An investor is considering a project that will generate $800,000 per year for four years.In addition to upfront costs,at the completion of the project at the end of the fifth year there will be shut-down costs of $500,000.If the cost of capital is 5%,based on the NPV,at what upfront costs does this project cease to be worthwhile?
A)$2.32 million
B)$2.44 million
C)$2.58 million
D)$2.84 million
E)$2.96 million

Question

Quizplus · Accepted Answer

To calculate the NPV, we need to discount all future cash flows to their present value using the cost of capital.

PV of cash inflows = $800,000 / (1+0.05)^1 + $800,000 / (1+0.05)^2 + $800,000 / (1+0.05)^3 + $800,000 / (1+0.05)^4 = $2,656,827.84

PV of shutdown costs = $500,000 / (1+0.05)^5 = $384,615.38

NPV = PV of cash inflows - PV of shutdown costs - upfront costs

We want to find the upfront costs that would make the NPV zero, since that would mean the project breaks even.

0 = $2,656,827.84 - $384,615.38 - upfront costs

Upfront costs = $2,272,212.46

Therefore, the project ceases to be worthwhile if the upfront costs are greater than $2.44 million (rounded to the nearest hundred thousand).

An Investor Is Considering a Project That Will Generate $800,000