1. The Cost of Capital

2. Cost of Capital Key Concepts
Know how to determine a firm’s cost of equity capital
Know how to determine a firm’s cost of debt
Know how to determine a firm’s overall cost of capital-WACC
Divisional and Project Costs of Capital
Flotation Costs and the Weighted Average Cost of Capital
Understand pitfalls of overall cost of capital and how to manage them

3. Determinants of Intrinsic Value: The Weighted Average Cost of Capital
Net operating
profit after taxes
Required investments
in operating capital −
Free cash flow
(FCF) =
FCF1
FCF2
FCF∞
Value = ··· +
(1 + WACC)1
(1 + WACC)2
(1 + WACC)∞
Weighted average
cost of capital
(WACC)
Market interest rates
Firm’s debt/equity mix
Cost of debt
Cost of equity
Market risk aversion
Firm’s business risk

4. Why Cost of Capital Is Important
We know that the return earned on assets depends on the risk of those assets
The return to an investor is the same as the cost to the company
Our cost of capital provides us with an indication of how the market views the risk of our assets
Knowing our cost of capital can also help us determine our required return for capital budgeting projects and valuation of the companies.

5. Required Return
The required return is the same as the appropriate discount rate and is based on the risk of the cash flows
We need to know the required return to value a company
We need to know the required return for an investment before we can compute the NPV and make a decision about whether or not to take the investment
We need to earn at least the required return to compensate our investors for the financing they have provided

6. Capital Components
Capital components are sources of funding that come from investors.
Accounts payable, accruals, and deferred taxes are not sources of funding that come from investors, so they are not included in the calculation of the cost of capital.
We do adjust for these items when calculating the cash flows of a project, but not when calculating the cost of capital.

7. Before-tax vs. After-tax Capital Costs
Tax effects associated with financing can be incorporated either in capital budgeting cash flows or in cost of capital.
Most firms incorporate tax effects in the cost of capital. Therefore, focus on after-tax costs.
Only cost of debt is affected.

8. Historical (Embedded) Costs vs. New (Marginal) Costs
The cost of capital is used primarily to make decisions which involve raising and investing new capital. So, we should focus on marginal costs.
Cost of additional dollar that the company must raise for a new project. The marginal cost rises as more and more capital is raised during a stated time period.

9. Weighted Average Cost of Capital
Capital Components:
Short-term debt Long-term debt
Preferred Stock Common stock
WACC = Rstd (1-T) Wstd +Rd (1-T)Wd + Rpf Wpf + RE WE
Where W’s are the weights of each source of financing and
Rstd = interest rate on short-term debt such as notes payable.
Rd = required return on a bond, for previously issued bonds it is the equal to yield to maturity.
Rpf and RE are required returns on preferred and common stock

10. Cost of Equity
The cost of equity is the return required by equity investors given the risk of the cash flows from the firm

11. Estimation of the Cost Of Equity
There are two major methods for determining the cost of equity
1. Dividend growth model
2. SML based on Capital Asset Pricing Model

12. The Dividend Growth Model Approach
Start with the dividend growth model formula and rearrange to solve for RE
Remind students that D1 = D0(1+g)
You may also want to take this time to remind them that return is comprised of the dividend yield (D1 / P0) and the capital gains yield (g)

13. Estimating the Growth Rate
Use the historical growth rate if you believe the future will be like the past.
Obtain analysts’ estimates: Value Line, Zack’s, Yahoo.Finance.
Use the sustainable growth (earnings retention) model.

14. Example: Estimating the Dividend Growth Rate
One method for estimating the growth rate is to use the historical average
Year Dividend Percent Change
(1.30 – 1.23) / 1.23 = 5.7%
(1.36 – 1.30) / 1.30 = 4.6%
(1.43 – 1.36) / 1.36 = 5.1%
(1.50 – 1.43) / 1.43 = 4.9%
Our historical growth rates are reasonably close, so we could feel reasonably comfortable that the market will expect our dividend to grow at around 5.1%. Note that when we are computing our cost of equity, it is important to consider what the market expects our growth rate to be, not what we may know it to be internally. The market price is based on market expectations, not our private information.
Another way to estimate the market consensus estimate is to look at analysts’ forecasts and take an average.
Average = ( ) / 4 = 5.1%

15. Dividend Growth Model Example
Suppose that your company is expected to pay a dividend of $1.50 per share next year. The steady growth in dividends as calculated in prior slide is 5.1% per year and the market expects that to continue. The current price is $25. What is the cost of equity?
So, investors are currently requiring a return of 11.1% on our equity capital.

16. Estimating the Dividend Growth Rate
Second method for estimating the growth rate is to use sustainable growth rate:
g = RR x ROE
RR= Retention Ratio (the percent of net income is retained for an vestment).
ROE= Return on Equity (NIAT/Equity)
NIAT=Net Income After Tax

17. Estimating the Dividend Growth Rate
Growth from earnings retention model: g = (Retention rate)(ROE) g = (1 – Payout rate)(ROE)
g = (1 – 0.66)(15%) = 5.1%. This is the same as g = 5.1% given earlier.

18. Advantages and Disadvantages of Dividend Growth Model
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%
Extremely sensitive to stock price volatility
Does not explicitly consider risk
Point out that there is no allowance for the uncertainty about the growth rate

19. The Cost of Equity SML Approach
From the firm’s perspective, the expected return is the Cost of Equity Capital:
To estimate a firm’s cost of equity capital, we need to know three things:
The risk-free rate, RF
The market risk premium,
The company beta,

20. Example - SML
Suppose your company has an equity beta of .58 and the current risk-free rate is 6.1%. If the expected market risk premium is 8.6%, what is your cost of equity capital?
RE = (8.6) = 11.1%
Since we came up with similar numbers using both the dividend growth model and the SML approach, we should feel pretty good about our estimate

21. Issues in Using CAPM
Most analysts use the rate on a long-term (10 to 20 years) government bond as an estimate of RF.
More…

22. Issues in Using CAPM (Continued)
Most analysts use a rate of 5% to 6.5% for the market risk premium (RPM)
Estimates of beta vary, and estimates are “noisy” (they have a wide confidence interval).

23. Example
Suppose the stock of Stansfield Enterprises, a publisher of PowerPoint presentations, has a beta of 2.5. The firm is 100-percent equity financed.
Assume a risk-free rate of 5-percent and a market risk premium of 10-percent.
What is the appropriate discount rate for an expansion of this firm?

24. Example (continued)
Suppose Stansfield Enterprises is evaluating the following non-mutually exclusive projects. Each costs $100 and lasts one year.
Project
Project b
Project’s Estimated Cash Flows Next Year
IRR
NPV at 30% A
2.5
$150
50%
$15.38 B
$130
30% $0 C
$110
10%
-$15.38

25. Using the SML to Estimate the Risk-Adjusted Discount Rate for Projects
Good projects
30%
2.5 A B C
Project
IRR
Bad projects 5%
Firm’s risk (beta)
An all-equity firm should accept a project whose IRR exceeds the cost of equity capital and reject projects whose IRRs fall short of the cost of capital.

26. Estimation of Beta Problems Solutions
Theoretically, the calculation of beta is straightforward:
Problems
Betas may vary over time.
The sample size may be inadequate.
Betas are influenced by changing financial leverage and business risk.
Solutions
Problems 1 and 2 (above) can be moderated by more sophisticated statistical techniques.
Problem 3 can be lessened by adjusting for changes in business and financial risk.
Look at average beta estimates of comparable firms in the industry.

27. Stability of Beta
Most analysts argue that betas are generally stable for firms remaining in the same industry.
That’s not to say that a firm’s beta can’t change.
Changes in product line
Changes in technology
Deregulation
Changes in financial leverage

28. Determinants of Beta Business Risk Financial Risk
Cyclicity of Revenues
Operating Leverage
Financial Risk
Financial Leverage

29. Cyclicality of Revenues
Highly cyclical stocks have high betas.
Empirical evidence suggests that retailers and automotive firms fluctuate with the business cycle.
Transportation firms and utilities are less dependent upon the business cycle.
Note that cyclicality is not the same as variability—stocks with high standard deviations need not have high betas.
Movie studios have revenues that are variable, depending upon whether they produce “hits” or “flops”, but their revenues are not especially dependent upon the business cycle.

30. Operating Leverage
The degree of operating leverage measures how sensitive a firm (or project) is to its fixed costs.
Operating leverage increases as fixed costs rise and variable costs fall.
Operating leverage magnifies the effect of cyclicity on beta.
The degree of operating leverage is given by:

31. Operating Leverage
The degree of operating leverage (DOL) measures the effect of a change in sales volume on earnings before interest and taxes (EBIT). It is defined as the percentage change in EBIT associated with a given percentage change in sales:
Operating leverage increases as fixed costs rise and variable costs fall.

32. Financial Leverage and Beta
Financial leverage is the sensitivity of a firm’s fixed costs of financing.
The relationship between the betas of the firm’s debt, equity, and assets is given by:
bAsset =
Debt + Equity
Debt
× bDebt +
Equity
× bEquity
Financial leverage always increases the equity beta relative to the asset beta.

33. Financial Leverage and Beta: Example
Consider Grand Sport, Inc., which is currently all-equity and has a beta of 0.90.
The firm has decided to lever up to a capital structure of 1 part debt to 1 part equity.
Since the firm will remain in the same industry, its asset beta should remain 0.90.
However, assuming a zero beta for its debt, its equity beta would become twice as large:

34. Advantages and Disadvantages of SML
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
A good example to illustrate how beta estimates can lag changes in the risk of equity, consider Keithley Industries (KEI) which was used as one of the portfolio stocks in the last chapter. It currently (Sept. 2000, based on calculations on Yahoo) has a beta of .59. Yet, its capital gains return over the last year (Sept 27, 1999 – Sept 27, 2000) has been about 835%!!!!!

35. Cost of Equity Based on Risk Premium
The bond yield plus risk premium approach:
RE = RD + ERP
ERP=Equity risk premium

36. Cost of Debt
The cost of debt is the required return on our company’s debt
We usually focus on the cost of long-term debt or bonds
The required return is best estimated by computing the yield-to-maturity on the existing debt
We may also use estimates of current rates based on the bond rating we expect when we issue new debt
Ask an investment banker what the coupon rate would be on new debt.
The cost of debt is NOT the coupon rate
After-tax Rd = R d (1-TC)
Point out that the coupon rate was the cost of debt for the company when the bond was issued. We are interested in the rate we would have to pay on newly issued debt, which could be very different from past rates.

37. Example: Cost of Debt
Suppose we have a bond issue currently outstanding that has 25 years left to maturity. The coupon rate is 9% and coupons are paid semiannually. The bond is currently selling for $ per $1000 bond. What is the cost of debt?
T = 50; PMT = 45; FV = 1000; PV = ; CPT I/Y = 5%; YTM = Rd =5(2) = 10%
Remind students that it is a trial and error process to find the YTM if they do not have a financial calculator or spreadsheet.

38. Example: Cost of Debt A 15-year, 12% semiannual bond sells for $1,153
Example: Cost of Debt A 15-year, 12% semiannual bond sells for $1, What’s rd? 60
60 + 1,000 1 2 30
i = ?
-1,153.72
...
5.0% x 2 = Rd = 10% N
I/YR PV FV
PMT
INPUTS
OUTPUT

39. Component Cost of Debt
Interest is tax deductible, so the after tax (AT) cost of debt is:
After-Tax Rd = Before –Tax Rd (1 - T)
After-Tax Rd = 10%( ) = 6%.

40. Cost of Preferred Stock
Preferred generally pays a constant dividend every period (DP)
Dividends are expected to be paid every period forever
Preferred stock is an annuity, so we take the annuity formula, rearrange and solve for RP
RP = DP / P0

41. Example: Cost of Preferred Stock
Your company has preferred stock that has an annual dividend of $3. If the current price is $25, what is the cost of preferred stock?
RP = 3 / 25 = 12%

42. Is preferred stock more or less risky to investors than debt?
More risky; company not required to pay preferred dividend.
However, firms want to pay preferred dividend. Otherwise, (1) cannot pay common dividend, (2) difficult to raise additional funds, and (3) preferred stockholders may gain control of firm.

43. What are the two ways that companies can raise common equity?
Directly, by issuing new shares of common stock.
Indirectly, by reinvesting earnings that are not paid out as dividends (i.e., retaining earnings).

44. Why is there a cost for reinvested earnings?
Earnings can be reinvested or paid out as dividends.
Investors could buy other securities, earn a return.
Thus, there is an opportunity cost if earnings are reinvested.

45. Cost for Reinvested Earnings (Continued)
Opportunity cost: The return stockholders could earn on alternative investments of equal risk.
They could buy similar stocks and earn rs, or company could repurchase its own stock and earn rs. So, rs, is the cost of reinvested earnings and it is the cost of equity.

46. The Weighted Average Cost of Capital
We can use the individual costs of capital that we have computed to get our “average” cost of capital for the firm.
This “average” is the required return on our assets, based on the market’s perception of the risk of those assets
The weights are determined by how much of each type of financing that we use

47. Capital Structure Weights
Notation
E = market value of equity = # outstanding shares times price per share
D = market value of debt = # outstanding bonds times bond price
P=market value of preferred stock=#outstanding shares times price per share
V = market value of the firm = D + E
Weights
wE = E/V = percent financed with equity
wd = D/V = percent financed with debt
WACC = wDRd(1-TC)+wP RP + w E RE
Note that for bonds we would find the market value of each bond issue and then add them together.
Also note that preferred stock would just become another component of the equation if the firm has issued it.
Finally, we generally ignore current liabilities in our computations. However, if a company finances a substantial portion of its assets with current liabilities, it should be included in the process.

48. Example: Capital Structure Weights
Suppose you have a market value of equity equal to $500 million and a market value of debt = $475 million.
What are the capital structure weights?
V = 500 million million = 975 million
wE = E/D = 500 / 975 = = 51.28%
wd = D/V = 475 / 975 = = 48.72%

49. Taxes and the WACC WACC = wERE + wdRd(1-TC)
We are concerned with after-tax cash flows, so we need to consider the effect of taxes on the various costs of capital
Interest expense reduces our tax liability
This reduction in taxes reduces our cost of debt
After-tax cost of debt = Rd(1-TC)
Dividends are not tax deductible, so there is no tax impact on the cost of equity
WACC = wERE + wdRd(1-TC)
Point out that if we have other financing that is a significant part of our capital structure, we would just add additional terms to the equation

50. Determining the Weights for the WACC
The weights are the percentages of the firm that will be financed by each component.
If possible, always use the target weights for the percentages of the firm that will be financed with the various types of capital.

51. Estimating Weights for the Capital Structure
If you don’t know the targets, it is better to estimate the weights using current market values than current book values.
If you don’t know the market value of debt, then it is usually reasonable to use the book values of debt, especially if the debt is short-term.

52. Extended Example – WACC - I
Equity Information
50 million shares
$80 per share
Beta = 1.15
Market risk premium = 9%
Risk-free rate = 5%
Debt Information
$1 billion in outstanding debt (face value)
Current quote = 110
Coupon rate = 9%, semiannual coupons
15 years to maturity
Tax rate = 40%
Remind students that bond prices are quoted as a percent of par value

53. Extended Example – WACC - II
What is the cost of equity?
RE = (9%) = 15.35%
What is the cost of debt?
T = 30; PV = -1100; PMT = 45; FV = 1000; CPT I/Y =
Rd = 3.927(2) = 7.854%
What is the after-tax cost of debt?
Rd(1-TC) = 7.854(1-.4) = 4.712%
Point out that students do not have to compute the YTM based on the entire face amount. They can still use a single bond.

54. Extended Example – WACC - III
What are the capital structure weights?
E = 50 million (80) = 4 billion
D = 1 billion (1.10) = 1.1 billion
V = = 5.1 billion
wE = E/V = 4 / 5.1 = .7843
wd = D/V = 1.1 / 5.1 = .2157
What is the WACC?
WACC = .7843(15.35%) (4.712%) = 13.06%
Video Note: This is a good place to show the “Economic Value Added” video to reinforce the contents of the Reality Bytes box in the text.

55. What factors influence a company’s WACC?
Uncontrollable factors:
Market conditions, especially interest rates.
The market risk premium.
Tax rates.
Controllable factors:
Capital structure policy.
Dividend policy.
Investment policy. Firms with riskier projects generally have a higher cost of equity.

56. Is the firm’s WACC correct for each of its divisions?
NO! The composite WACC reflects the risk of an average project undertaken by the firm.
Different divisions may have different risks. The division’s WACC should be adjusted to reflect the division’s risk and capital structure.

57. Divisional and Project Costs of Capital
Using the WACC as the discount rate is only appropriate for projects that are the same risk as the firm’s current operations
If we are looking at a project that is NOT the same risk as the firm, then we need to determine the appropriate discount rate for that project
Divisions also often require separate discount rates
It is important to point out that the WACC is not very useful for companies that have several disparate divisions.
www: Click on the web surfer icon to go to an index of business owned by General Electric. Ask the students if they think that projects proposed by the “Real Estate Group” should have the same discount rate as projects proposed by “Aviation Services.” You can go through the list and illustrate why the divisional cost of capital is important for a company like GE.
If GE’s WACC was used for every division, then the riskier divisions would get more investment capital and the less risky divisions would lose the opportunity to invest in positive NPV projects.

58. The Pure Play (Comparable Companies) Approach
Find one or more companies that specialize in the product or service that we are considering
Compute the beta for each company
Take an average
Use that beta along with the CAPM to find the appropriate return for a project of that risk
Often difficult to find pure play companies

59. The Risk-Adjusted Divisional Cost of Capital
Estimate the cost of capital that the division would have if it were a stand-alone firm.
This requires estimating the division’s beta, cost of debt, and capital structure.

60. Using WACC for All Projects - Example
What would happen if we use the WACC for all projects regardless of risk?
Assume the WACC = 15%
Project Required Return IRR
A 20% 17%
B 15% 18%
C 10% 12%
Ask students which projects would be accepted if they used the WACC for the discount rate? Compare 15% to IRR and accept projects A and B.
Now ask students which projects should be accepted if you use the required return based on the risk of the project? Accept B and C.
So, what happened when we used the WACC? We accepted a risky project that we shouldn’t have and rejected a less risky project that we should have accepted. What will happen to the overall risk of the firm if the company does this on a consistent basis? Most students will see that the firm will become riskier.

61. Capital Budgeting & Project Risk
Project IRR
The SML can tell us why:
Incorrectly accepted negative NPV projects
Hurdle rate
bFIRM
Incorrectly rejected positive NPV projects Rf
Firm’s risk (beta)
A firm that uses one discount rate for all projects may over time increase the risk of the firm while decreasing its value.

62. Subjective Approach
Consider the project’s risk relative to the firm overall
If the project is more risky than the firm, use a discount rate greater than the WACC
If the project is less risky than the firm, use a discount rate less than the WACC
You may still accept projects that you shouldn’t and reject projects you should accept, but your error rate should be lower than not considering differential risk at all

63. Subjective Approach - Example
Risk Level
Discount Rate
Very Low Risk
WACC – 8%
Low Risk
WACC – 3%
Same Risk as Firm
WACC
High Risk
WACC + 5%
Very High Risk
WACC + 10%

64. Flotation Costs
The required return depends on the risk, not how the money is raised
However, the cost of issuing new securities should not just be ignored either
Basic Approach
Compute the weighted average flotation cost
Use the target weights because the firm will issue securities in these percentages over the long term

65. NPV and Flotation Costs - Example
Your company is considering a project that will cost $1 million. The project will generate after-tax cash flows of $250,000 per year for 7 years. The WACC is 15% and the firm’s target D/E ratio is .6 The flotation cost for equity is 5% and the flotation cost for debt is 3%. What is the NPV for the project after adjusting for flotation costs?
fA = (.375)(3%) + (.625)(5%) = 4.25%
PV of future cash flows = 1,040,105
NPV = 1,040, ,000,000/( ) = -4,281
The project would have a positive NPV of 40,105 without considering flotation costs
Once we consider the cost of issuing new securities, the NPV becomes negative
D/E = .6; Let E = 1; then D = .6
V = = 1.6
D/V = .6 / 1.6 = .375; E/V = 1/1.6 = .625
PMT = 250,000; N = 7; I/y = 15; CPT PV = 1,040,105

66. Comments about flotation costs:
Flotation costs depend on the risk of the firm and the type of capital being raised.
The flotation costs are highest for common equity. However, since most firms issue equity infrequently, the per-project cost is fairly small.
We will frequently ignore flotation costs when calculating the WACC.

67. Quick Quiz
What are the two approaches for computing the cost of equity?
How do you compute the cost of debt and the after-tax cost of debt?
How do you compute the capital structure weights required for the WACC?
What is the WACC?
What happens if we use the WACC for the discount rate for all projects?
What are two methods that can be used to compute the appropriate discount rate when WACC isn’t appropriate?
How should we factor in flotation costs to our analysis?