Chapter 15 Capital Structure Decisions: Part 1 ANSWERS TO END-OF-CHAPTER QUESTIONS 15-1

a. Capital structure is the manner in which a firm’s assets are financed; that is, the righthand side of the balance sheet. Capital structure is normally expressed as the percentage of each type of capital used by the firm--debt, preferred stock, and common equity. Business risk is the risk inherent in the operations of the firm, prior to the financing decision. Thus, business risk is the uncertainty inherent in a total risk sense, future operating income, or earnings before interest and taxes (EBIT). Business risk is caused by many factors. Two of the most important are sales variability and operating leverage. Financial risk is the risk added by the use of debt financing. Debt financing increases the variability of earnings before taxes (but after interest); thus, along with business risk, it contributes to the uncertainty of net income and earnings per share. Business risk plus financial risk equals total corporate risk. b. Operating leverage is the extent to which fixed costs are used in a firm’s operations. If a high percentage of a firm’s total costs are fixed costs, then the firm is said to have a high degree of operating leverage. Operating leverage is a measure of one element of business risk, but does not include the second major element, sales variability. Financial leverage is the extent to which fixed-income securities (debt and preferred stock) are used in a firm’s capital structure. If a high percentage of a firm’s capital structure is in the form of debt and preferred stock, then the firm is said to have a high degree of financial leverage. The breakeven point is that level of unit sales at which costs equal revenues. Breakeven analysis may be performed with or without the inclusion of financial costs. If financial costs are not included, breakeven occurs when EBIT equals zero. If financial costs are included, breakeven occurs when EBT equals zero.

15-4

Operating leverage affects EBIT and, through EBIT, EPS. Financial leverage has no effect on EBIT--it only affects EPS, given EBIT.

15-5

If sales tend to fluctuate widely, then cash flows and the ability to service fixed charges will also vary. Such a firm is said to have high business risk. Consequently, there is a relatively large risk that the firm will be unable to meet its fixed charges, and interest payments are fixed charges. As a result, firms in unstable industries tend to use less debt than those whose sales are subject to only moderate fluctuations.

15-8

The tax benefits from debt increase linearly, which causes a continuous increase in the firm’s value and stock price. However, financial distress costs get higher and higher as more and more debt is employed, and these costs eventually offset and begin to outweigh the benefits of debt.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS 15-9

a. Present situation (50% debt): WACC = wd rd(1-T) + wcers = (0.5)(10%)(1-0.15) + (0.5)(14%) = 11.25%. V=

FCF ( EBIT )(1  T ) ($13.24)(1  0.15) = $100 million.   WACC WACC 0.1125

70 percent debt: WACC = wd rd(1-T) + wcers = (0.7)(12%)(1-0.15) + (0.3)(16%) = 11.94%. V=

FCF ( EBIT )(1  T ) ($13.24)(1  0.15) = $94.255 million.   WACC WACC 0.1194

30 percent debt: WACC = wd rd(1-T) + wcers = (0.3)(8%)(1-0.15) + (0.7)(13%) = 11.14%. V=

FCF ( EBIT )(1  T ) ($13.24)(1  0.15) = $101.023 million.   WACC WACC 0.1114

15-10 a. BEA’s unlevered beta is bU=b/(1+ (1-T)(D/S))=1.0/(1+(1-0.40)(20/80)) = 0.870. b. b = bU (1 + (1-T)(D/S)). At 40 percent debt: bL = 0.87 (1 + 0.6(40%/60%)) = 1.218. rS = 6 + 1.218(4) = 10.872% c. WACC = wd rd(1-T) + wcers = (0.4)(9%)(1-0.4) + (0.6)(10.872%) = 8.683%. V=

FCF ( EBIT )(1  T ) ($14.933)(1  0.4) = $103.188 million.   WACC WACC 0.08683

15-11 Tax rate = 40% bU = 0.8

rRF = 5.0% rM – rRF = 6.0%

From data given in the problem and table we can develop the following table: Levered wce  D/S  rd rd(1 – T) rsb  WACCc wd  betaa 0 0.2 0.4 0.6 0.8

100% 80% 60% 40% 20%

0.00 0.25 0.67 1.50 4.00

6.0% 7.0% 8.0% 9.0% 10.0%

3.60% 4.20% 4.80% 5.40% 6.00%

0.80 0.92 1.12 1.52 2.72

9.80% 10.52% 11.72% 14.12% 21.32%

9.80% 9.26% 8.95% 8.89% 9.06%

Notes: a These beta estimates were calculated using the Hamada equation, b = bU[1 + (1 – T)(D/S)]. b These rs estimates were calculated using the CAPM, rs = rRF + (rM – rRF)b. c These WACC estimates were calculated with the following equation: WACC = wd(rd)(1 – T) + (wce)(rs). The firm’s optimal capital structure is that capital structure which minimizes the firm’s WACC. The WACC is minimized at a capital structure consisting of 60% debt and 40% equity. At that capital structure, the firm’s WACC is 8.89%.

Chapter 16 Capital Structure Decisions: Part II ANSWERS TO END-OF-CHAPTER QUESTIONS 16-4

The value of a growing tax shield is greater than the value of a constant tax shield. This means that for a given initial level of debt a growing firm will have more value from the debt tax shield than a non-growing firm. Thus for a given face value of debt, D, and unlevered value of equity, U, a growing firm will have a smaller wD, a larger levered cost of equity, reL, and a larger WACC. So the MM model will underestimate the value of the levered firm and its cost of equity and WACC.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS 16-4

a. bL = bU[1 + (1 - T)(D/S)]. bU =

bL 1.8 1.8 = = = 1.125. 1  (1  T )( D / S) 1  (1  0.4)(0.5 / 0.5) 1.6

b. rsU = rRF + (rM - rRF)bU = 10% + (5%)1.125 = 10% + 5.625% = 15.625%. c. $2 Million Debt: VL = VU + TD = $10 + 0.25($2) = $10.5 million. rsL = rsU + (rsU - rRF)(1 - T)(D/S) = 15.625% + (15.625% - 10%)(0.75)($2/$8.5) = 15.625 + 5.625% (0.75)($2/$8.5) = 16.62%. $4 Million Debt: VL = $10 + 0.25($4) = $11.0 million. rsL = 15.625% + 5.625%(0.75)($4/$7) = 18.04%. $6 Million Debt: VL = $10 + 0.25($6) = $11.5 million. rsL = 15.625% + 5.625% (0.75)($6/$5.5) = 20.23%.

d. $6 Million Debt: VL = $8.0 + 0.40($6) = $10.4 million. rsL = 15.625% + 5.625%(0.60)($6/$4.4) = 20.23%. The mathematics of MM result in the required return, and, thus, the same financial risk premium. However, the market value debt ratio has increased from $6/$11.5 = 52% to $6/$10.4 = 58% at the higher tax rate. Hence, a higher tax rate reduces the financial risk premium at a given market value debt/equity ratio. This is because a higher tax rate increases the relative benefits of debt financing. 16-5

a. VU =

EBIT $2 million = = $20 million. rsU 0.10

b. rsU = 10.0%. (Given) rsL = rsU + (rsU - rd)(D/S) = 10% + (10% - 5%)($10/$10) = 15.0%. c. SL =

EBIT  rd D $2  0.05($10) = $10 million. = rsL 0.15

SL + D = VL = VU + TD. $10 + $10 = $20 = VL = $20 + (0)$10 = $20 million.

d. WACCU = rsU = 10%. For Firm L, we know that WACC must equal rsU = 10% according to Proposition I. But, we can demonstrate this as follows: WACCL = (D/V)rd + (S/V)rs = ($10/$20)5% + ($10/$20)15% = 2.5% + 7.5% = 10.0%.

e. VL = $22 million is not an equilibrium value according to MM. Here’s why. Suppose you owned 10 percent of Firm L’s equity, worth 0.10($22 million - $10 million) = $1.2 million. Your cash flow is equal to 10% of the dividends paid by the levered firm. Because it is a zero-growth firm, its dividends are equal to its net income: Dividends = Net income = EBIT – rdD = $2,000,000 – 0.05($1,000,000) = $1,500,000. Your 10% share is 0.10($1,500,000) = $150,000. Therefore, your annual cash flow is $150,000. Now consider the following strategy. You could (1) sell your stock in firm L for 0.10($2 million) = $1.2 million. Then you could borrow an amount (at 5%) equal to 10 percent of Firm L’s debt, or 0.10($10 million) = $1 million. You would have $1.2 million + $1 million = $2.2 million. You could spend $2 million of this to buy 10% of Firm U’s stock, and invest the remaining $200,000 in risk-free debt. Your cash stream would now be: (a) 10 percent of firm U’s diviedends, which is $200,000: 0.10(EBITU) = 0.10($2 million) = $200,000; plus (b) the return on the extra $200,000 profit you invested in risk-free debt, which is $10,000: rd(profit) = 0.05($200,000) = $10,000; minus (c) the interest expense on the $1 million you borrowed, which is $50,000: rd(loan) = 0.05($1 million)] = $50,000. Your net cash flow from this strategy is $200,000 + $10,000 - $50,000 = $160,000. Since the second strategy produces $160,000 annually while your position in L produces only $150,000, all investors would prefer the second strategy. The pressure to sell L’s stock would cause its price to fall, and the pressure to buy U’s stock would cause its price to increase. This would continue until VL = VU. 16-6

a. VU =

EBIT(1  T ) $2(1  0.4) = = $12 million. rsU 0.10

VL = VU + TD = $12 + (0.4)$10 = $16 million. b. rsU = 0.10 = 10.0%. rsL = rsU + (rsU - rd)(1 - T)(D/S) = 10% + (10% - 5%)(0.6)($10/$6) = 10% + 5% = 15.0%. c. SL =

( EBIT  rd D)(1  T ) [$2  0.05($10)]0.6 = = $6 million. rsL 0.15

VL = SL + D = $6 + $10 = $16 million. d. WACCU WACCL

= rsU = 10.00%. = (D/V)rd(1 - T) + (S/V)rs = ($10/$16)5%(0.6) + ($6/$16)15% = 7.50%.

16-9

a. VU = SU =

EBIT $1,600,000 = = $14,545,455. rsU 0.11

VL = VU = $14,545,455. b. At D = $0: rs = 11.0%; WACC = 11.0%

At D = $6 million: rsL = rsU + (rsU – rd)(D/S)  $6,000,000  = 11% + (11% - 6%)   = 11% + 3.51% = 14.51%.  $8,545,455  WACC = (D/V)rd + (S/V)rs  $8,545,455   $6,000,000  =  14.51%  6% +   $14,545,455   $14,545,455  = 11.0%. At D = $10 million:  $10,000,000  rsL = 11% + 5%   = 22.00%.  $4,545,455   $10,000,000   $4,545,455  WACC =   6% +   22%  $14,545,455   $14,545,455  = 11.0%.

Leverage has no effect on firm value, which is a constant $14,545,455 since WACC is a constant 11%. This is because the cost of equity is increasing with leverage, and this increase exactly offsets the advantage of using lower cost debt financing. c. VU = [(EBIT - I)(1 - T)]/rsU = [($1,600,000 - 0)(0.6)]/0.11 = $8,727,273. VL = VU + TD = $8,727,273 + 0.4($6,000,000) = $11,127,273

d. At D = $0: rs = 11.0%. WACC = 11.0%. At D = $6 million: VL = VU + TD = $8,727,273 + 0.4($6,000,000) = $11,127,273. rsL = rsU + (rsU - rd)(1 - T)(D/S) = 11% + (11% - 6%)(0.6)($6,000,000/$5,127,273) = 14.51%. WACC = (D/V)rd(1 - T) + (S/V)rs =($6,000,000/$11,127,273)(6%)(0.6) + ($5,127,273/$11,127,273)(14.51%) = 8.63%. At D = $10 million: VL = $8,727,273 + 0.4($10,000,000) = $12,727,273. rsL = 11% + 5%(0.6)($10,000,000/$2,727,273) = 22.00%. WACC = ($10,000,000/$12,727,273)(6%)(0.6) + ($2,727,273/$12,727,273)(22%) =7.54%. Summary: (in millions) D $0 6 10

V $ 8.73 11.13 12.73

D/V 0% 53.9 78.6

rs 11.0% 14.5 22.0

WACC 11.0% 8.6 7.5

Value (Millions of Dollars) 15 14 13 12 11 10 9 8

25

50

75

100

D/V (%)

e. The maximum amount of debt financing is 100 percent. D = V, and hence

At this level

VL= VU + TD = D $8,727,273 + 0.4D = D D - 0.4D = $8,727,273 0.6D = $8,727,273 D = $8,727,273/0.6 = $14,545,455 = V.

Since the bondholders are bearing the same risk as the equity holders of the unlevered firm, rd is now 11 percent. Now, the total interest payment is $14,545,455(0.11) = $1.6 million, and the entire $1.6 million of EBIT would be paid out as interest. Thus, the investors (bondholders) would get $1.6 million per year, and it would be capitalized at 11 percent: VL =

$1,600,000 = $14,545,455. 0.11

Cost of Capital (%) 25

krsS

20

15

10

WACC 5

krdd(1-T) (1-T) 25

50

75

100

D/V (%)

f. (1) Rising interest rates would cause rd and hence rd(1 - T) to increase, pulling up WACC. These changes would cause V to rise less steeply, or even to decline. (2) Increased riskiness causes rs to rise faster than predicted by MM. Thus, WACC would increase and V would decrease.