Steinberg Corporation and Dietrich Corporation are identical firms except that Dietrich is more levered. Both companies will remain in business for one more year. The companies’ economists agree that the probability of the continuation of the current expansion is 90 percent for the next year, and the probability of a recession is 10 percent. If the expansion continues, each firm will generate earnings before interest and taxes (EBIT) of $4.5 million. If a recession occurs, each firm will generate earnings before interest and taxes (EBIT) of $1.9 million. Steinberg’s debt obligation requires the firm to pay $990,000 at the end of the year. Dietrich’s debt obligation requires the firm to pay $2.0 million at the end of the year. Neither firm pays taxes. Assume a discount rate of 14 percent.
| a-1. | What is the value today of Steinberg’s debt and equity? (Enter your answers in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your answers to the nearest whole dollar amount. (e.g., 32)) |
| Steinberg’s | |
| Equity value | $ |
| Debt value | $ |
| a-2. | What is the value today of Dietrich’s debt and equity? (Enter your answers in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your answers to the nearest whole dollar amount. (e.g., 32)) |
| Dietrich’s | |
| Equity value | $ |
| Debt value | $ |
| b. | Steinberg’s CEO recently stated that Steinberg’s value should be higher than Dietrich’s because the firm has less debt and therefore less bankruptcy risk. Do you agree or disagree with this statement? | ||||
|
A-1 What is the value today of Steinberg’s debt and equity?
a. The total value of a firm’s equity is the discounted expected cash flow to the firm’s stockholders.
If the expansion continues, each firm will generate earnings before interest and taxes of $4.5 million. If there is a recession each firm will generate earnings before interest and taxes of only $1.9 million .
Since Steinberg owes its bondholders $990,000 at the end of the year, its stockholders will receive $3510000 (= $4 ,500,000 million – $990,000) if the expansion continues. If there is a recession, its stockholders will only receive $910,000 (= $1900,000 – $990,000).
The market value of Steinberg’s equity is:
{(0.90)($3510000) + (0.10)($910000)} / 1.14 = 2850877.2
The value of Steinberg’s equity is $2850877.2.
Steinberg’s bondholders will receive $750,000 regardless of whether there is a recession or a continuation of the expansion.
The market value of Steinberg’s debt is:
{(0.90)($990,000) + (0.10)($990,000)} / 1.15 = $868421.05
The value of Steinberg’s debt is $868421.05.
| Steinberg’s | |
| Equity value | 2850877.2$ |
| Debt value | 868421.05$ |
2-a What is the value today of Dietrich’s debt and equity
owes its bondholders $2 million at the end of the year, its stockholders will receive $2.5 million (= $4.5 million – $2 million) if the expansion continues. If there is a recession, its stockholders will receive nothing since the firm’s bondholders have a more senior claim on all $1900,000 of the firm’s earnings.
The market value of Dietrich’s equity is:
{(0.90)($2,500,000) + (0.10)($0)} / 1.14 = $1973684.2
The value of Dietrich’s equity is $1973684.2
Dietrich’s bondholders will receive $2 million if the expansion continues and $1900,000 if there is a recession.
The market value of Dietrich’s debt is:
{(0.90)($2,000,000) + (0.10)($1900,000)} / 1.14 = $174561.4
The value of Dietrich’s debt is $174561.4
| Dietrich’s | ||
| Equity value | 1973684.2$ | |
| Debt value | 1745614$ | |
2-b
|
||
. The value of Steinberg is the sum of the value of the firm’s debt and equity.
The value of Steinberg is:
VL = B + S
= $2850877.2+ $868421.05
= $3719298
The value of Steinberg is $3719298.
The value of Dietrich is the sum of the value of the firm’s debt and equity.
The value of Dietrich is:
VL = B + S
= $1973684.2 + 1745614
= $3719298
The two firm’s have the same value. The risk of bankruptcy per se does not affect a firm’s value. It is the actual costs of bankruptcy that decreases firm value. Note: this problem assumes that there are no bankruptcy costs.
The value of Dietrich is also $3719298
