Question

Suppose DFB restructures its existing debt and will pay $80 million in interest each year for the next 10 years, and then repay the principal of $1.6 billion in year 10. These payments are risk free, and DFB’s marginal tax rate will remain 25% throughout this period. If the risk-free interest rate is 5%, by how much does the interest tax shield increase the value of DFB?

A) $470 million.
B) $154 million.
C) $642 million.
D) $530 million

Answer 1

The present value of the interest tax shield that increases the value of DFB is $154 million, which is calculated by finding the present value of the annual tax shield using the formula for the present value of an annuity with a 5% discount rate over 10 years.

Step-by-step explanation:

To calculate how much the interest tax shield increases the value of DFB, we need to calculate the present value of the tax savings from the interest payments. Since DFB is restructuring its existing debt to pay $80 million in interest each year for the next 10 years, with a marginal tax rate of 25%, the annual tax shield is 25% × $80 million = $20 million. The present value of this annual tax shield, discounted at the risk-free rate of 5%, is the sum of the present values of all tax shields over the 10-year period.

Using the formula for present value of an annuity:

PV = C × [(1 - (1 + r)^-n) / r]

Where C is the annual cash flow (tax shield), r is the discount rate, and n is the number of periods:

PV = $20 million × [(1 - (1 + 0.05)^-10) / 0.05]

PV = $20 million × [7.72173]

PV = $154.43 million

Therefore, the interest tax shield increases the value of DFB by $154 million, which corresponds to option B.

Answer 2

The interest tax shield increases the value of DFB by $154 million. This is calculated by discounting the annual tax savings from the $80 million interest payments at the firm's marginal tax rate of 25% and using a risk-free rate of 5%.

Step-by-step explanation:

To calculate the increase in value of DFB due to the interest tax shield, we must compute the present value of the tax savings from the $80 million in interest payments. With DFB's marginal tax rate at 25%, the annual tax savings is $80 million times 25%, or $20 million. To find the present value of these savings, we discount them using the risk-free rate of 5%. Using the formula for the present value of an annuity, we calculate the present value of the tax shield over 10 years, which is:

PV = Tax Savings per year * [(1 - (1 + r)^(-n)) / r]

Here, r is the discount rate (5%) and n is the number of periods (10 years). The calculation yields:

PV = $20 million * [(1 - (1 + 0.05)^(-10)) / 0.05]

PV = $20 million * 7.721

PV = $154.43 million

Therefore, the interest tax shield increases the value of DFB by $154 million.