Question

The tax rate is 40%. The company will have the risk free debt 5000 in issue. And the debt will also grow at 3% per year. The risk free rate is 5%. What is rD? What is the Present value of the company’s interest tax shield?

Answer 1

rD = Cost of Debt after tax. Companies can reduce their tax liability by showing the interest on borrowings as an expense. These tax savings reduce the overall cost of debt.

rD = (Risk-free rate + Credit Spread) * (1-tax rate)

In our case the debt is risk free so Credit Spread = 0%

Hence, rD = (5% + 0%) * (1-40%)

rD = 5% * 60% = 3%

Company's interest tax shield = Savings from reduced taxes

Company's interest expense = 5000 * 5% = 250

Tax rate = 40%

Company's interest tax shield = Tax rate * Interest expense

Company's interest tax shield = 40% * 250

Company's interest tax shield = 100

The debt is expected to grow at 3% per year for perpetuity; this means that the Interest tax shield will also grow at 3%.

Hence Growth Rate =3%

As per Gordon's Growth Model

PV of growing perpetuity = Payment (in our case interest tax shield) / (Rate of return - Growth rate)

PV of Growing Interest Tax shield = 100 / (5% - 3%)

PV of Growing Interest Tax shield = 5000