Chapter 13 Capital Structure and Leverage 411now have $100,000 of debt with a cost of 12%; hence, its interest expense will be
$12,000. This interest must be paid regardless of the state of the economy—if it is
not paid, the company will be forced into bankruptcy and stockholders will be
wiped out. Therefore, we show a $12,000 cost in Column 4 as a! xed number for
all sales levels. Column 5 shows pretax income; Column 6, the applicable taxes;
and Column 7, the resulting net income. When net income is divided by the equity
investment—which now will be only $100,000 because $100,000 of the $200,000
total assets were! nanced with debt—we! nd the ROE under each demand state.
If demand is terrible and sales are zero, a very large loss will be incurred and the
ROE will be –43.2%. However, if demand is wonderful, ROE will be 76.8%. The
expected ROE is the probability-weighted average, which is 16.8% if the company
uses 50% debt.
Typically, using debt increases the expected rate of return for an investment.
However, debt also increases risk to the common stockholders. This situation
holds with our example—! nancial leverage raises the expected ROE from 12% to
16.8%, but it also increases the risk of the investment as measured by the coef! -
cient of variation, which rises from 1.23 to 1.76.
Figure 13-4 graphs the data in Table 13-2. It demonstrates that using! nancial
leverage increases the expected ROE but that leverage also " attens out the proba-
bility distribution, increases the probability of a large loss, and thus increases the
risk borne by stockholders.
We can also calculate Bigbee’s EPS if it uses 50% debt. With Debt " $0,
10,000 shares would be outstanding; but if half the equity were replaced by debt
(Debt " $100,000), only 5,000 shares would be outstanding. We can determine
the EPS that would result at each of the possible demand levels under the dif-
ferent capital structures.^4 With no debt, EPS would be –$3.60 if demand were
terrible, $2.40 if demand were normal, and $8.40 if demand were wonderful.
With 50% debt, EPS would be –$8.64 if demand were terrible; $3.36 if demand
were normal; and $15.36 if demand were wonderful. Expected EPS would be
$2.40 with no debt but $3.36 with 50%! nancial leverage.
The EPS distributions under the two! nancial structures are graphed in
Figure 13-5, where we use continuous distributions rather than the discrete
(^4) We assume in this example that the! rm could change its capital structure by repurchasing common stock at its book
value of $100,000/5,000 shares " $20 per share. However, the! rm may have to pay a higher price to repurchase its
stock on the open market. If Bigbee had to pay $22 per share, it could repurchase only $100,000/$22 " 4,545 shares;
and in this case, expected EPS would be only $16,800/(10,000 # 4,545) " $16,800/5,455 " $3.08 rather than $3.36.
ROE Probability Distributions for Bigbee Electronics,
F I G U R E 1 3! 4 With and Without Leverage
0 ROE (%)
Probability
Density
50% Debt
0% Debt
12 16.8