13 Chapter Capital Structure and Leverage
Business vs. financial risk Optimal capital structure Operating leverage Capital structure theory
Campus Deli Inc.'s Optimal Capital Structure Assume that you have just been hired as business manager of Campus Deli (CD), which is located adjacent to the campus. Sales were $1,100,000 last year; variable costs were 60 percent of sales; and fixed costs were $40,000. Therefore, EBIT totaled $400,000. Because the university's enrollment is capped, EBIT is expected to be constant over time. Because no expansion capital is required, CD pays out all earnings as dividends. Assets are $2 million, and 80,000 shares are outstanding. The management group owns about 50 percent of the stock, which is traded in the over-the-counter market. CD currently has no debt--it is an all-equity firm and its 80,000 shares outstanding sell at a price of $25 per share, which is also the book value. The firm's federal-plus-state tax rate is 40 percent. On the basis of statements made in your finance text, you believe that CD's shareholders would be better off if some debt financing were used. When you suggested this to your new boss, she encouraged you to pursue the idea, but to provide support for the suggestion. In today's market, the risk-free rate, rRF , is 6 percent and the market risk premium, RPM , is 6 percent. CD's unlevered beta, bU , is 1.0. CD currently has no debt, so its cost of equity (and WACC) is 12 percent. If the firm were recapitalized, debt would be issued, and the borrowed funds would be used to repurchase stock. Stockholders, in turn, would use funds provided by the repurchase to buy equities in other fast-food companies similar to CD.
C. To develop an example of the effects of financial leverage, that can be presented to CD's management as an illustration, consider two hypothetical firms, Firm U, with zero debt financing, and Firm L, with $10,000 of 12 percent debt. Both firms have $20,000 in total assets and a 40 percent federal-plus-state tax rate, and they have the following EBIT probability distribution for next year: Probability 0.25 0.50 0.25 EBIT $2,000 3,000 4,000
(1) Complete the partial income statements and the firms' ratios
Table IC 13-1. Income Statements and Ratios
Assets Equity Probability Sales Oper. costs EBIT Int. (12%) EBT Taxes (40%) Net income BEP ROE TIE
Firm U (Unleveraged) $20,000 $20,000 $20,000 $20,000 $20,000 $20,000 0.25 6,000 4,000 2,000 0 2,000 800 1,200 10.0% 6.0% 0.50 9,000 6,000 3,000 0 3,000 1,200 1,800 0.25 $12,000 8,000 $ 4,000 0 $ 4,000 1,600 $ 2,400 20.0% 12.0%
Firm L (Leveraged) $20,000 $20,000 $20,000 $10,000 $10,000 $10,000 0.25 6,000 4,000 2,000 1,200 800 320 480 10.0% 4.8% 1.7 0.50 $ 9,000 6,000 $ 3,000 $ $ % % 0.25 $12,000 8,000 $ 4,000 1,200 $ 2,800 1,120 $ 1,680 20.0% 16.8% 3.3
$ $ $ $
$ $ $ $
$ $ $ $
15.0% 9.0%
E(BEP) E(ROE) E(TIE)
BEP ROE TIE
15.0% 9.0% 2.5 3.5% 2.1% 0
% %
% 4.2% 0.6
(2) Be prepared to discuss each entry in the table and to explain how this example illustrates the effect of financial leverage on expected rate of return and risk.
1. How is the firm's basic-earning power, BEP = EBIT/Total assets, affected by financial leverage?
2.
Which firm has the higher expected ROE?
3. Which firm has more financial risk? Measure the financial risk, in a stand-alone risk sense.
4. How do each firm's ROE compare when EBIT = $2,000? When EBIT = $3,000?
5. How does leverage affect expected ROE?
6. How is TIE affected when using 50% debt? What would happen to TIE if less debt were used? If more debt were used?
D. Now consider the optimal capital structure for CD. (1) To begin, define the terms "optimal capital structure" and "target capital structure." The optimal capital structure is the capital structure at which the tax-related benefits of leverage are exactly offset by debt's risk-related costs. At the optimal capital structure: (1) the total value of the firm is maximized, (2) the WACC is minimized, and the price per share is maximized. The target capital structure is the mix of debt, preferred stock, and common equity with which the firm plans to raise capital. Sequence of events in a recapitalization. Firm announces the recapitalization. New debt is issued. Proceeds are used to repurchase stock. o The number of shares repurchased is equal to the amount of debt issued divided by price per share. After speaking with a local investment banker, you obtain the following estimates of the cost of debt at different debt levels (in thousands of dollars): Amount D/A D/E Bond Borrowed Ratio Ratio Rating rd $0 0 0 -- -- 250 500 750 1,000 0.125 0.250 0.375 0.500 0.1429 0.3333 0.6000 1.0000 AA A BBB BB 8.0% 9.0 11.5 14.0
Why do the bond rating and cost of debt depend upon the amount of debt borrowed? As the firm borrows more money, the firm increases its financial risk causing the firm's bond rating to decrease, and its cost of debt to increase. (2) Why does CD's bond rating and cost of debt depend on the amount of money borrowed?
(3) Assume that shares could be repurchased at the current market price of $25 per share. Calculate CD's expected EPS and TIE at debt levels of $0, $250,000, $500,000, $750,000, and $1,000,000. How many shares would remain after recapitalization under each scenario?
At D = $0: EPS =
[EBIT rd (D)](1 T ) [$400,000 rd (0)](1 0.4) $400,000(0.6) = = Shares outstanding 80,000 80,000
= $3.00.
EBIT $400,000 TIE = Interest = = . 0
At D = $250,000: Shares repurchased = $250,000/$25 = 10,000. Remaining shares outstanding = 80,000 10,000 = 70,000. EPS =
[$400,000 0.08 ($250,000)](0.6) = $3.26. 70,000
TIE =
$400,000 = 20 . $20,000
At D = $500,000: Shares repurchased = Remaining shares outstanding =
At D = $750,000: Shares repurchased = Remaining shares outstanding =
At D = $1,000,000: Shares repurchased = $1,000,000/$25 = 40,000. Remaining shares outstanding = 80,000 40,000 = 40,000. EPS =
[$400,000 0.14($1,000,000)](0.60) = $3.90. 40,000
TIE =
$400,000 = 2.9 . $140,000
Finding Optimal Capital Structure The firm's optimal capital structure can be determined two ways: o Minimizes WACC. o Maximizes stock price. Both methods yield the same results. Maximizes stock price: Using the Hamada equation, what is the cost of equity if CD recapitalizes with $250,000 of debt? $500,000? $750,000? $1,000,000?
the Hamada equation: bL = bU[1 + (1 T)(D/E)].
rRF = 6.0% bU = 1.0 Tax rate = 40.0% Amount Borrowed $ 0 250 500 750 1,000
e
rM rRF = 6.0% Total assets = $2,000
Debt/Assets Ratio 0.00% 12.50 25.00 37.50 50.00
Debt/Equity Ratio 0.00% 14.29
Levered Beta 1.00 1.09
rs e 12.00% 12.51
100.00
1.60
15.60
Calculated using the CAPM, rs = rRF + (rM rRF)b, given the risk-free rate, the risk
premium, market and using the levered beta as calculated with the Hamada equation. What effect does more debt have on a firm's cost of equity? If the level of debt increases, the riskiness of the firm increases. We have already observed the increase in the cost of debt. However, the riskiness of the firm's equity also increases, resulting in a higher rs.
Minimizes WACC: Considering only the levels of debt discussed, what is the capital structure that minimizes CD's WACC?
rRF = 6.0% bU = 1.0 Tax rate = 40.0% Amount Borrowed
a
rM rRF = 6.0% Total assets = $2,000
Debt/Asset s Ratiob
0.00% 12.50 25.00 37.50 50.00
Notes:
a b c d e f
Equity/Assets Debt/Equity Ratioc Ratiod
100.00% 87.50 75.00 62.50 50.00 100.00 0.00% 14.29
Levered Betae
1.00 1.09
rsf
12.00% 12.51
rda
0.0% 8.0
rd(1 T)
0.0% 4.8
WACCg
12.00% 11.55
$
0 250 500 750
1,000
1.60
15.60
14.0
8.4
12.00
Data given in problem. Calculated as amount borrowed divided by total assets. Calculated as 1 D/A. Calculated as amount borrowed divided by equity (total assets less amount borrowed). Calculated using the Hamada equation, bL = bU[1 + (1 T)(D/E)]. Calculated using the CAPM, rs = rRF + (rM rRF)b, given the risk-free rate, the market risk premium, and using the
levered beta as calculated with the Hamada equation.
g
Calculated using the WACC equation, WACC = wdrd(1 T) + wcrs.
(6) What would be the new stock price if CD recapitalizes with $250,000 of debt? $500,000? $750,000? $1,000,000? Recall that the payout ratio is 100 percent, so g = 0. We can calculate the price of a constant growth stock as DPS divided by rs minus g, where g is the expected growth rate in dividends:
P0
D1 rs - g
EPS rs
DPS rs
Since in this case all earnings are paid out to the stockholders, DPS = EPS.
Further, because no earnings are plowed back, the firm's EBIT is not expected to grow, so g = 0. Here are the results: Debt Level $ 0 250,000 500,000 750,000 1,000,000 *Maximum DPS $3.00 3.26 rs 12.00% 12.51 Stock Price $25.00 26.03
3.90
15.60
25.00
(7) Is EPS maximized at the debt level that maximizes share price? Why or why not? We have seen that EPS continues to increase beyond the $500,000 optimal level of debt. Therefore, focusing on EPS when making capital structure decisions is not correct-- while the EPS does take account of the differential cost of debt, it does not account for the increasing risk that must be borne by the equity holders.
D.
(8)
Considering only the levels of debt discussed, what is CD's optimal capital structure?
D.
(9)
What is the WACC at the optimal capital structure? Initial debt level: Debt/Total assets = 0%, so Total assets = Initial equity = $25 $2,000,000. WACC = 80,000 shares =
Answer:
$500,000 $1,500,000 (9%)(0.60) + (13.2%) $2 ,000,000 $2 ,000,000
= 1.35% + 9.90% = 11.25%. Note: If we had (1) used the equilibrium price for repurchasing shares and (2) used market value weights to calculate WACC, then we could be sure that the WACC at the price-maximizing capital structure would be the minimum. Using a constant $25 purchase price, and book value weights, inconsistencies may creep in.
Modigliani and Miller proved, under a very restrictive set of assumptions, that the value of a firm will be maximized by financing almost entirely with debt. Why, according to MM, is debt beneficial? MM argued that using debt increases the value of the firm because interest is tax deductible. The government, in effect, pays part of the interest, and this lowers the cost of debt relative to the cost of equity, making debt financing more attractive than equity financing. Put another way, since interest is deductible, the more debt a company uses, the lower its tax bill, and the more of its operating income flows through to investors, so the greater its value. What assumptions underlie the MM theory? Are these assumptions realistic? MM's key assumptions are as follows: 1. 2. 3. 4. There are no brokerage costs. There are no taxes. Investors can borrow at the same rate as corporations. Investors have the same information as managers about the firm's future investment opportunities. 5. All of the firm's debt is riskless, regardless of how much it uses. (There are no bankruptcy costs.) 6. EBIT is not affected by the use of debt.
These assumptions are obviously unrealistic--investors do incur brokerage fees and personal income taxes; they cannot borrow at the same rate as corporations; and they do not have the same information as the firm's managers regarding future investment opportunities. Also, corporate debt is risky, especially if a firm uses lots of debt, and the interest rate will rise as the debt level increases.
Figure IC 13-1. Relationship between Capital Structure and Stock Price
Value of Firm's Stock
0
D1
D2
Leverage, D/A
G.
Put labels on Figure IC 13-1, and then discuss the graph as you might use it to explain to your boss why CD might want to use some debt. The use of debt permits a firm to obtain tax savings from the deductibility of interest. So the use of some debt is good; however, the possibility of bankruptcy increases the cost of using debt. At higher and higher levels of debt, the risk of bankruptcy increases, bringing with it costs associated with potential financial distress. Customers reduce purchases, key employees leave, and so on. There is some point, generally well below a debt ratio of 100%, at which problems associated with potential bankruptcy more than offset the tax savings from debt. Theoretically, the optimal capital structure is found at the point where the marginal tax savings just equal the marginal bankruptcy-related costs. However, analysts cannot identify this point with precision for any given firm, or for firms in general. Analysts can help managers determine an optimal range for their firm's debt ratios, but the capital structure decision is still more judgmental than based on precise calculations.
You might expect the price of a mature firm's stock to decline if it announces a stock offering. Would you expect the same reaction if the issuing firm were a young, rapidly growing company? If a mature firm sells stock, the price of its stock would probably decline. A mature firm should have other financing alternatives, so a stock issue would signal that its earnings potential is not good. A young, rapidly growing firm, however, may have so many good investment opportunities that it simply cannot raise all the equity it needs as retained earnings, and investors know this. Therefore, the stock price of a young, rapidly growing firm would probably not fall because of a new stock issue, especially if the firm's managers announce that they are not selling any of their own shares in the offering.