Fundamentals of Corporate Finance 3rd ed Jonathan Berk Ch16.docx

1、Fundamentals of Corporate Finance 3rd ed Jonathan Berk Ch16Chapter 16Capital StructureNote: All problems in this chapter are available in MyFinanceLab. An asterisk (*) indicates problems with a higher level of difficulty. 1. Plan: In order to calculate the NPV of the project, we must first compute t

2、he free cash flows for that year by calculating the average of the two likely scenarios for cash flows that year. We can then compute the NPV using the NPV formula. Knowing the free cash flows, the discount rate, and the initial investment, we can compute the NPV as well as the equity value. Finally

3、, we can compute the cash flows of the levered equity by computing the risk-free rate of the debt payments and subtracting that from the two likely scenarios for the cash flows used in part (a). Finally, the initial value of the project can be found by subtracting the debt payments of the project fr

4、om the equity value. Execute:a. b. Equity valuec. Debt payments = 100,000, equity receives 20,000 or 70,000 Initial value, by MM, is Evaluate: The NPV rule states to accept a project with positive NPV, such as this project; therefore all else being equal, the company should undertake the project. 2.

5、 Plan: We can find the total market value of the firm without leverage by computing the total value of equity knowing the $2 million in initial capital and the $2 million needed to fund your research. We can compute the fraction of the firms equity you will need to sell to raise the additional $1 mi

6、llion you need using the total value of the firm and the new value of equity after borrowing to get the percentage of equity that must be sold. Finally, we can compute the firms value of equity in both cases, knowing the fraction of the firms equity you will need to sell in both cases. Execute:a. To

7、tal value of equityb. MM says the total value of firm is still $4 million. $1 million of debt implies the total value of equity is $3 million. Therefore, 33% of equity must be sold to raise $1 million.c. In (a), 50% $4 M = $2 M. In (b), 2/3 $3 M = $2 M. Thus, in a perfect market, the choice of capit

8、al structure does not affect the value to the entrepreneur. Evaluate: In this case, changing the capital structure does not affect the value to the owner of the firm, and therefore the owners have more flexibility with their capital structure. 3. Plan: We can use Eq. 16.1 to compute the current mark

9、et value of Acorts equity. To determine its expected return, we will compute the cash flows to equity. The cash flows to equity are the cash flows of the firm net of the cash flows to debt (repayment of principal plus interest). Execute:a. EValue in 1 year b. D = Therefore, c. Without leverage, with

10、 leverage,d. Without leverage, with leverage, Evaluate: The current market value of Acorts equity when unlevered is nearly double the current market value of Acorts equity when levered. The expected return is greater with debt than without, yet the lowest possible realized return of Acorts equity is

11、 less when unlevered as opposed to levered. *4. Plan: We can compute the debt payments and equity dividends for each firm using the capital structure of each firm. We can use Eq. 16.1 to compute the unlevered equity and levered equity of both firms. Execute:a. ABCXYZFCFDebt PaymentsEquity DividendsD

12、ebt PaymentsEquity Dividends$ 8000800500300$ 100001,000500500b. Unlevered Equity = Debt + Levered Equity. Buy 10% of XYZ debt and 10% of XYZ equity, get 50 + (30,50) = (80,100).c. Levered Equity = Unlevered Equity + Borrowing. Borrow $500, buy 10% of ABC, receive (80,100) - 50 = (30, 50). Evaluate:

13、MM Proposition I states that in a perfect capital market, the total value of a firm is equal to the market value of the free cash flows generated by its assets and is not affected by its choice of capital structure. By adding leverage, the returns of the unlevered firm are effectively split between

14、low-risk debt and much higher risk levered equity. Returns of levered equity fall twice as fast as those of unlevered equity if the cash flows decline. Leverage increases the risk of equity even when there is no risk that the firm will default. 5. Plan: We can use Eq. 16.3 to compute the expected re

15、turn of equity in both cases. Execute:a. re = ru + d/e(ru - rd) = 12% + 0.50(12% - 6%) = 15%b. re = 12% + 1.50(12% - 8%) = 18%c. Returns are higher because risk is higherthe return fairly compensates for the risk. There is no free lunch. Evaluate: With no debt, the WACC is equal to the unlevered equ

16、ity cost of capital. As the firm borrows at the low cost of capital for debt, its equity cost of capital rises according to Eq. 16.3. The net effect is that the firms WACC is unchanged. As the amount of debt increases, the debt becomes more risky because there is a chance the firm will default; as a

17、 result, the debt cost of capital also rises. 6. Plan: We can use Eq. 16.3 to compute the cost of equity using the cost of debt, using 95% equity (E) and 5% debt (D). Its unlevered cost of equity, rU, is 9.2%. Execute: At a cost of debt of 6%: Evaluate: With no debt, the WACC is equal to the unlever

18、ed equity cost of capital. As the firm borrows at the low cost of capital for debt, its equity cost of capital rises according to Eq. 16.3. The net effect is that the firms WACC is unchanged. As the amount of debt increases, the debt becomes more risky because there is a chance that the firm will de

19、fault; as a result, the debt cost of capital also rises. 7. Plan: We can find the net income of the firm using the EBIT, interest expense, and the corporate tax rate. We can compute the interest tax shield using Eq. 16.4. Execute:a. Net incomeb. Net income + Interest = 120 + 125 = $245 millionc. Net

20、 income This is 245 - 195 = $50million lower than part (b).d. Interest tax shield = 125 40% = $50 million Evaluate: The gain to investors from the tax deductibility of interest payments is referred to as the interest tax shield. The interest tax shield is the additional amount that a firm would have

21、 paid in taxes if it did not have leverage but can instead pay to investors. 8. Plan: We can find the net income of the firm using the EBIT, interest expense, and the corporate tax rate. Execute:a. Net income will fall by the after-tax interest expense to $20.750 - 1 (1 - 0.35) = $20.10 million.b. F

22、ree cash flow is not affected by interest expenses. Evaluate: Leverage merely changes the allocation of cash flows between debt and equity, without altering the total cash flows of the firm in a perfect capital market. In a perfect capital market, the total value of a firm is equal to the market val

23、ue of the free cash flows generated by its assets and is not affected by its choice of capital structure. 9. Braxton Enterprises currently has debt outstanding of $35 million and an interest rate of 8%. Braxton plans to reduce its debt by repaying $7 million in principal at the end of each year for

24、the next five years. If Braxtons marginal corporate tax rate is 40%, what is the interest tax shield from Braxtons debt in each of the next five years?Year 012345Debt3528211470Interest2.82.241.681.120.56Tax Shield1.120.8960.6720.4480.22410. Plan: We can use Eq. 16.5 to compute the present value of t

25、he tax shield. Execute: Evaluate: We know that in perfect capital markets, financing transactions have an NPV of zero. However, the interest tax deductibility makes this a positive-NPV transaction for the firm. The total value of the levered firm exceeds the value of the firm without leverage due to

26、 the present value of the tax savings from debt. There is an important tax advantage to the use of debt financing. 11. Plan: We can use Eq. 16.3 to compute the value of the firms equity and debt. We can use our answers in parts (b) and (c) to compute the percentage of the value of debt. Execute:a. N

27、et income = 1000 (1 - 40%) = $600. Thus, equity holders receive dividends of $600 per year with no risk.b. Net income Debt holders receive interest of $500 per year D = $10,000.c. With leverage = 6,000 + 10,000 = $16,000 Without leverage = $12,000 Difference = 16,000 - 12,000 = $4,000d. corporate ta

28、x rate Evaluate: MM Proposition I states that in a perfect capital market, the total value of a firm is equal to the market value of the free cash flows generated by its assets and is not affected by its choice of capital structure. By adding leverage, the returns of the unlevered firm are effective

29、ly split between low-risk debt and much higher risk levered equity. Returns of levered equity fall twice as fast as those of unlevered equity if the cash flows decline. Leverage increases the risk of equity even when there is no risk that the firm will default. 12. Plan: We must compute the value of

30、 the tax shield in each year and then compute the present value of the tax shields. Execute:Year 012345Debt10075502500Interest10 7.552.50Tax Shield4 3210PV$8.30 Evaluate: The present value of the annual tax shields is $8.30 million. 13. Plan: We can use Eq. 16.4 to compute the interest tax shield. W

31、e can use Eq. 16.5 to compute the present value of the interest tax shield. Execute:a. Interest tax shieldb. PV(Interest tax shield)c. Interest tax shield = $10 5% 35% = $0.175 million. Evaluate: We know that in perfect capital markets, financing transactions have an NPV of zero. However, the interest tax deductibility makes this a positive-NPV transaction for the firm. The total value of the levered firm exceeds the value of the firm without leverage due to the present value of the tax savings from debt. There is an important tax