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FSU / Finance / FIN 4424 / How do you calculate retained earnings?

How do you calculate retained earnings?

How do you calculate retained earnings?


Exam 2 Study Guide

How do you calculate retained earnings?

Chapter 9-

Cost of Capital=minimum acceptable return on a new project, you have to ‘hurdle’ your  initial investment and earn AT LEAST the cost to invest in the project. (Also known as the  hurdle rate)  

-Its an opportunity cost in investors eyes- think about the rate of returns that  can be earned elsewhere in the market at the same level of risk, possible opportunities  that would be lost if the project were to be taken on.  

Components are equity, debt and preferred stock. Turned into a weighted average rate  of return that is required by shareholders and debt holders. We also discuss several other topics like How do you calculate run time complexity?

WACC- risk adjusted weighted average cost of capital. If project’s risk is similar to  companies overall risk the WACC can be used as a discount rate.  

What are the three types of risk that are relevant in capital budgeting?

After-tax Cost of Debt- Interest on debt is deductible and reduces taxable profit.  

To find the After Tax Cost of Debt…(rd = cost of debt, Tc =corporate tax rate) Rd (1-Tc)

*8 percent coupon bond with YTM of 15%; company wants to issue new bonds with  similar YTM and at par. Tax rate is marginal and 40 percent. After-tax cost of debt?

Rd=15%=YTM 15*(1-.40)=9%


Cost of Pref. Stock

Rps=cost of PS


P0=price of stock at time 0 (make sure adjusted for flotation costs if given) *To adjust for flotation costs take whatever percent given, ex. 7%, away from the  market price, ex. $40. (40*93%=$37.2 would be the adjusted price)

What is hamada’s equation?

We also discuss several other topics like The relationship between the marginal propensity to consume and the marginal propensity to save can best be described as?

Equation= Rps= D / P0 

Cost of Equity

1) Cost of Retained Earnings- opportunity cost involved with reinvesting earnings  instead of giving them out, stockholders themselves could invest them and  create value for themselves; by not distributing the earnings this opportunity is  taken away. The company should at least produce the return the stockholders  could make for it to be worth it to keep the funds inside the company. To estimate:

Rs=Rrf + B (rm – rrf) ????B= beta, Rrf=risk free rate, Rm=market rate  

Or… Rs= D1/P0 + g ???? D1=dividend at time 1, P0= price at time 0, g=growth rt Note: There are subjective ways to value cost of retained earnings. Sometimes they  take the long-term bond yield and add 2-5% buffer or risk premium. They do this  because risky firms with low ratings on debt are probably going to also have high risk equity that is usually more expensive than long-term debt.

2) Cost of New Common Stock

Rns=(D1/(P0(1-F)) + g ???? F-flotation costs Don't forget about the age old question of What is fermentative organisms?

P0(1-F)=The adjusted stock price

*Flotation costs make retained earnings a cheaper source of financing than new  stock issuances.  If you want to learn more check out How parents and teachers contribute to gender socialization?


WACC= (rs *(S/(D+S+PS))+(rd (1-Tc)*D/(D+S+PS))+(rps (PS/(D+S+PS)) Don't forget about the age old question of What is groupthink?

WACC=( rs*ws)+(rd*wd)+(rps*wps)

Rs=cost fo equity( RE or new stock)

Rps=Cost Pref. Stock

Rd(1-T)=After-tax Cost of Debt

D;S;PS=market values of each

And the fraction in first equation is used for the weights, simplified in second eq.

Value of Operations to get Intrinsic Stock Price 

The primary source of value is the value of operations.  


A secondary source comes from non-operating assets, like short-term investments.  Add Value of Ops and Short Term investments to get Total Value.  Subtract Debt and Preferred Stock to get the Value of Equity.

Divide By shares outstanding and get the estimated intrinsic value of the stock.

**Can also value stock price through Price Multiples.

1) PE ratio (price to earnings) - share price relative to earnings per share -P/E * Expected Earnings =Price

-Used often with IPOs

-Can compare earnings with industry earnings If you want to learn more check out What are esteem needs?

-Underwrites will price IPO based on earnings from peer firms

*However, they’re schemers because they only look at peers with higher  PE ratios! Leads to overvaluation which is bad for the company but good for their  own wallets!

2)  PEG ratio (P/E)/g; includes growth

-Problem with it: the units do not make sense

-Ratio below 1 may indicate a good buy for investors

-g is hard to estimate so throws of worth of the ratio

Note: When a stock is overvalued a company will issue more to get money at  overvalued price and it will drive down to true amount, When a stock is undervalued the  company will buy it back because they know it’s a good deal and that the price is likely  to go up.

Chapter 10-

Capital Budgeting –All about whether or not to invest in a project, which project to  choose.

The most used method presently to test a projects worth is Net Present Value.

NPV???? Present value of Inflows-Present Value of Outflows

The difference between market value of a project and its cost.

=-Initial Outlay+ CF/(1+r)+….CFn/(1+r)n 

Steps to Find:

1) Estimate future cash flows

2) Estimate required return

3) Find PV of the cash flows and subtract the initial outlay.

• If positive, the project is making money. (The return>cost of capital) • If 0, the return is still equal to the cost of capital, so it still meets the minimum  acceptable return the company requires. So it is okay and common for NPVs to  equal 0.

• If negative, the project does not meet the company standards and should be  rejected.

**Problem: Does not take into account size of the project.

**Stock at efficient market NPV=0 because return expected=required return.  

Note: When comparing projects that have similar NPVS, look at Margin for Error. Ex: How much can the projects cash flows can be reduced and still produce a positive  NPV. This considers and compares riskiness of the projects.

IRR???? The rate when NPV equals 0.

• This is to show the return that is needed for the project that makes the PV of  inflows and PV of outflows cancel each other out to 0.

Accept if greater than required return. 

-Managers like to compare rates so they sometimes favor IRR, also it is simple to  communicate

-Normally NPV and IRR produce the same decision, but sometimes this does not happen and IRR is UNRELIABLE. Like when there are…

• Non-conventional cash flows (more cash flows than just the IO are negative,  usually everything after the IO is positive, sign changes [-++-+] would be non conventional)

• Mutually Exclusive Projects- (You can use one or the other project, not both.) *When there are non-conventional cash flows, there is more than 1 IRR. In this case the  IRR is considered useless! And not even worth calculating!

*With mutually exclusive projects, sometimes the Initial Outlays are very different. One  project may get a huge return/IRR but it only generates a little wealth for the company  when compared to the other choice.  

Ex. Project A- IO=100, IRR=60% NPV=500

Project B- IO=1000, IRR=40%, NPV=1500

*If deciding on IRR, one would pick A, but on NPV one would pick B. What really is the  deciding factor is how much wealth is being produced. Even though A has a great return,  B is still producing WAY more wealth and is more beneficial to the company and  shareholders. Goal of Financial Management: maximize shareholder wealth! When  deciding between mutually exclusive projects go with NPV decision making!!!  

Note: This will also happen between IRR and NPV if larger cash flows occur earlier in  the projects life. IF they occur earlier the IRR will be higher than a project that has the  larger cash flows later on.

NPV Profile

-Shows a projects NPV against different costs of capital.

-Crossover Rate is found by taking the differences of the projects cash flows, and  solving for IRR.

-When line A is above Line B, it has a greater NPV. But, after the crossover point line B  has a greater NPV.  

-The differences between the projects can result from timing of cash flows, or size  differences.

Profitability Index- less frequently used


*Only with traditional projects with initial outlay

*A plus is that is gives a degree of risk: how much the profit will cover the initial outlay. *Really doesn’t give any more info than NPV and IRR.

Payback Period-

=Number of Years Prior to Full Recover+ (Unrecovered Cost at Start of Year/Cash Flow  during Full Recovery Year)

-Number of years to recover funds, Accept if meets companies arbitrary cut off date -Ignores Time Value of Money completely

-Cash flows beyond payback period are ignored when making decision, what is it makes  Millions and is not considered because does not meet the payback period requirement! -Does not tell us how much wealth the project generates

Discounted Payback Period

First, Discount all of the Cash Flows to make up for the Time Value of Money Problem. Then, do the same equation.

**The payback methods do provide information on liquidity and risk. (Shorter=More  liquid)

MIRR- IRR makes the mistake of assuming the cash flows are reinvested at IRR and not  the cost of capital. MIRR assumes cash flows are reinvested at WACC, cost of capital.  PV of Costs=TV/(1+MIRR)n

1) Take the present value of cash outflows (negative). If this is just the IO then just  use that. (It is already in Present Value because at time 0).

2) Then, take the future value of all inflows and sum. (Compound to the TERMINAL  YEAR(TV))

3) The MIRR will be the discount rate that causes the PV of the terminal value to  equal the cost. Plug everything into the equation and solve for MIRR. *This is superior to IRR in that it shows more of a TRUE rate of return on the project. Conclusion: Always go with the greatest NPV, because that demonstrates which  project will be the most wealth producing.

Chapter 11-

Cash Flow Estimation

-When doing capital budgeting, Incremental Cash Flows and Operating Cash Flows are  important. *Do Not take Sunk costs into consideration.  

Incremental Cash Flows= Any cash flows the company will have taking on the project  minus cash flows if the firm does NOT take on the project. (Opportunity costs,  externalities (lost sales from other projects))

Sunk Cost= already incurred cost that cannot be recovered, ex: 50,000 spent to rusty  pipes 2 years ago

Depreciable Basis= Cost+Shipping+Installation

Operating Cash Flows





-Taxes(% of EBIT)


=Net OP. Cash Flow

If there is a salvage value the cash flow is…

Salvage Value-Book Value=Gain or Loss

Apply tax to the gain or loss and subtract from sale value. Get the terminal Cash Flow.  *Sale at a loss provides a tax credit! (subtracting a negative, so really adding it) Once all the cash flows are settled, you can use NPV, MIRR, payback, etc… Ex. A company has asked to evaluate an acquisition of a new equipment. The basic price  is $70,000, and it would cost another $15,000 to modify it for special use by your firm.  Use straight line depreciation for 3 years and there is a salvage value of $20,000. Use of  the equipment requires Net working capital of $4,000. Will save the company $25,000 a  year in before tax operating costs. Tax rate=40%. Cost of cap. =10%

A) What is the year 0 net cash flow?  

• Price-modification-NWC

• -70,000-15,000-4,000= -89,000

B) What are the net operating cash flows in year 1, 2 and 3?

• To get Depreciation Tax Shield: Depreciable Basis * 1/3

• 70,000+15,000=85,000*1/3=28333.33=Dep. Expense/Year

• Depr. Expense*Tax Rate=Shield 

• 28333.33*.4=113,33.33

• Year 1: After tax savings-Depreciation Tax Shield=Net Cash Flow • =25,000(1-.4)-11,333.33=3666.67

• Since Depreciation Tax shield and Annual savings are the same, the cash  flow for year 2 and 3 are the same.

C) What is the additional end-of project cash flow?

Salvage Value=$20,000

Tax=20,000 (.4)=-8,000

• 20,000-BV remaining in year 4

• 85,000(0)=BV=0, because fully depreciated

• If not fully depreciated, then would have to subtract remaining book  value from sale of salvage.  

Return on Net working Capital=4,000


D) What is the NPV and should it be accepted?

• PV inflows – Initial Outlay

• -89,000+3333.3+3030.3+14,776.6=-67859.8

• So, the Project should be rejected because negative NPV.

Risk in Capital Budgeting

-Measured by standard deviation

1) Stand-Alone: risk created by a specific project, measured by variability of the single  project, how risky is the project itself?

2) Corporate Risk: harder to calculate than stand-alone, assessed with intuition and the  potential impact of a project on earnings. Measured by project’s corporate beta (how it  aligns with companies other projects) How risky is the project when combined with the  companies other endeavors (assets, projects) Diversification within the firm.  

3) Market Risk- systemic risk, beta, how will the project impact investors? Will it  maximize shareholder wealth? What effect will the project have on the company’s  beta?

Sensitivity Analysis- How NPV or IRR are affected by changes in inputs

-All variables are fixed except the one you are testing

-Use to answer, “What if…ex. Costs are $10,000 more?”

1) Find the ‘base case’ output (NPV or IRR) at the ‘base case’ input value (what we are  measuring the sensitivity of)

2) Find value of NPV or IRR at a new input level.

3) Find % change in output and % change in input.

4) Divide change in output % by the change in input % and get the sensitivity. Graph (example)

-Steeper=Riskier, which means more sensitive to small changes

-Negative: does not reflect diversification, the variable changing is not necessarily likely  (like sales may have a steep line, but in reality the sales figure is unlikely to change at all  so it doesn’t matter), ignores relationships between variables (bc have to keep all others  constant)

-Positive: Shows some stand-alone risk, Identifies threatening variables that need to be  watched out for, gives breakeven info

Scenario Analysis

-examines different possible situations

-Best case, Most likely case, worst case

-Pair Probability of scenario with its outcome and take a weighted like average.


-Negatives: only considers a few outcomes, there are definitely more case than best,  worst and most likely…, Assumes inputs are all clumped together (does not account for  some bad happening with some best case simultaneously), focuses mainly on stand

alone risk

Simulation Analysis- computerized continuous probability distribution of NPV or IRR  based on simulated values that repeats the process 1,000 times or more. -“Garbage in, garbage out”

*All of the analyses do not provide decision rules and ignore diversification. Focus on  stand alone risk.  

*Critical Value(CV) measures a projects stand-alone risk

Real Options-responding to market changes through actions

-alert managers look for real options, while smarter ones create them 1) Investment Timing Options-procrastinating on starting a project is bad, but waiting  can actually payoff sometimes. For example, on risky projects it is better to see how  some things play out before starting a project, more knowledge=less risk Other Real Options are 2) Growth Options and choosing to 3) abandon the project.

Ex. Decision Tree w/ Real Option

Decision Probability Cash Flow r=14% IO=-50Million n=3years High  .25 33 Mil

Market .5 25 mil

Low .25 5 Mil

*There is a real option present: wait a year because so much variation/risk. See how  market goes; knowledge=less risk in decision making.

Use Standard Deviation to show risk in the project, shows variation between outcomes.

The Standard Deviation comes out to  

be $24.02 Million, which shows there is  

a big chance of losing a lot!

So to weigh the option of waiting a  

year, start Initial investment at time 1,  

and push everything back one year  

when discounting.

When doing this the standard deviation  

becomes 8.57, which is a lot less risky.  

Note: 1 standard deviation away from  

the mean in either direction covers 68% of the outcomes, 2 standard deviations covers  95% and 3 covers 99%. (if normally distributed)

Also, It is not always the best to wait. If there is little risk of negative NPV it is probably  better to go ahead with the project. Magnitude of numbers matter!

Ch. 15- Capital Structure Decisions

How to mix Debt and Equity…

Leverage= (DEBT)/(DEBT+EQUITY)

*similar leverages within industries

*The more assets a company has the more debt they can take on.

-This is why high tech companies and pharmaceutical companies take on LESS debt,  they do not have as many assets as collateral.  

*Leverage magnifies risk and return

Many Theories on what ratio is the best.

1) Tax Trade-off Theory: balance the costs of debt to the tax benefits, interest tax  shield

2) Dynamic Tradeoff Theory: No exact optimal #, equates for costs of readjustment,  realizes the optimal number is not static and when the ratio moves away from  the optimal amount the company needs to readjust.

3) Pecking Order- For financing, use retained earnings first, then debt, and then  equity as a last resort. It is a bad signal to investors to issue equity, stock price  falls after they do.

4) Dynamic Pecking Order Theory: announce earnings and THEN issue the stock,  shows transparency to investors and gets rid of the information problem Pecking  order theory has

5) Market Timing Theory-issue bonds when interest is low, stock offering when  stock price is high. Most intuitive because gets the most value

6) Agency Theory: Set the debt amount so that manager behave, but not to too  much that they would pass up a positive NPV in decision making . More debt  means there is less chance for managers to misuse, but too much debt can cause  an underinvestment.

Financial Flexibility= Shown by a companies use of leverage and cash holdings.  Affects decisions to issue debt the most.

Modigliani and Miller

*Debt can cover taxes but too much increases bankruptcy costs.

*There is an optimal ratio.

-compares value and cost of capital to Leverage.

When there are no  

taxes or bankruptcy  

costs, the capital  

structure is irrelevant

because taking the debt  

on will not cover any  

tax expenses and you  

can take as much debt  

on without worrying  

about bankruptcy costs.

The cost of capital stays  

the same because no  

bankruptcy costs.

In a world with taxes  

and no bankruptcy, a  

firm’s value increases  

with the more debt it  

takes on!

Also, cost of capital  

goes down with the  

more debt because of  

the tax shield.

In the real world, the firm’s value increases  with debt to an optimal point and then starts  to fall. This is because the bankruptcy costs  start to outweight the tax benefits.

The cost of capital should be minimized and it  is at the right amount of debt.

Hamada’s Equation-used to determine effects of financial leverage has on a firm, shows  business risk. Used to find the optimal structure.

The (D/E) is the weight of the  

debt to the weight of the  


When weight of debt goes up,  

beta rises.

Beta represents the business risk  

and leveraging affect.

The B1 in the equation, also Bu, is  

Beta with 0 debt.  

-Use the CAPM to find cost of equity from the found Beta! Rs=rm+BLev(RPM)

*If market to book ratio is high the stock may be overvalued and the company should  issue stock.  

*Goal should be to minimize cost of capital.

*The theories do not account for why 0 leveraged firms sometimes do really well. Has to  do with executives in charge. More conservative personalities will take on less debt. IPO Process

1) File a 100 page document to the SEC called an S-1

2) It gets approved be preliminary prospectus

3) Filing Price Range is set and solicit feedback about how much it is worth through  roadshows, book building and marketing.  

-If good feedback, choose to set IPO price higher.

4) Final Prospectus is made, the offer price is finalized.

If the IPO is underpriced, after the first day the price will pop.

To calculate IPO underpricing or money left on the table: (Price at end of 1st Day on  market-Offer)*number of shares

*Sometimes for free marketing, they intentionally set the price low to get a POP in  price, which creates buzz.

-IPOs generally underperform for the initial years when compared to the average firm. Underwriters- investment bankers that raise capital for the company from investors Syndicate-group of investment bank that work on the IPO

-Sometimes underwriters are schemers and hand pick certain peer firms to base the  stock price on, they pick a “peachy offer price” that is based on the highest valued peer

firms. This is unethical and has been uncovered through research, the IPO comes out  overvalued. The stock will generally do well in the first 6 months, and underwriters will  buy shares to up the price.

Also, if you as a regular investor can get allocation and can buy IPO shares that means  the big investors probably do not want it.  

Proceeds-Underwriting Fee(typically7%)=Net Proceeds 

Gross Spread=underwriters fees 

Shelf Registration: Get securities approved ahead of time to shorten the process of the  IPO and accelerate the offer. This helps if the company needs immediate cash. -used to be allowed only for large companies but now more can do this, and smaller  companies should not necessarily do this, must be investment grade to do this -many problems with underwriters not doing due diligence with the accelerated  offers

SEO: seasoned equity offering, follow-on offerings, lack the announcement effect, they  face underpricing, but the gross spread is more negotiable.

Dilution is when the company offers completely new shares.

-When short selling is high for a company, they are likely to issue because it shows that  the stock price is expected to drop.  

-Short selling signals overvalued stock

-Issuing will cause the stock price to drop

Repurchase: If a company thinks its stock is undervalued it will repurchase the shares at  a low price and through supply and demand the stock price will go up.

Private Placement Offers- to small group of investors, not public, Lacks announcement  affects, w/o SEC review; cost effective way for small businesses to raise capital. Flotation Costs: loss of capital from information problems between firms and investors

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