Answer to Question #197269 in Economics for Brian Yusuf

Question

OPQ Inc. considers investment in three mutually exclusive projects. Project A costs $120,000 in Year 0 and generates the free cash flow of $40 thousand per annum during the first three years, and $30 thousand in Years 4 and 5. Project B also costs $120,000 in Year 0 and generates the free cash flow of $30 thousand in Years 1 and 2, and $40 thousand in Years 3 through 5. Project C costs $200,000 in Year 0 and generates the free cash flow of $50 thousand in Years 1 and 2, and $80 thousand in Years 3 through 5. OPQ Inc. considers applying the 14% cost of capital as a discount rate for Projects A and B. Project C is riskier than Projects A and B. Therefore, OPQ Inc. management believes that they should apply the 17% cost of capital as a discount rate for Project C. What is the NPV and the IRR of each project? Which project should OPQ Inc. choose based on the NPV numbers? Which project should OPQ Inc. choose based on the IRR figures?

Answer 1

$NPVa = -120,000 + 40,000/1.14 + 40,000/1.14^2 + 40,000/1.14^3 + 30,000/1.14^4 + 30,000/1.14^5 = 6,208.75.$

$NPVb = -120,000 + 30,000/1.14 + 30,000/1.14^2 + 40,000/1.14^3 + 40,000/1.14^4 + 40,000/1.14^5 = 856.63.$

$NPVc = -200,000 + 50,000/1.17 + 50,000/1.17^2 + 80,000/1.17^3 + 80,000/1.17^4 + 80,000/1.17^5 = 8,391.26.$

IRR is the cost of capital at which NPV = 0, so it is the highest for Project C.

OPQ Inc. should choose Project C based on the NPV and IRR figures.