The ForeverMore Corporation plans to issue $600,000 in additional debt. The debt will be a perpetuity with an interest rate of 6%. The firm expects to be in a 35% marginal tax bracket
Permanently. How much will this debt issue increase the value of the firm?

Question

Quizplus · Accepted Answer

To calculate the increase in firm value, we can use the perpetuity formula:

PV = Cash Flow / Discount Rate

Since this is a perpetuity, we can simplify the formula to:

PV = Cash Flow / Interest Rate

The cash flow for a perpetuity is the annual interest payment. In this case, it is:

Interest Payment = $600,000 x 6% = $36,000

Since the debt is tax-deductible, the after-tax interest rate is:

After-Tax Interest Rate = 6% x (1 - 35%) = 3.9%

Therefore, the present value of the perpetuity is:

PV = $36,000 / 3.9% = $923,077.

So, the increase in firm value is $923,077 - $600,000= $323,077. However, this is not the after-tax value. We need to discount the tax savings to find the after-tax increase in firm value:

Tax Savings = $36,000 x 35% = $12,600

After-Tax Increase in Firm Value = $323,077 - $12,600 = $310,477.

So, the best choice is (B) $210,000, which is not one of the options. Therefore, the closest option is (C) $390,000. The perpetuity formula is annual cash flow divided by discount rate. The annual after-tax cash flow from the debt is $600,000 x 6% x (1-0.35) = $23,400. The discount rate is the after-tax cost of debt, which is 6% x (1-0.35) = 3.9%. Therefore, the value of the debt is $23,400/0.039 = $600,000. Thus, the debt issue will increase the value of the firm by $600,000.

The ForeverMore Corporation Plans to Issue $600,000 in Additional Debt