1. Risk, Cost of Capital and Valuation
MSBC 5060 Chapter 13
Risk, Cost of Capital and Valuation

2. Chapter Overview Recall a capital budgeting decision looks like this:
Invest only if NPV > 0.
If PV of future CFs is greater than the cost
We know which CFs to use
Total CF = OCF – DNWC - NCS
Now we need to figure out what R to use 

3. A capital budgeting decision looks like this:
Now we need to figure out what R to use:
R is the required return of the project
It is the amount investors need to earn
Based on the risk of the company’s business
consumer products, consumer durables, luxury goods…
Pay CFO, Get CF1 through CFN
Recall: If R < IRR, then NPV > 0
R is the return the company’s investors require
What the investors Earn = the company’s Cost
The Required Return is the Cost of Capital

4. Chapter Overview So only do a project if:
The return is more than the cost
Same as saying the project has a positive NPV
But what is the cost of the capital to the company?
The cost of capital is what investors demand from the company
What do investors demand?
It depends on the investor:
Some investors buy the company’s Equity or Stock
And they earn an expected return on the stock
How do we calculate E(R)?
CAPM or Dividend Discount Model
Some investors buy the company’s Debt or Bonds
And they earn a yield to maturity (YTM) on the bond
How do we calculate YTM?
YTM equates the price to the cash flows

5. (We’ll get to the “(1 – T)” part later)
Chapter Overview
Determine a firm’s cost of capital raised from selling ownership stakes
Return paid to stock or equity holders (RE)
Determine a firm’s cost of capital raised from borrowing money
Return paid to bond or debt holders (RD)
Determine a firm’s Weighted Average Cost of Capital:
Average these costs by their balance-sheet weights:
Call it the Weighted Average Cost of Capital
WACC = WERE + WDRD(1 - T)
(We’ll get to the “(1 – T)” part later)

6. Chapter Outline 13.1 The Cost of Equity Capital
13.2 Estimating the Cost of Equity Capital (RE) with the CAPM
13.3 Estimation of the Equity Beta (Did this in Chapter 11)
13.4 The Determinants of Beta
13.5 Estimating RE using the Dividend Discount Model
13.7 Cost of Fixed Income Securities (RD)
13.8 Calculating The Weighted Average Cost of Capital
13.6 Cost of Capital for Different Divisions or Projects
Valuation (Using the WACC)
13.10 Estimating Eastman Chemical’s Cost of Capital
13.11 Accounting for Flotation Costs

7. I will use only D for Debt and E for Equity
Notation:
In this chapter, the text book uses both:
D = Debt or B = Bond
and
E = Equity or S = Stock
Page 401 (Equation 13.1): Rs
The Return on the company’s stock
Page 410 (Equation 13.3): βDebt and βEquity
The betas for the company’s debt and equity
Page 417 (Equation 13.5): S, B
The market weight of company’s stocks and bonds
I will use only D for Debt and E for Equity

8. Simple Capital Budgeting Problem:
Why is the WACC used for Capital Budgeting?
In other words:
Why is the WACC the denominator for NPV calculations?
Simple Capital Budgeting Problem:
Consider a 1 year project that costs $100
and pays $110 in 1 year
If the discounted future CFs of a project is greater than the cost
Then the NPV > 0  Accept the project
If the discount rate is 5%
Then NPV = -$100 + $110/(1.05) = $4.76

9. Another way to think about this:
What is the IRR of this project?
0 = -$100 + $110/(1.10)  The IRR = 10%
What is the “return” on the $100 invested?
R = ($110/$100) – 1 = 10%  Return = 10%
If we require 5% and the return is 10%,
then the project adds value
NPV > 0 means a project’s return is greater than the required return
So how do we calculate the required return? 

10. How Much Return Does a Project Require?
Assume (for now) that the proposed project’s risk is the same as the company’s other projects
It’s has the same risk as the company’s existing business
What return do investors require on the company’s existing business?
It depends on the risk of that business
The riskier the business, the higher the required return
We can use the market-determined price of the firm’s stocks and bonds

11. How Much Return (Continued)
Here’s the key point:
The RETURN to investors is the same as the company’s COST
What the investors receive, the company pays
Conclusion:
The appropriate discount rate is the investors’ required return
Which is based on the project’s risk
A project must earn at least the required return to compensate investors for providing the money
If the project earns exactly the required return, then the NPV = 0
If the project earns less, then investors are not being compensated for the risk they are incurring in that project
Then the NPV < 0
So the company should not use the investors capital for that project

12. (We’ll get to the “1 – T” part later)
Calculating the Cost of Capital
The Required Return equals the Cost of Capital:
The Cost of Capital raised from selling ownership (Equity or Stocks)
The Cost is the Required Return on Equity = RE
The Cost of Capital raised from borrowing money (Debt or Bonds)
The Cost is the Required Return on Debt = RD
Each of these costs are weighted by the portion used to finance the company activities
The Weight of Equity = WE
The Weight of Debt = WD
This is the WACC and is used to calculate NPV
WACC = WERE + WDRD(1 - T)
(We’ll get to the “1 – T” part later)
How do we calculate each of these terms 

13. 13.2 The Cost of Equity (RE) using CAPM
The cost of equity is the return required by equity investors given the risk of the cash flows from the firm
All the risk? The total risk? Measured by the standard deviation? (s)
NO!
Investors need only be compensated for the Market Risk!
Measured by Beta (b)
Calculate the cost of equity (which is equal to the required return) using the CAPM (or the Security Market Line equation)
The CAPM shows the expected return on a company’s equity is:
E(R) = Rf + b[E(RM) – Rf]
The return expected by the investor is the same as the return required by the investor and therefore the cost of equity to the firm
RE = Rf + b[E(RM) – Rf]

14. Calculating RE Using the CAPM
According to the CAPM, the cost of equity to the firm is:
RE = Rf + b[E(RM) – Rf]
Example (P&G):
Assume the risk-free rate is 0.53%
The company has an equity beta of 0.46
The expected market risk premium is 8.60%
Calculate the cost of equity capital:
RE = Rf + b[E(RM) – Rf] = 0.53% (8.60%) = 3.96%

15. 13.4 Determinants of Beta Formally: Cyclicality of Revenues
Not the same volatility of revenues
Biotech vs. Steel
Operating Leverage
The mix of fixed and variable costs
Financial Leverage
The mix of debt and equity financing
All three have an impact on the variability of the Net Income
available to the stockholders
Variability of NI (EPS) affects stock price volatility and risk

16. Cyclicality of Revenues
Function of the product produced by the company
Does the company make
Consumer products
βP&G = 0.46
Not very cyclical
Office Products and Supplies
βOffice Depot = 2.95
Very cyclical

17. Degree of Operating Leverage
Mix of Fixed and Variable costs
DOL increases as fixed costs rise relative to variable costs
DOL magnifies the effects of cyclicality on EBIT
Formula:
DOL =
%D Sales
%D EBIT

18. Financial Leverage Mix of Debt and Equity financing
Increases as fixed interest payments rise
Financial Leverage magnifies the effects of cyclicality on NI (and EPS)
Financial Leverage is measured by the usual leverage measures
Debt/Equity is the most common financial leverage measure in this context

19. Operating Leverage and Financial Leverage
Three alternatives
All VC (DOL = 1.00), No Debt  %ΔNI = %ΔSal
All Fixed (DOL = 2.00), No Debt  %ΔNI > %ΔSales
All VC (DOL = 1.00), Yes Debt  %ΔNI > %ΔSales
All VC - No Debt
All FC - No Debt
All VC - Debt
Sales
$1,000
$1,100
Variable Costs
$500
$550 $0
Fixed Costs
EBIT
$600
Interest Expense
$250 NI
$300
%ΔSales
10%
%ΔEBIT
20%
%ΔNI
Operating Leverage
%ΔEBIT = %ΔSales
%ΔEBIT > %ΔSales
Financial Leverage
%ΔNI = %ΔEBIT
%ΔNI > %ΔEBIT
Total Leverage
%ΔNI = %ΔSales
%ΔNI > %ΔSales

20. More about Financial Leverage
What is the effect on the firm’s Equity Beta from more debt?
Recall a Portfolio’s Beta is the weighted average beta of the components
So the Company’s Total Beta is the weighted average beta of the stocks and bonds issued to finance the company
βPortfolio = E/V βEquity + D/V βDebt
But the Total Beta is really Asset Beta
βAssets = E/V βEquity + D/V βDebt

21. βEquity = βAssets [1 + D/E] βEquity = βAssets [1 + (1-T)D/E]
Beta and Financial Leverage
We have this relationship:
βAssets = E/V βEquity + D/V βDebt
But think about βDebt
βDebt = Cov(RDebt,RMkt)/Var(RMkt)
Covariance of debt and the market is close to zero
βDebt ≈ 0
βAssets = E/V βEquity + 0
Since V = E + D:
βAssets = E/(E + D) βEquity
βEquity = βAssets (E + D)/E
βEquity = βAssets (E/E + D/E)
βEquity = βAssets [1 + D/E]
βEquity = βAssets [1 + (1-T)D/E]

22. Example: CMG is financed only with equity (no debt)
This referred to as an “unlevered firm”
The beta of its stock is 0.56
What is the beta of its assets given that it has no debt?
βEquity = βAssets (1 + D/E) = βAssets (1 + 0/E) = βAssets (1)
βEquity = βAssets = 0.56
If CMG were to issue enough debt to buy back 20% of its outstanding stock, what would happen to the beta of the remaining stock?
D/E = 0.20/0.80 = 0.25
βEquity = βAssets (1 + D/E) = 0.56 ( ) = 0.70
The market risk of the stock increases by 25%
Solely from a financing decision!

23. RE = Rf + βEquity[E(RM) – Rf]
Recap: Determinants of Equity Beta
Cyclical nature of the product
Degree of operating Leverage
DOL = %ΔEBIT/%ΔSales
Is this a business decision or nature of the product?
Financial Leverage
βEquity = βAssets (1 + D/E)
We use βEquity to calculate RE
RE = Rf + βEquity[E(RM) – Rf]
We Use RE to calculate WACC
WACC = WERE + WDRD(1 – TC)

24. Some Beta Terminology βE = βL and βA = βU Corporate Finance Question:
Corporate Finance: Equity Beta βE and Asset Beta βA
Investments: Levered Beta βL and Unlevered Beta βU
βE = βL and βA = βU
Corporate Finance Question:
Given the Asset Beta (βA cyclicality and DOL), what do financing decisions do to equity risk (Equity Bata βE) and the cost of equity capital?
βA  βE
Investments Question:
Given the Levered Beta (the CAPM beta, βL )what does the company’s risk look like without the leverage (βU)?
βL  βU

25. Calculating Unlevered Beta
Before (Corporate finance notation)
Given βA what is βE?
βE = βA [1 + (1-T)D/E]
Now (Investments notation)
Given βL what is βU?
βL = βU [1 + (1-T)D/E]
βU = βL/[1 + (1-T)D/E]

26. What Happens to Equity Return?
Equity Risk:
βE = βA [1 + (1 - T)D/E]
βL = βU [1 + (1 - T)D/E]
Equity Return:
RE = RA + (RA – RD)(1 – T)D/E
RL = RU + (RU – RD)(1 – T)D/E
(This is MMII with taxes)

27. 13.5 Calculate RE Using the Div Growth Model
Another way to calculate RE is to start with the constant dividend growth rate model and solve for R (Really RE):
P0 = D1/(RE – g)
RE = D1/P0 + g
Example:
A company is expected to pay a $1.50 dividend next year
There has been a steady growth in dividends of 5.1% per year and the market expects that to continue
The current price is $25
Calculate the cost of equity capital:
= $1.50/$ = = 11.1%

28. The cost of equity capital is 14.90%
Example using the Div Growth Model:
A company will pay a $4.95 dividend in one year
There has been a steady growth in dividends of 5% per year and the market expects that to continue forever
The current price is $50
Calculate the cost of equity capital (RE).
D1 = 4.95; P0 = $50; g = 5%
RE = D1/P0 + g
=$4.95/$ = = 14.90%
The cost of equity capital is 14.90%

29. Advantages and Disadvantages of the CAPM (or SML) Approach
Explicitly adjusts for systematic risk
Applicable to all companies, as long as we can compute beta
Disadvantages
Have to estimate the expected market risk premium, which does vary over time
Have to estimate beta, which also varies over time
We are relying on the past to predict the future, which is not always reliable

30. Advantage and Disadvantages of Dividend Growth Approach: Advantage
Easy to understand and use
Disadvantages
Only applicable to companies currently paying dividends
Not applicable if dividends aren’t growing at a reasonably constant rate
Extremely sensitive to the estimated growth rate
An increase in g of 1% increases the cost of equity by 1%

31. 13.7 Cost of Fixed Income (RD)
The Cost of Debt to the company is the same as the Return Required by the lenders
Return Required is the Amount Earned
Determined by the price
Required Return is the Yield To Maturity (YTM)
The higher the required return (YTM)
The lower the price
The lower the required return (YTM)
The higher the price

32. PV = C/(1 + R)1 + C/(1 + R)2 + … + FV/(1 + R)N
Calculating the Cost of Debt (RD)
Recall YTM calculations from Chapter 8:
YTM is the R that equates the PV of the CFs to the price:
PV = C/(1 + R)1 + C/(1 + R)2 + … + FV/(1 + R)N
Example:
A $1,000 bond makes Semi-Annual payments and has 20 years to maturity. The coupon rate is 10%. The price is $
Calculate the return required by people holding this debt as a function of the price paid:
=rate(nper, pmt, pv, [fv], type])
=rate(40,50, ,1000) = 0.055
RD = YTM = 2 x = 11.00%
Holders of this bond require an 11% return
What if the bond’s price was $1,092.01? YTM = 9%
What if the bond’s price was $1,000? YTM = 10%

33. The YTM on Existing Debt is the Required Return NOT the Coupon Rate!
Bond holders earn the YTM, not the coupon rate
The coupon rate was the required return when the bond was issued
At that time YTM = Coupon Rate
And the bond was issued at par
If the bond’s price has gone down, bond holders get the coupons plus the capital appreciation
If the Par > Price, then the YTM > Coupon Rate
If the bonds price has gone up, bond holders get the coupons less the capital appreciation
If the Par < Price, then the YTM < Coupon Rate

34. 13.8 Weighted Average Cost of Capital
Use the individual costs of capital: RE and RD
To get the “average” cost of capital for the firm
The WACC is the required return on the assets employed in the firm’s projects
Based on
The market’s perception of the risk of those projects
And the way the firm chooses to finance the assets
Meaning the weights of equity and debt
The weights are determined by how much of each kind of financing the firm chooses

35. WACC Notation E = Market Value of Equity
= Shares Outstanding x Price per Share
D = Market Value of Debt
= # outstanding bonds x Price per Bond
V = Market value of the firm = D + E
Weights
WE = E/V = percent financed with equity
WD = D/V = percent financed with debt

36. Capital Structure Weight Calculations
A firm’s assets are financed with:
10 million shares of stock at price of $50 per share
$90 million face value bonds at 105% of par.
Calculate the Capital Structure Values:
E = 10 million x $50 = $500 million
D = $90 million x 105% = $94.5 million
V = E + D = $500 + $94.5 = $594.5
Calculate the Weights:
WE = $500/$594.5 = 84.10%
WD = $94.5/$594.5 = 15.90%

37. Taxes and the WACC WACC = WERE + WDRD(1 – TC)
What really matters is the after-tax cost of capital
Interest expense (the cost of debt) reduces the company’s taxes
If the cost of debt (RD) is 8%
And the Tax rate is 35%
Then the firm can deduct 35%(8%) = 2.8%
of the 8% cost of debt from its taxes
Its after-tax cost of debt is (1 – 35%)(8%) = 5.2%
WACC accounting for the after-tax cost of Debt:
WACC = WERE + WDRD(1 – TC)

38. Taxes and the WACC Note that when we calculated a project’s CFs:
CF = OCF – DNWC – NCS
OCF = (Sales – Costs)(1 – T) + Dep x T
OCF = (Sales – FC – VC)(1 – T) + Dep x T
We did not account for INTEREST EXPENSE as a cost.
We will account for it now as a FINANCING EXPENSE
Not included as an operating cost
Included as part of the WACC
So Interest Expense is included in the WACC
But NOT Included as part of the operations

39. 13.6 Cost of Capital for Divisions and Projects
What if the project is not the same as the company’s average project?
The company’s WACC is appropriate discount rate for projects that have the same risk as the firm’s current average operations
If we are looking at a project that does not have the same risk as the rest of the company
Need to determine the discount rate (WACC) for that project
Large companies with multiple divisions often require separate discount rates for each division
What if a company uses a single WACC for all projects? 

40. Figure 13.5 Page 414

41. Cost of Capital for Divisions and Projects
Find companies in the same field as the proposed project
Companies in only one business are called “pure plays”
Calculate: RE
Look up the betas for “pure plays” in the industry
Adjust the betas to account for
Differences in DOL
Financial leverage
Apply the CAPM
Calculate: RD
Look up the bonds for “pure plays” in the industry
Calculate the YTM
Calculate WACC for the project

42. 13.11 Floatation Costs
Incurred by the firm and paid to investment banks
Decreases money received from an issue
Floatation costs do not increase the rate paid
RE and RD
Floatation costs increase the amount issued in order for the firm to get the required funds
Example:
If floatation costs are 5% and the firm need $1,000 from bonds
Must sell $1,000/(1 – 0.05) = $1,053
The extra $53 is a time-zero cost

43. 13.9 Valuation (Using the WACC)
Example: Valuing a Project (Example Page 414)
Warehouse costs $60m
Will save $12m per year for 6 years
Negative incremental costs are positive OCF
Target D/E ratio is 0.60
$0.60 Debt for each $1.00 of Equity
So Value = Assets = Debt + Equity = $1.60
Weight of Debt: WD = 0.60/1.60 = 0.375
Weight of Equity: WE = 1.00/1.60 = 0.625
Cost of Debt: RD = 5.15%
Cost of Equity: RE = 10.00%
Tax Rate = 34%
WACC = WERE + WDRD(1 – TC)
= 0.625(0.10) (0.0515)(1 – 0.34) = 7.52%
Go to Valuation Example Spreadsheet 

44. Example: Valuing a Firm (Example Page 414)
Acquire a competitor
Horizontal merger so assume target has same risk as acquirer
Acquirer WACC:
RD = 5% and RE = 10%
has $4b debt and $2b stock 
Tax Rate = 20%
WACC = WERE + WDRD(1 – TC) = 1/3(0.10) + 2/3(0.05)(1 – 0.2) = 6.00%
Target CFs:
EBIT = $150 and will grow at 10% for 5 years and then 2% forever
NCS, ΔNWC and Deprecation Expense are each a fixed % of EBIT
But unlike a project, a going concern (a firm) does not end
We need to value all the activity after some arbitrary date
The value of the firm after that date is called the Terminal Value

45. Terminal Value This example uses two methods:
Present Value on a future date of all activity after that date
Usually value it as a growing perpetuity
But what is growing?
Revenue
EBITDA
EBIT
NI (Earnings)
Cash Flows (OCF – ΔNWC – NCS)
For a going concern we’ll call this “Free Cash Flows” (FCF)
This example uses two methods:
Grow CFs (now FCFs) at an assumed rate
2% growth so divided by an “(R – g)”
Multiply EBITDA by an assumed multiple
EV/EBITDA multiple
Recall a multiple is just the inverse of an “(R – g)”

46. What’s Next: WACC = WERE + WDRD(1 – TC)
Because income from debt does not vary (fixed income)
And because debt holders are paid first
The return required by debt holders is less than the return required by equity holders
In other words, the cost of debt (generally) is less than the cost of equity
RD < RE
So it seems like a firm can minimize WACC by increasing debt
Since WACC is the denominator of the NPV calculations:
And a firm’s value is the sum of the NPVs of its projects
It seems like a firm can increase its value by increasing debt
So we’ll talk “Capital Structure”
Talk about the mix of debt and equity