1. CHAPTER 14 COST OF CAPITAL
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2. 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
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)
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3. 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
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4. Cost of Equity
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
There are two major methods for determining the cost of equity
Dividend growth model
SML, or CAPM
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5. 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)
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6. Example: Dividend Growth Model
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?
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7. 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 the Yahoo! Finance stock screener 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%
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8. 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
Point out that there is no allowance for the uncertainty about the growth rate
Lecture Tip: Some students may question how you value the stock for a firm that doesn’t pay dividends. In the case of growth-oriented, non-dividend-paying firms, analysts often look at the trend in earnings or use similar firms to project the future date of the first expected dividend and its future growth rate. However, such processes are subject to greater estimation error, and when companies fail to meet (or even exceed) estimates, the stock price can experience a high degree of variability. It should also be pointed out that no firm pays zero dividends forever – at some point, every going concern will pay dividends. Microsoft is a good example. Many people believed that Microsoft would never pay dividends, but even it ran out of investments for all of the cash that it generated and began paying dividends in 2003.
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9. 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 “Bonds” under Investing on the home page.
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10. 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 good about our estimate
The similarity is completely dependent on estimates of the risk-free rate and market risk premium.
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11. Advantages and Disadvantages of SML
Explicitly adjusts for systematic risk
Applicable to all companies, as long as we can estimate 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 using 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 Citigroup (C), which was used in an example in the slides in the previous chapter. In Sept. 2012, (based on calculations on Yahoo) Citigroup had a beta of 2.6. Yet, its capital gains return from Sept 2002 to Sept 2012 was almost -90%!! On the positive side, in Sept. 2012, APPL had a beta of .88, yet its capital gains return over the past 10 years was over 9,000%!!!!!.
Lecture Tip: Students are often surprised when they find that the two approaches typically result in different estimates. Suggest that it would be more surprising if the results were identical. Why? The underlying assumptions of the two approaches are very different. The constant growth model is a variant of a growing perpetuity model and requires that dividends are expected to grow at a constant rate forever and that the discount rate is greater than the growth rate. The SML approach requires assumptions of normality of returns and/or quadratic utility functions. It also requires the absence of taxes, transaction costs, and other market imperfections.
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12. Example – Cost of Equity
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 = [2(1.06) / 15.65] = 19.55%
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.
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13. 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
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.
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.
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14. 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 $1,000 bond.
What is the cost of debt?
N = 50; PMT = 45; FV = 1000; PV = ; CPT I/Y = 5%; YTM = 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 application.
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15. Cost of Preferred Stock
Reminders
Preferred stock generally pays a constant dividend each period
Dividends are expected to be paid every period forever
Preferred stock is a perpetuity, so we take the perpetuity formula, rearrange and solve for RP
RP = D / P0
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16. 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%
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17. 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 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
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18. Capital Structure Weights
Notation
E = market value of equity = # of outstanding shares times price per share
D = market value of debt = # of outstanding bonds times bond price
V = market value of the firm = D + E
Weights
wE = E/V = percent financed with equity
wD = D/V = percent 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 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.
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.
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19. 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 million = 975 million
wE = E/V = 500 / 975 = = 51.28%
wD = D/V = 475 / 975 = = 48.72%
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20. Taxes and the WACC
We are concerned with after-tax cash flows, so we also 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 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.
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21. 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
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22. Extended Example: WACC - II
What is the cost of equity?
RE = (9) = 15.35%
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%
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 or they could also base everything on 100 (PV = -110; FV = 100; PMT = 4.5).
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23. 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%
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24. Table 14.1 Cost of Equity
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25. Table 14.1 Cost of Debt
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26. Table 14.1 WACC
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27. Chapter 14
END OF CHAPTER
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