No Limitation Transportation (NLT) currently has $50 million in debt outstanding and the interest rate is 10%, The firm plans to increase the outstanding debt amount by 5% each year. If NLT has a marginal corporate tax rate of 40%, and if the interest tax shields have the same risk as the loan, what is the present value of the interest tax shield from the debt?A.$20 millionB.$40 millionC.$10 millionD.$2 million
Question
No Limitation Transportation (NLT) currently has 20 millionB.10 millionD.$2 million
Solution
The interest tax shield is the amount of money a company saves in income taxes because of the tax deductibility of interest expense.
The annual interest expense for NLT is 10% of 5 million.
The tax shield for each year is the interest expense multiplied by the tax rate, which is 2 million.
However, NLT also plans to increase the outstanding debt amount by 5% each year, which means the interest expense and thus the tax shield will increase each year.
To find the present value of the tax shield, we need to discount the tax shield for each year by the interest rate and sum these discounted values. This is a growing perpetuity problem, and the formula for the present value of a growing perpetuity is:
PV = A / (r - g)
where: A = annual payment = $2 million r = discount rate = 10% = 0.10 g = growth rate = 5% = 0.05
Substituting these values into the formula gives:
PV = 2 million / 0.05 = $40 million
Therefore, the present value of the interest tax shield from the debt is 40 million.
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