A firm has a project with an NPV of −$52 million. If it has access to risk-free government financing that can create a permanent annual tax shield of $5 million, what is the APV of the project assuming the risk-free interest rate is 6 percent?
A)−$52 million
B)$5 million
C)$31 million
D)$83 million

Question

Quizplus · Accepted Answer

The formula for APV is APV = NPV + PV of financing side effects.

The financing side effect in this case is the tax shield, which is a perpetuity. Therefore, the present value of the tax shield is calculated using the perpetuity formula:

PV of tax shield = Tax shield / Discount rate 
PV of tax shield = $5 million / 0.06 
PV of tax shield = $83.33 million

Thus, APV = NPV + PV of financing side effects 
APV = -$52 million + $83.33 million 
APV = $31.33 million

Therefore, the APV of the project is $31 million.

A Firm Has a Project with an NPV of −$52