1. Cost of capital
Chapter 12

2. Key concepts and skills
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
Understand pitfalls of overall cost of capital and how to manage them
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

3. Chapter outline The cost of capital: Some preliminaries
The cost of equity
The costs of debt and preferred stock
The weighted average cost of capital
Divisional and project costs of capital
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

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.
‘We’ meaning the firm here.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

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 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.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

6. Cost of equity
The cost of equity is the return required by equity investors given the risk of the cash flows from the firm.
There are two main methods for determining the cost of equity:
1. Dividend growth model
2. SML or CAPM
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

7. Dividend growth model method
Start with the dividend growth model formula and rearrange to solve for RE
Remind students that D1 = D0 – g.
You may also want to take this opportunity to remind them that return comprises the dividend yield (D1 / P0) and the capital gains yield (g).
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

8. Dividend growth model method—Example
Your company is expected to pay a dividend of $4.40 per share next year. (D1)
Dividends have grown at a steady rate of 5.1% per year and the market expects that to continue. (g)
The current stock price is $50. (P0)
What is the cost of equity?
So investors are currently requiring a return of 13.9% on our equity capital.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

9. Estimating the dividend growth rate—Example
One method for estimating the growth rate is to use the historical average.
Year Dividend % 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 may feel reasonably confidently 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 might 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%
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

10. Advantages and disadvantages of dividend growth model method
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
Does not explicitly consider risk
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

11. The SML method Compute cost of equity using the SML Risk-free rate, Rf
Market risk premium, E(RM) – Rf
Systematic risk of asset, 
You will often also hear this referred to as the capital asset pricing model approach.
www: Click on the information icon to go to Bloomberg’s website. Both betas and 3-month T-bills are available on this site. To get betas, enter a ticker symbol to get the stock quote, then choose profile. To get the T-bill rates, go to Markets and then US Treasuries. < is an another site providing similar quotes.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

12. SML approach—Example Company’s equity beta = 1.2
Current risk-free rate = 7%
Expected market risk premium = 6%
What is the cost of equity capital?
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

13. Advantages and disadvantages of SML method
Explicitly adjusts for systematic risk
Applicable to all companies, as long as beta is available
Disadvantages
Must estimate the expected market risk premium, which does vary over time
Must estimate beta, which also varies over time
Relies on the past to predict the future, which is not always reliable
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

14. Cost of equity—Example 12.1
Data:
Beta = 1.2
Market risk premium = 8%
Current risk-free rate = 6%
Analysts’ estimates of growth = 8% per year
Last dividend = $2
Current stock price = $30
Using SML: RE = 6% + 1.2(8%) = 15.6%
Using DGM: RE = [2(1.08) / 30] = 15.2%
Since the two models are reasonably close, we can assume that our cost of equity is probably about 15.4% (an average).
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

15. Cost of debt
The cost of debt = the required return on a company’s debt.
We usually focus on the cost of long-term debt or bonds.
Method 1 = Compute the yield to maturity on existing debt.
Method 2 = Use estimates of current rates based on the bond rating expected on new debt.
The cost of debt is NOT the coupon rate.
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.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

16. Cost of debt—Example
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?
50 [N]; PMT = 45 [PMT]; 1000 [FV]; [+/-][PV] ; [CPT] [I/Y] = 5%; YTM = 5(2) = 10%
Remind students that it is a process of trial and error to find the YTM if they do not have a financial calculator or spreadsheet.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

17. Cost of preference shares
Reminders
Preference shares generally pay a constant dividend every period.
Dividends are expected to be paid every period forever.
Preference share valuation is an annuity, so we take the annuity formula, rearrange and solve for RP.
RP = D/P0
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

18. Cost of preference shares— Example
Your company has preference shares that have an annual dividend of $3. If the current price is $25, what is the cost of a preference share?
RP = 3 / 25 = 12%
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

19. Weighted average cost of capital
Use the individual costs of capital to compute a weighted ‘average’ cost of capital for the firm.
This ‘average’ = the required return on the firm’s 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 is used.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

20. Determining the weights for the WACC
Weights = percentages of the firm that will be financed by each component.
Always use the target weights, if possible.
If not available, use market values.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

21. Capital structure weights
Notation
E = market value of equity = number of outstanding shares times price per share
D = market value of debt = number outstanding bonds times bond price
V = market value of the firm = D + E
Weights
wE = E/V = percentage financed with equity
wD = D/V = percentage financed with debt
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 simply 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.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

22. Capital structure weights—Example
Suppose you have a market value of equity equal to $500 million and a market value of debt equal to $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%
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

23. Taxes and the WACC— Classical tax system
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.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

24. WACC = (E/V) x RE + (P/V) x RP + (D/V) x RD x (1- TC)
Where:
(E/V) = % of common equity in capital structure
(P/V) = % of preferred stock in capital structure
(D/V) = % of debt in capital structure
RE = firm’s cost of equity
RP = firm’s cost of preferred stock
RD = firm’s cost of debt
TC = firm’s corporate tax rate
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

25. WACC I— Extended example
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 percentage of par value.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

26. WACC II—Extended example
What is the cost of equity?
RE = (9) = 15.35%
What is the cost of debt?
N = 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.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

27. WACC III—Extended example
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%
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

28. Taxes and the WACC— Imputation tax system
In an imputation system shareholders (if residents) are given a tax credit for the local taxes paid. This will alter the cost of equity for the firm.
We have to adjust the WACC formula to take into account the tax advantage of imputation.
WACC = wERE(1-TC) + wDRD(1-TC)
This adjustment assumes all shareholders can take advantage of the tax credits.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

29. Summary of capital cost calculations—Table 12.1
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

30. Summary of capital cost calculations—Table 12.1 (cont.)
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh
12-30 30

31. Factors that Influence a company’s WACC
Market conditions, especially interest rates, tax rates and the market risk premium
The firm’s capital structure and dividend policy
The firm’s investment policy
Firms with riskier projects generally have a higher WACC
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

32. Cost of equity—Domino’s Pizza
The information is available at the Sydney Morning Herald website < or at <
Click on the information icon to reach the Sydney Morning Herald page, which gives the current quote for Domino’s .
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

33. Cost of equity—Domino’s Pizza (cont.)
This data in the textbook is taken from <
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

34. Cost of equity—Domino’s Pizza (cont.)
Domino’s earning summary from yahoo finance.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

35. Cost of equity—Domino’s Pizza (cont.)
Cost of equity using CAPM
Assume equity market risk premium= 6%
Risk-free rate= 5.25% (Australian government bond rate)
Beta = 0.85 (from yahoo finance)
RE= (0.06)= or 10.35%
Cost of equity using dividend growth model
Growth = 13.8% (using key statistics from yahoo finance)
Last dividend = $0.124
Current share price = $ 5.07
RE= 0.124( )/5.07
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

36. Cost of debt—Domino’s Pizza
The following is extracted from Domino’s Pizza’s corporate website:
Overall weighted average debt cost
The complete example is from the textbook; we advise you to refer to textbook for details of the assumptions behind the calculations.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

37. WACC—Domino’s Pizza Weights calculated using the total market value
Total market value = $ million
Equity = $ million
Debt = $20.7 million
Weights
WE = 0.94; WD = 0.06
WACC
0.94(0.1315)+0.06(0.082)(1-0.3) = 12.71%
Tax rate of 30% is taken.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

38. Divisional and project costs of capital
Using the WACC as our discount rate is only appropriate for projects that are the same risk level as the firm’s current operations.
If we are looking at a project that is NOT the same risk level as the firm, 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.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

39. Risk-adjusted WACC
A firm’s WACC reflects the risk of an average project undertaken by the firm.
‘Average’  risk = the firm’s current operations
Different divisions/projects may have different risks.
The division’s or project’s WACC should be adjusted to reflect the appropriate risk and capital structure.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

40. Using WACC for all projects
What would happen if we used the WACC for all projects, regardless of risk?
Assume the WACC = 15%
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.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

41. Using WACC for all projects (cont.)
Assume the WACC = 15%.
Adjusting for risk changes the decisions.
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.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

42. Divisional risk and the cost of capital—Figure 12.1
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

43. Pure play approach
Find one or more companies that specialise in the product or service being considered.
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.
Pure-play companies are difficult to find.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

44. 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 when not considering differential risk at all.
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

45. 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%
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

46. 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?
Copyright © 2011 McGraw-Hill Australia Pty Ltd
PPTs t/a Essentials of Corporate Finance 2e by Ross et al.
Slides prepared by David E. Allen and Abhay K. Singh

47. Chapter 12
END