Practice Question
Find the correct answer for the following prompts:
A) You are considering an investment at a price of $190,000, and its after-tax net cash flows will increase by $30,000 per year and remain at this level forever. If the appropriate cost of capital is 15%, what is the NPV?
B) Project A requires a $1,290 initial investment and returns $600 per year forever, and Project B requires a $2,407 initial investment and returns $700 per year forever. What is the crossover point?
C) You’re considering a project with an initial cost of $70,189 with annual cash inflows of $17,304 per year forever. What is the discount rate that will produce a profitability index of 4.0?
A) $10,000
B) 8.95%
C) 6.16%
PV of perpetuity = C / r = 30,000 / 0.15 = 200,000
NPV = 200,000 - 190,000 = $10,000
Let r be the rate where NPVs are equal:
(600 / r) - 1,290 = (700 / r) - 2,407
Solve: 1,117 = 100 / r → r = 100 / 1,117 ≈ 8.95%
PI = PV / Initial = 4.0 → PV = 4.0 × 70,189 = 280,756
280,756 = 17,304 / r → r = 17,304 / 280,756 ≈ 6.16%