# 10

Dr. Kevin Bracker; Dr. Fang Lin; and jpursley

### Chapter Learning Objectives

Upon completion of this chapter, students should be able to:

• Define cost of capital and explain its relevance
• Explain basic sources of financing
• Calculate the financing weights and explain why market values are preferred to book values
• Calculate the after-tax cost of debt
• Explain why the Yield-to-Maturity is preferred to the coupon rate as the before-tax cost of debt and why debt is expressed as an after-tax cost
• Calculate the cost of preferred stock
• Calculate the cost of common stock using an average of the three different approaches (dividend valuation, SML, and bond yield plus risk premium)
• Explain why we use three different approaches for the cost of common stock financing and issues associated with each of the three methods
• Calculate the cost of capital and use it to evaluate capital budgeting projects
• Explain two key situations where the cost of capital needs modified before it can be used to evaluate capital budgeting projects
• Explain the concept of a target capital structure
• Diagram the cost of capital and value of the firm as the ratio of debt/equity increases
• Explain why the target capital structure may be different for different firms

# What is the Marginal Cost of Capital?

The Marginal Cost of Capital (MCC), which is sometimes called the Opportunity Cost of Capital (OCC) or Weighted Average Cost of Capital (WACC), tells us how much we are paying for our financing. This will help us determine the required return for our investment projects. Specifically, under two basic assumptions (discussed below), the MCC will be the required return that we use when performing capital budgeting analysis from Chapter Eight.

Let’s expand on the idea that the Marginal Cost of Capital represents our cost of financing and, in turn, the required return for our capital budgeting projects. Firms need to raise capital in order to invest in various capital budgeting projects. For instance, if a company wants to spend $500 Million to launch a new satellite they need to find a way to pay for that. There are two primary ways in which companies can raise capital — (A) debt or (B) equity. ## Debt The firm can issue bonds in order to raise capital. ## Equity The firm can have stockholders provide capital in one of three ways. ### PREFERRED STOCK Issuing shares of preferred stock will help provide capital for the firm. ### COMMON STOCK Issuing shares of common stock will help provide capital for the firm. ### INTERNAL EQUITY Any profits that the firm makes and doesn’t pay out to shareholders in the form of dividends can be used to provide capital for future periods. Since this money technically belongs to existing common stockholders, it is considered a form of common stock financing. Some models separate out internally generated equity from the issuance of additional shares, however we will not do this. For the purposes of our class, we will treat both newly issued common stock and internally generated equity as the same since they both represent capital provided by common stockholders. Once we figure out where our financing is coming from, we must figure out how much it is costing us. The details of this are discussed below. Our Marginal Cost of Capital calculation incorporates the cost from each source along with how much financing is being provided from each source. This gives us an average cost for each dollar of financing that we are using as a firm. Once we know how much each dollar of financing is costing us, we can determine if we are using that financing appropriately. For instance, pretend that our MCC is 9.5%. Then, we have the opportunity to invest in a capital budgeting project that has an IRR of 8.5%. That means we are paying 9.5% to raise money and then investing this money to earn 8.5%. Since we are earning less on our investments than it is costing us to raise our money, the project is not worthwhile. On the other hand, if we have a project that will generate an IRR of 12% we will earn more on our investment project than it is costing us to raise our money. This makes the project profitable and we should pursue it. We cannot properly evaluate our capital budgeting projects without having a reasonable estimate of our cost of capital. One of the themes for this chapter is that when we are estimating the costs of each source of financing, we are going to focus on estimating the required return for investors who buy those securities. The idea is that we have been focusing on stocks and bonds previously in this class from the perspective of investors. However, the return that these investors receive is paid by the corporations. Therefore, the investors’ required return is the firm’s cost of capital. This means that we are going to rely on concepts we already have covered that focus on required return, but now instead of referring to it as the required return, we will call it a cost of capital. # When is the MCC appropriately used as the required return for capital budgeting? As mentioned previously, there are two basic conditions that must be met before we can use the MCC as the required return in capital budgeting analysis. These assumptions are as follows: 1. The risk of the project must be of average risk for the firm. The MCC is influenced by the perceived riskiness of the firm as a whole. Since investors set the MCC by “charging” the firm enough to compensate for the risk of investing in the firm. The higher the perceived risk, the more investors will demand as a rate of return (cost of financing). Since the firm can be thought of as the sum of all of its various projects, then we can say that the MCC appropriately captures the risk of the average project. Many projects will be more risky or less risky than what is considered “average.” If we undertake high-risk projects, the average risk of the firm will increase (causing the MCC to increase) so we need to earn more to compensate us for the risk of that project. The opposite holds for low-risk projects. Anytime we evaluate a high-risk project we should use a required return higher than the MCC and anytime we evaluate a low-risk project we should use a required return lower than the MCC. 2. The financing weights should not change in a significant manner due to financing the project. The MCC is based on the financing weights for the firm as a whole. If we alter that financing mix to undertake a project we must account for it. Therefore, if the financing weights for the project are significantly different than our present financing mix, we need to use the weights associated with the project. Another complication that is more difficult to correct is that drastically different financing weights may alter the risk of the firm and thus change financing costs. Specifically, increasing the amount of debt financing should increase the risk of the firm (and result in higher financing costs from each source of financing) while increasing the amount of equity financing should lower the risk of the firm (and result in lower financing costs from each source of financing). # The Key Components of the Cost of Capital There are four critical components that must be estimated in order to estimate the cost of capital. Note: We will be ignoring the role of flotation costs for this course. However, if you are interested in this topic, an optional discussion of flotation costs is provided at the appendix of the chapter. Once these are estimated, we use the following equation to estimate the MCC $MCC=W_{debt}k_{i}+W_{pref}k_{p}+W_{com}k_{s}$ Where Wdebt represents the proportion of total financing coming from LT Debt ki represents the after-tax cost of debt financing Wpref represents the proportion of total financing coming from preferred stock kp represents the cost of preferred stock financing Wcom represents the proportion of total financing coming from common stock ks represents the cost of common stock financing Note that the weights should all be plugged into the formula as a decimal (10% = 0.10) while the costs should be written as a percentage (10% = 10) # Estimating the Market Value Weights of the Financing Components The weights represent the market value weights of each of the components, not the book value. (Note: In many instances, the book value of debt can be a close approximation for the market value of debt. However, if we can estimate the market value we should always use it.) We first estimate the market value of debt, market value of preferred stock and market value of common stock by multiplying the number of shares (or bonds) times the value of each share (or bond). Then we sum up the value of each component. This represents the market value of the firm. The appropriate weight is the market value of that component divided by the market value of the firm. Market values are preferred because they are always current, taking into account investors’ current outlook on our firm’s prospects and risks and are the best measure of what the securities are worth. # Estimating the After-Tax Cost of Debt The after-tax cost of debt is found through the following equation $k_{i}=YTM(1-T)$ Where ki represents the after-tax cost of debt YTM represents the Yield-to-Maturity on the debt T represents the marginal tax rate on interest It is critical to note that we must use the after-tax cost of debt as opposed to the before-tax cost of debt. Interest appears on the income statement before taxes. This means that each dollar paid in interest lowers our tax bill. The Federal government is paying part of our interest bill for us through this reduction in tax expense. Unfortunately, dividends are paid after taxes, so this adjustment is only for debt, not preferred or common stock. In addition, it is important to note that we use the YTM here as the before-tax cost of debt instead of the coupon rate. It is easy to think that the coupon rate would be better as that is the actual dollar amount paid to investors each year. However, that ignores the true cost to the firm (return to the investor). If investors pay a premium to buy the bond (pay more than$1000), then the effective cost of the bond will be less than the coupon rate. Alternatively, if investors buy the bond at a discount, then the effective cost of the bond will be higher than the coupon rate. Consider a zero-coupon bond. This is not free financing just because it doesn’t pay a coupon payment. Instead, the firm will receive substantially less than $1000 per bond today, but be forced to pay out the$1000 at the bond’s maturity with the difference (spread over the life of the bond) representing the cost of interest. The YTM takes into account coupon payments and spreading the premium/discount out over the life of the bond.

While we typically will only encounter one source of debt financing in this class, it is not uncommon for firms to end up issuing many bonds with different coupons and times to maturity. In order to estimate the cost of debt in this type of situation, a weighted average of each bond can be used.

# Estimating the Cost of Preferred Stock

The cost of preferred stock is found through the following equation

$k_{p}=\frac{D}{P_{0}}=\frac{(par value)(dividend rate)}{P_{0}}$

Where

kp represents the cost of preferred stock financing
D represents the dividend on preferred stock (alternatively found by taking the par value times the dividend rate on the preferred)
P0 represents the current price of the preferred stock

Note that here (as with other costs), we are merely solving for the investors’ required return on preferred stock as their return is the firm’s cost of financing from preferred. One common mistake students sometimes make here is to use the common dividend instead of preferred. Be careful to use the right dividend. Another common mistake is that when this formula is applied, the answer comes out as a decimal (8% would be 0.08). Assuming you are plugging the other costs in as percent, make sure you do the same with this. You can’t enter the cost of debt as 6 (for 6%) and the cost of preferred as 0.08 (for 8%)…you need to be consistent.

# Estimating the Cost of Common Stock

Common stock gets a little trickier. There is not one correct formula for estimating the cost of common stock financing. Instead there are three. First, we can go back to the constant growth pricing model and solve for ks. This will give us the following formula:

$k_{s}=\frac{D_{1}}{P_{0}}+g=\frac{D_{0}(1+g)}{P_{0}}+g$

Where

ks represents the cost of common stock financing
D1 represents the forecasted dividend next year
D0 represents the current dividend
P0 represents the current price of the common stock
g represents the forecasted constant growth rate

Note that the two formulas are essentially the same. D1 equals D0(1 + g). We use the first version if we are given D1 in the problem and we use the 2nd version if we are given D0 in the problem. Be careful to read the problem carefully and choose the right version for the specific dividend provided.

Because the above formula is derived from the constant growth model, it does not work as well in non-constant growth situations. It also only works for firms that pay dividends. Therefore, while it can be useful in some situations (dividend paying firms with stable growth rates), it would be worthwhile to think about other ways to estimate the required return our common stockholders are charging to provide capital.

One alternative approach is to refer to the Security Market Line. We introduced this in Chapter Seven as a way to estimate the required return associated with common stock. This allows us to estimate the cost of stock financing using the following formula:

$k_{s}=k_{RF}+\beta(\bar{k_{m}}-k_{RF})$

Where

ks represents the cost of common stock financing
kRF is the risk-free rate of interest (often approximated by the yield on 10-year Treasury Bond)
β is the beta for our firm’s stock
$\bar{k_{M}}$ is the expected return on the market

However, while this does not require firms to pay dividends or have stable growth rates, there is some concern as to how well the security market line holds up in practice. Therefore, like the dividend growth model, the SML approach is not perfect. Is there another way we can estimate the cost of common stock financing?

A less theoretical, but still valid, model can also be used to estimate what investors are demanding as appropriate compensation for providing equity capital to the firm. This model simply assumes that stocks are riskier than bonds, so adds a risk premium to the Yield-to-Maturity on our bonds. The exact risk premium to be added is open for debate and will fluctuate based on many factors (economy, investor demographics, etc), however a range of 3% to 7% is probably most appropriate. Thus, we get the following formula

$k_{s}=YTM+Risk Premium$

Where

ks represents the cost of common stock financing
YTM represents the Yield-To-Maturity on our firm’s debt financing

This model is also flawed. Specifically, it is not clear exactly what the risk premium for stocks should be. Second, firms that don’t use long-term debt financing (and there are quite a few firms that do not use long-term debt financing) won’t have bonds outstanding for us to estimate their YTM. Therefore, we have to guess at what their YTM would be (which would introduce more error) or skip this model.

The best approach when estimating the cost of equity financing is to estimate it under all three equations (assuming we can), then take an average of the three methods. However, we may run into a situation where one of the methods produces an answer way out of line with the other two. In this case, it is probably best to eliminate the outlier and only use the two “more reasonable” answers. Also, in some instances, we may not be able to use one of the three cost of equity approaches. In these cases, we just rely on an average of the one’s we can estimate.

# MCC Example

Calculate the Marginal Cost of Capital Based on the following information.

 Price per share of Common Stock $45 Price per share of Preferred Stock$60 Price per Bond ($1000 par value)$865 Number of shares of Common Stock Outstanding 2,300,000 Number of shares of Preferred Stock Outstanding 500,000 Number of Bonds Outstanding 60,000 Coupon Rate on Bonds 5% Time Remaining Until Maturity for Bonds 15 years Marginal Tax Rate 25% Par Value of Preferred Stock $50 Dividend Rate on Preferred Stock 9% Common Stock Dividend (D1)$3.00 Dividend Growth Rate (Common) 6% Risk-Free Rate 5% Beta 1.2 Expected Return on the Market 12% Risk Premium on Stocks over Bonds 4.50%

## Step 1: Find the Weights

MVdebt =60,000*865 = $51,900,000 MVpreferred = 500,000*$60 = $30,000,000 MVcommon = 2,300,000*45 =$103,500,000
1b. $875 ## Problem 2 If the par value of our preferred stock is$30 and the dividend rate is 5% of par while the current price is $16.50, what is the cost of preferred stock? ## Problem 3 The price of our common stock is$25. The constant growth rate in dividends is 8% and our current dividend (D0) is $0.75. Also, the risk-free rate of interest is 5% and the expected return on the market is 12%. Beta for this stock is 0.8. Finally, we estimate a risk premium of 5% for stocks relative to bonds and the current YTM on our long-term debt is 9%. Find the estimated cost of capital for common stock under each of the 3 methods. ## Problem 4 You have the following information about XYZ Corp:  Asset Book Value Market Value Bonds$20,000,000 $24,000,000 Preferred Stock$4,000,000 $5,000,000 Common Stock$10,000,000 $35,000,000  Constant growth on common 6.5% YTM on bonds 11% Beta 1.35 Treasury bond yield 5% Price of common stock$34 Tax rate 40% Coupon rate on bonds 10% Risk prem. stocks over bonds 5% Expected market return (km) 12% Expected Common Dividend (D1) 2.75 Number of pref. shares 100,000 Per share dividend on preferred $6.50 4a. What is the marginal cost of capital for this firm? 4b. If you have a capital budgeting project that will generate after tax cash flows of$25,000 per year for the next four years and costs $75,000, should you take it? ## Problem 5 The following information is available about ACME Inc. Balance Sheet:  LT 10% Coupon Bonds (10,000 bonds)$10,000,000 Preferred Stock (40,000 shares) ($50 par with a 10% dividend) 2,000,000 Common Stock (1,000,000 shares) 20,000,000 The market values are$1060 for each $1000 par value bond,$53 for each share of preferred, and \$41.25 for each share of common. The bonds are recorded on the balance sheet at their par value and mature in 10 years.

 Beta 1.3 Current Treasury bond rate 6% Risk Premium for stocks over bonds 5% Tax Rate 40% Growth rate in dividends 10% Expected market return 13% Dividend (D0) 2.25

5a. What are the appropriate weights for the opportunity cost of capital?
5b. What are the appropriate costs of debt, preferred, and common (use an average of the 3 methods for common)?
5c. What is the marginal cost of capital?

# Student Resources

Floatation Costs in Appendix B 