1. Cost of Capital Chapter 14 Notes to the Instructor:
The PowerPoints are designed for an introductory finance class for undergraduates with the emphasis on the key points of each chapter
Each chapter’s PowerPoint is designed for active learning by the students in your classroom
Not everything in the book’s chapter is necessarily duplicated on the PowerPoint slides
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2. Chapter Outline The Cost of Capital – Overview The Cost of Equity
The Cost of Debt
The Cost of Preferred Stock
The Weighted Average Cost of Capital (WACC)
Divisional and Project Costs of Capital
Floatation Costs relative to WACC

3. Why the 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
Lecture Tip: Students often find it easier to grasp the intricacies of cost of capital estimation when they understand why it is important. A good estimate is required for: -good capital budgeting decisions – neither the NPV rule nor the IRR rule can be implemented without knowledge of the appropriate discount rate
-financing decisions – the optimal/target capital structure minimizes the cost of capital
-operating decisions – cost of capital is used by regulatory agencies in order to determine the “fair” return in some regulated industries (e.g. utilities)

4. Why the Cost of Capital Is Important
Our cost of capital provides us with an indication of how the market views the risk of our assets
4. Knowing our cost of capital can also help us determine our required return for capital budgeting projects
Lecture Tip: Students often find it easier to grasp the intricacies of cost of capital estimation when they understand why it is important. A good estimate is required for: -good capital budgeting decisions – neither the NPV rule nor the IRR rule can be implemented without knowledge of the appropriate discount rate
-financing decisions – the optimal/target capital structure minimizes the cost of capital
-operating decisions – cost of capital is used by regulatory agencies in order to determine the “fair” return in some regulated industries (e.g. utilities)

5. The Cost of Equity Business risk Financial risk
The cost of equity is the return required by equity investors given the risk of the cash flows from the firm:
Business risk
Financial risk

6. Dividend growth model (aka: the Gordon Model) 2. SML, or the CAPM
The Cost of Equity
There are two major methods for determining the cost of equity:
Dividend growth model (aka: the Gordon Model)
2. SML, or the CAPM

7. The Dividend Growth Model (The Gordon Model)
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)

8. 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?

9. 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 fairly 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. So, another way to estimate the market consensus estimate is to look at analysts’ forecasts and take an average.
Lecture Tip: It is noted in the text that there are other ways to compute g. Rather than use the arithmetic mean, as in the example, the geometric mean (which implies a compound growth rate) can be used. OLS regression with the log of the dividends as the dependent variable and time as the independent variable is also an option. Another way to estimate g is to assume that the ROE and retention rate are constant. If this is the case, then g = ROE*retention rate.
Lecture Tip: Here’s a good real-world exercise to illustrate real-world growth rates. You can assign this as homework, or do it in class if your classroom has Internet access. Go to screen.yahoo.com/stocks.html and find the “Analysts Estimates Est. 5 Yr EPS growth” box, and use up more than 30%. In August of 2008, using the S&P 500 index stocks found 91 stocks. A search of the S&P 600 (small-cap stocks) found 135 stocks (more small-cap stocks were expected to have very high growth rates than large-cap stocks).
Average = ( ) / 4 = 5.1%

10. The SML Approach
Use the following information to compute our cost of equity:
Risk-free rate, Rf
Market risk premium, E(RM) – Rf
Systematic risk of asset, 
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 finance.yahoo.com. 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 key statistics. To get the T-bill rates, click on “Rates” under Bonds on the home page.

11. Example - SML Suppose your company has: an equity beta of .58
the current risk-free rate is 6.1%
the expected market risk premium is 8.6%
The similarity is completely dependent on estimates of the risk-free rate and market risk premium.
What is the cost of equity using the SML valuation technique?
RE = (8.6) = 11.1%

12. How Did We Do?
Since we came up with similar numbers using both the dividend growth model (11.1%) and the SML approach (11.1%), we should feel good about our estimate!

13. Example – Cost of Equity
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 $15.65.
What is our cost of equity using the SML?
RE = 6% + 1.5(9%) = 19.5%

14. Example – Cost of Equity
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 $15.65.
Since the two models are reasonably close, we can assume that our cost of equity is probably around 19.5%. Again, though, this similarity is a function of the inputs selected and is not indicative of the true similarity that could be expected.
What is our cost of equity using the DGM?
RE= [2(1.06) / 15.65] = 19.55%

15. 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 (as opposed to short-term debt like notes payable)
Point out that the cost of debt is rarely the coupon interest rate as 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.

16. Cost of Debt
The required return is best estimated by computing the yield-to-maturity on the existing long-term debt (the YTM).
The computation of the YTM was presented in the chapter on Bond Valuation
Lecture Tip: Consider what happens to corporate bond rates and mortgage rates as the Federal Reserve board changes the fed funds rate. If the Federal Reserve raises the fed funds rate by a quarter point, virtually all bond rates, from government to municipal to corporate, will increase after this action.

17. Example: Cost of Debt: computing the YTM
Suppose we have a corporate 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 $1,000 bond.
What is the cost of debt?

18. HP 12-C 25 years/2 = 50 periods = N $-908.72 = PV
$90/2 = $45 = Payment (PMT)
YTM = i = ?
$1,000 = FV
5.00 (x2 = 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 application.
14-18

19. TI BA II Plus $ -908.72 = PV $1,000 = FV YTM = I/Y = ?
25 yrs/2 = 50 payments = N
5%(5 x 2 = 10%
$ = PV
$90/2 = $45 (PMT)
$1,000 = FV
Remind students that it is a trial and error process to find the YTM if they do not have a financial calculator or spreadsheet application.
YTM = I/Y = ?
1st
2nd
14-19

20. Capital Structure Weights
To compute the WACC, we first need the weights of each source of funds: namely debt, preferred stock and equity

21. Capital Structure Weights
Let’s simplify with an example of just debt and equity.
We often use the market value of both debt and equity

22. Capital Structure Valuation
Debt’s Market Value = (# of outstanding bonds ) x (the market price of one bond)
Equity’s Market Value = (# shares of outstanding common stock) x (the market price of one share of common stock)
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.

23. Capital Structure Valuation
A firm’s market value is simply the added value of both the debt and the equity:
V = 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.

24. Capital Structure Weights
WD = D/V
This is the % financed with debt
WE = E/V
This is the % financed with equity
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.
Lecture Tip: It may be helpful to mention and differentiate between the three types of weightings in the capital structure equation: book, market and target. It is also helpful to mention that the total market value of equity incorporates the market value of all three common equity accounts on the balance sheet (common stock, additional paid-in capital and retained earnings).
Lecture Tip: The cost of short-term debt is usually very different from that of long-term debt. Some types of current liabilities are interest-free, such as accruals. However, accounts payable has a cost associated with it if the company forgoes discounts. The cost of notes payable and other current liabilities depends on market rates of interest for short-term loans. Since these loans are often negotiated with banks, you can get estimates of the short-term cost of capital from the company’s bank. The market value and book value of current liabilities are usually very similar, so you can use the book value as an estimate of market value.

25. Student Alert! WD + WE = 100% or WD + WPS + WE = 100%
The capital structure weights must always add up to 100%
WD + WE = 100% or
WD + WPS + WE = 100%

26. Example: Capital Structure Weights
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 + $475 million = $975 million
wD = D/V = 475 / 975 = = 48.72%
wE = E/V = 500 / 975 = = 51.28%

27. Taxes and the WACC Wait a minute!
Debt and Equity are not equal in the eyes of the firm.
Debt gets a tax advantage and Equity does not.
We are concerned with after-tax cash flows, so we also need to consider the effect of taxes on the various costs of capital
Dividends are not tax deductible, so there is no tax impact on the cost of equity

28. Taxes and the WACC Interest expense reduces our tax liability
This reduction in taxes reduces our cost of debt
Thus, our real cost of debt is actually the AFTER-TAX cost of debt or …
After-tax cost of debt = RD(1-TC)

29. Taxes and the WACC WACC = WDRD(1-TC) + WE RE
Our new equation for the WACC is:
WACC = WDRD(1-TC) + WE RE
This is one of the most powerful relationships in finance.
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 and consider any tax consequences.
Lecture Tip: If the firm utilizes substantial amounts of current liabilities, equation 14.7 from the text should be modified as follows: WACC = (E/V)RE + (D/V)RD(1-TC) + (P/V)RP + (CL/V)RCL(1-TC) where CL/V represents the market value of current liabilities in the firm’s capital structure and V = E + D + P + CL.

30. Putting All the Pieces Together – WACC 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
Remind students that bond prices are quoted as a percent of par value
The firm’s tax rate is 40%

31. WACC Example = 7.854% 1. What is the cost of debt?
N = 30; PV = -1,100; PMT = 45; FV = 1,000; CPT I/Y =
RD = 3.927(2)
= 7.854%
Point out that students do not have to compute the YTM based on the entire face amount. They can still use a single bond or they could also base everything on 100 (PV = -110; FV = 100; PMT = 4.5).
2. What is the cost of equity (using the CAPM)?
RE = (9) = 15.35%

32. WACC Example RD (1 – TC) = 7.854 (1 - .40) = 4.712%
What is the AFTER-TAX
cost of debt?
RD (1 – TC) = ( )
= 4.712%

33. WACC Example 4. What are the capital structure weights?
Debt = 1 billion ($1.10) = $1.1 billion
Equity = 50 million ($80) = $4 billion
Value of the Firm = = $5.1 billion

34. WACC Example (Plug and Chug)
Compute the Weighted Average
Cost of Capital (the WACC)
WACC = WDRD(1-TC) + WE RE
WACC = (4.712%) (15.35%)
= 13.06%

35. Formulas
Cost of Equity (Dividend Growth Model)
Cost of Equity (CAPM)

36. Formulas (continued) WACC = WDRD(1-TC) + WE RE Rps = D_ P0
Cost of Preferred Stock
After-tax cost of debt = RD(1-TC)
WACC = WDRD(1-TC) + WE RE