, 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  zerogrowth stock
Cumulative  if a year is missed, must double up/make up for missed dividends when they are paid
Noncumulative  no need to make up for missed dividends
○ Stated/Liquidating Value
Usually $100
○ Preferred Stock and Debt
Dividends are not taxdeductible
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)t1 …. 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)t1]/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 PV1 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
Zerocoupon 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 zerocoupon 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 timeto 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 timetomaturity 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
Liquidity/Marketability Premium
Taxability 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 YieldtoCall
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 investmentgrade bond
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)
Nonconstant growth  the everything else category
Draw a timeline and lay out all cash flows (and growth rates) Deal with the righthand 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  forwardlooking, 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  zerogrowth stock
Cumulative  if a year is missed, must double up/make up for missed dividends when they are paid
Noncumulative  no need to make up for missed dividends Stated/Liquidating Value  Usually $100
Preferred Stock and Debt  Dividends are not taxdeductible  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)t1 …. 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)t1]/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 PV1
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 about zerocoupon 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 zerocoupon 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 timetomaturity 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 timetomaturity
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
Liquidity/Marketability Premium
Taxability 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
YieldtoCall
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 investmentgrade bond
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)
Nonconstant 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 nonconstant growth
Draw a timeline and lay out all cash flows (and growth rates)
Deal with the righthand 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  forwardlooking, 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  zerogrowth stock
Cumulative  if a year is missed, must double up/make up for missed dividends when they are paid
Noncumulative  no need to make up for missed dividends
Stated/Liquidating Value
Usually $100
Preferred Stock and Debt
Dividends are not taxdeductible
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
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: Nonconventional 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 benefitcost 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 prespecified 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 longterm projects