0. Chapter 12
Cost of
Capital

1. 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

2. Chapter Outline 12.1 The Cost of Capital: Some Preliminaries
12.2 The Cost of Equity
12.3 The Costs of Debt and Preferred Stock
12.4 The Weighted Average Cost of Capital
12.5 Divisional and Project Costs of Capital

3. 12.1 The Cost of Capital: Some Preliminaries

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 in a security, is the cost of that security to the issuing company
Our cost of capital is 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

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
The investment will have a positive NPV only if its return exceeds the required return
We need to earn at least the required return to compensate our investors for the financing they have provided

6. Required Return
The cost of capital depends primarily on the “USE” of the funds, not the source
The riskier the investment or project – the higher the cost of capital!
Note: The following terms are interchangeable
Required return
Appropriate discount rate
Cost of capital

7. 12.2 The Cost of Equity

8. 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 major methods for determining the cost of equity
Dividend growth model
SML or CAPM

9. The Dividend Growth Model Approach
Start with the dividend growth model formula and rearrange to solve for RE
RE is the return that shareholders require on the stock and can be interpreted as the firm’s cost of equity capital
D1 is the next period’s projected dividend
P0 is the price per share of stock
g is the growth rate
Remind students that D1 = D0 – 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)

10. The Dividend Growth Model Approach
For a publicly traded dividend paying company:
P0 and D0 can be observed in the market
g (the expected growth rate) must be estimated
D1 = D0 x (1 + g)
RE = D1 / P0 + g

11. Example: Estimating the Dividend Growth Rate
One method for estimating the growth rate is to use the historical average
Calculate the change in the dividend on a year-to-year basis and then express the change as a %
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%

12. Estimating the Dividend Growth Rate
A second method for estimating the growth rate is to use analysts’ forecasts of future growth rates

13. Dividend Growth Model Example
Suppose that your company is expected to pay a dividend of $1.50 per share 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. What is the cost of equity? RE = D1 / P0 + g
So, investors are currently requiring a return of 11.1% on our equity capital.

14. 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%
Does not explicitly consider risk
No allowance for the degree of certainty or uncertainty surrounding the estimated growth rate in dividends
Point out that there is no allowance for the uncertainty about the growth rate

15. The Security Market Line (SML) Approach From Previous Chapter
Using the SML, we can write the expected return on the company’s equity, E(RE), as:
Risk-free rate, Rf
U.S. Treasury bill benchmark
Systematic risk of asset,  = Market Risk
Widely available on publicly traded companies
Market risk premium, (E(RM ) – Rf )
Based on large common stocks
You will often hear this referred to as the Capital Asset Pricing Model Approach as well.
www: Click on the web surfer 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. Other sites that provide betas include and

16. 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

17. Example – Cost of Equity Using both the SML and DGM Approach
Suppose our company has a beta of 1.5. The market risk premium is expected to be 9% and the current risk-free rate is 6%. We have used analysts’ estimates to determine that the market believes our dividends will grow at 6% per year and our last dividend was $2. Our stock is currently selling for $ What is our cost of equity?
Using SML:
RE = 6% + 1.5(9%) = 19.5%
Using DGM: RE = D1 / P0 + g
RE = [2(1.06) / 15.65] = 19.5%
Since the two models are reasonable close, we can assume that our cost of equity is probably around 19.5%

18. The Cost of Equity Example 12.1
Review:
The Cost of Equity
Example 12.1
Page 349

19. Advantages and Disadvantages of SML
Explicitly adjusts for systematic (Market) risk
Applicable to all companies, as long as we can compute beta
Not restricted to just those companies with steady dividend growth
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%!!!!!

20. Advantages and Disadvantages of SML
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
If the estimates are poor, the resulting cost of equity will be inaccurate

21. 12.3 The Costs of Debt and Preferred Stock

22. Cost of Debt
In addition to ordinary equity, firms use debt and, to a lesser extent, preferred stock to finance their investments
The “cost of debt” is the required return on our company’s debt
The return that lenders require on the firm’s debt
The interest rate the firm must pay on new borrowing
We can observe these interest rates in the financial markets
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.

23. Cost of Debt We usually focus on the cost of long-term debt or bonds
If the firm already has bonds outstanding, then the required return is best estimated by computing the yield-to-maturity on the existing debt
The cost of debt is NOT the coupon rate –which indicates what the firm’s cost of debt was when the bonds were issued, not the cost of debt today.
We must use the “yield” in today’s market: yield-to-maturity

24. Cost of Debt
We can also use estimates of current rates based on the bond rating we expect when we issue new debt
If we expect the bonds to be rated AA:
Then we simply use the interest rate associated with newly issued AA-rated bonds

25. 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?
Hint: Calculate the Yield-to-Maturity (YTM)
N = 50; PMT = 45; FV = 1000; PV = ;
I = 5%; YTM = 5(2) = 10%
Pmt Computation: (1,000 x .09) / 2 (semiannually) = $45
N Computation: 25 years x 2 (coupons are paid semiannually or twice per year)
Remind students that it is a trial and error process to find the YTM if they do not have a financial calculator or spreadsheet.

26. Cost of Debt Example 12.2 (Pg 350)
Suppose the General Tool Company issued a 30-year, 7 percent bond eight years ago. The bond is currently selling for 96 percent of its face value, or $ What is General Tool’s cost of debt?
N = 30 – 8 = 22; PMT = 1000 x .07 = 70;
FV = 1000; PV = x .96 = -960;
I = 7.37%; YTM = 7.37%
General Tool’s cost of debt, RD, is 7.37% (assuming annual coupons)
Note: since the bond is selling at $960 and the face value = $1,000, the bond is selling at a discount, therefore, the YTM of 7.37% is greater than the coupon rate of 7%

27. Cost of Debt
Question: Why is the coupon rate a bad estimate of a firm’s cost debt?

28. Cost of Debt
Answer: the coupon rate – indicates what the firm’s cost of debt was when the bonds were issued, not the cost of debt today.
We must use the firm’s cost of debt in today’s market.
Yield-to-maturity (YTM), estimates the firm’s cost of debt today.

29. Cost of Preferred Stock
Preferred stock has a fixed dividend paid every period forever
So a share of preferred stock is essentially a “Perpetuity”.
The cost of preferred stock, RP, is thus:
RP = D / P0
Where D is the fixed dividend and P0 is the current price per share of the preferred stock
The cost of preferred stock is simply equal to the dividend yield on the preferred stock.

30. Cost of Preferred Stock - Example
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 = D / P0
RP = 3 / 25 = 12%

31. 12.4 The Weighted Average Cost of Capital (WACC)

32. Weighted Average Cost of Capital
Now that we have the costs associated with the main sources of capital the firm employs: Equity and Debt: we need to determine the specific mix: The firms “Capital Structure”.
This mix or “average” is the required return on our assets, based on the market’s perception of the risk of those assets
Weights are determined by how much of each type of financing (equity or debt) that we use

33. Capital Structure Weights
Capital Structure Weight Calculations
wE = E/V = percent financed with equity
wD = D/V = percent financed with debt
Where:
E = “market value” of equity = # outstanding shares times price per share
D = “market value” of debt = # outstanding bonds times bond price
If there are multiple bond issues, we repeat this calculation for each and then add up the results
V = “market value” of the firm = D + E
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.

34. 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 = market value of the firm = = 975 million
wE = E/V = 500 / 975 = = 51.28%
wD = D/V = 475 / 975 = = 48.72%

35. Taxes and the WACC
We are always 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 = (E/V) x RE + (D/V) x RD x (1-TC)
WACC = wERE + wDRD(1-TC)
WACC = the overall return the firm must earn on its existing assets to maintain the value of the stock
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

36. Weighted Average Cost of Capital (WACC)
WACC is the required return on any investments by the firm that have essentially the same risk as existing operations
If we were evaluating the cash flows from a proposed expansion of our existing operations, WACC is the discount rate we would use
i.e. in an NPV calculation

37. 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

38. Extended Example – WACC - II
What is the cost of equity?
RE = (9) = 15.35%
What is the cost of debt?
If the firm already has bonds o/s, then the required return = yield-to-maturity on the existing debt
N = 30; PV = -1100; PMT = 45; FV = 1000; I =
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.

39. 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 = wERE + wDRD(1-TC)
WACC = .7843(.1535) (.04712)
WACC =
WACC = or 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.

40. Table 12.1 – Page 355 Summary of Capital Cost Calculations
Know the information in this table.

41. Chapter 12: Suggested Homework and Test Review
Chapter Review and Self-Test Problems: 12.1 & 12.2, Page 359
Questions and Problems: 1, 2, 5, 7 abc, 10, and 24 (Pages 361, 362 and 364)
Know: The formulas in Table 12.1 on page 355
Know how to calculate:
The Cost of Equity (Dividend growth and SML)
The Cost of Debt (bonds - YTM)
The Cost of Preferred Stock
The Weighted Average Cost of Capital, WACC
The capital structure weights (debt and equity) required for the WACC calculation
Study the examples presented in this presentation
Know chapter theories, concepts, and definitions