1. 1 The Cost of Capital Timothy R. Mayes, Ph.D. FIN 3300: Chapter 11

2. 2 What is the “Cost” of Capital? v When we talk about the “cost” of capital, we are talking about the required rate of return on invested funds v It is also referred to as a “hurdle” rate because this is the minimum acceptable rate of return v Any investment which does not cover the firm’s cost of funds will reduce shareholder wealth (just as if you borrowed money at 10% to make an investment which earned 7% would reduce your wealth)

3. 3 The Appropriate Hurdle Rate: An Example v The managers of Rocky Mountain Motors are considering the purchase of a new tract of land which will be held for one year. The purchase price of the land is $10,000. RMM’s capital structure is currently made up of 40% debt, 10% preferred stock, and 50% common equity. This capital structure is considered to be optimal, so any new funds will need to be raised in the same proportions. v Before making the decision, RMM’s managers must determine the appropriate require rate of return. What minimum rate of return will simultaneously satisfy all of the firm’s capital providers?

4. 4 RMM Example (cont.) Because the current capital structure is optimal, the firm will raise funds as follows:

5. 5 RMM Example (Cont.) The following table shows three possible scenarios: Obviously, the firm must earn at least 9.8%. Any less, and the common shareholders will not be satisfied.

6. 6 The Weighted Average Cost of Capital v We now need a general way to determine the minimum required return v Recall that 40% of funds were from debt. Therefore, 40% of the required return must go to satisfy the debtholders. Similarly, 10% should go to preferred shareholders, and 50% to common shareholders v This is a weighted-average, which can be calculated as:

7. 7 Calculating RMM’s WACC v Using the numbers from the RMM example, we can calculate RMM’s Weighted-Average Cost of Capital (WACC) as follows: v Note that this is the same as we found earlier

8. 8 Finding the Weights v The weights that we use to calculate the WACC will obviously affect the result v Therefore, the obvious question is: “where do the weights come from?” v There are two possibilities: Book-value weights Market-value weights

9. 9 Book-value Weights v One potential source of these weights is the firm’s balance sheet, since it lists the total amount of long- term debt, preferred equity, and common equity v We can calculate the weights by simply determining the proportion that each source of capital is of the total capital

10. 10 Book-value Weights (cont.) The following table shows the calculation of the book-value weights for RMM:

11. 11 Market-value Weights v The problem with book-value weights is that the book values are historical, not current, values v The market recalculates the values of each type of capital on a continuous basis. Therefore, market values are more appropriate v Calculation of market-value weights is very similar to the calculation of the book-value weights v The main difference is that we need to first calculate the total market value (price times quantity) of each type of capital

12. 12 Calculating the Market-value Weights The following table shows the current market prices:

13. 13 Market vs Book Values v It is important to note that market-values is always preferred over book-value v The reason is that book-values represent the historical amount of securities sold, whereas market- values represent the current amount of securities outstanding v For some companies, the difference can be much more dramatic than for RMM v Finally, note that RMM should use the 10.27 WACC in its decision making process

14. 14 The Costs of Capital v As we have seen, a given firm may have more than one provider of capital, each with its own required return v In addition to determining the weights in the calculation of the WACC, we must determine the individual costs of capital v To do this, we simply solve the valuation equations for the required rates of return

15. 15 The Cost of Debt v Recall that the formula for valuing bonds is: v We cannot solve this equation directly for k d, so we must use an iterative trial and error procedure (or, use a calculator) v Note that k d is not the appropriate cost of debt to use in calculating the WACC, instead we should use the after-tax cost of debt

16. 16 The After-tax Cost of Debt v Recall that interest expense is tax deductible v Therefore, when a company pays interest, the actual cost is less than the expense v As an example, consider a company in the 34% marginal tax bracket that pays $100 in interest v The company’s after-tax cost is only $66. The formula is:

17. 17 The Cost of Preferred Equity v As with debt, we calculate the cost of preferred equity by solving the valuation equation for k P : v Note that preferred dividends are not tax-deductible, so there is no tax adjustment for the cost of preferred equity

18. 18 The Cost of Common Equity v Again, to find the cost of common equity we simply solve the valuation equation for k CS : v Note that common dividends are not tax-deductible, so there is no tax adjustment for the cost of common equity

19. 19 Flotation Costs v When a company sells securities to the public, it must use the services of an investment banker v The investment banker provides a number of services for the firm, including: Setting the price of the issue, and Selling the issue to the public v The cost of these services are referred to as “flotation costs,” and they must be accounted for in the WACC v Generally, we do this by reducing the proceeds from the issue by the amount of the flotation costs, and recalculating the cost of capital

20. 20 The Cost of Debt with Flotation Costs v Simply subtract the flotation costs (F) from the price of the bonds, and calculate the cost of debt as usual: v Note that we still must adjust this calculation for taxes

21. 21 The Cost of Preferred with Flotation Costs v Simply subtract the flotation costs (F) from the price of preferred, and calculate the cost of preferred as usual:

22. 22 The Cost of Common Equity with Flotation Costs v Simply subtract the flotation costs (F) from the price of common, and calculate the cost of common as usual:

23. 23 A Note on Flotation Costs v The amount of flotation costs are generally quite low for debt and preferred stock (often 1% or less of the face value) v For common stock, flotation costs can be as high as 25% for small issues, for larger issue they will be much lower v Note that flotation costs will always be given, but they may be given as a dollar amount, or as a percentage of the selling price

24. 24 The Cost of Retained Earnings v The firm may choose to finance new projects using only internally generated funds (retained earnings) v These funds are not free because they belong to the common shareholders (i.e., there is an opportunity cost) v Therefore, the cost of retained earnings is exactly the same as the cost of new common equity, except that there are no flotation costs: