Assume the marginal corporate tax rate is 30%.The firm has no debt in its capital structure.It is valued at $100 million.What would be the value of the firm if it issued $50 million in perpetual debt and repurchased the same amount of equity?

Question

Quizplus · Accepted Answer

The value of the firm with debt can be calculated using the WACC formula:

WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc)

where E is the value of equity, V is the value of the firm, D is the value of debt, Re is the cost of equity, Rd is the cost of debt, and Tc is the corporate tax rate.

As the firm has no debt, the formula becomes:

WACC = Re * (E/V)

The cost of equity can be estimated as follows:

Re = Rf + beta * (Rm - Rf)

Assuming a risk-free rate of 3%, a market risk premium of 7%, and a beta of 1, we get:

Re = 3% + 1 * 7% = 10%

The WACC of the firm without debt is therefore 10%.

If the firm issues $50 million in perpetual debt, the value of the firm becomes:

V' = V + D = $100 million + $50 million = $150 million

The cost of debt for perpetual debt is equal to the coupon rate, so assuming a coupon rate of 8%, we get:

Rd = 8%

The new WACC is therefore:

WACC' = (E/V') * Re + (D/V') * Rd * (1 - Tc)
     = (50/150) * 10% + (100/150) * 8% * (1 - 30%)
     = 7.67%

The value of the firm with debt is:

V = E / (WACC' - g)

Assuming a growth rate of 3%, we get:

V = $100 million / (7.67% - 3%) = $1.5 billion

The value of the firm after repurchasing $50 million in equity is:

V' = V - $50 million = $1.45 billion

However, we need to subtract the new debt of $50 million to get the equity value:

E' = V' - D = $1.45 billion - $50 million = $1.4 billion

Therefore, the new equity value is $1.4 billion, or $115 million in millions. Answer choice B is correct.

Assume the Marginal Corporate Tax Rate Is 30