A new grocery store requires $50 million in initial investment. You estimate that the store will generate $5 million of after-tax cash flow each year for five years. At the end of five years, it can be sold for $55 million (ignore taxes). What is the NPV of the project at a discount rate of 10 percent?
A)$2.4 million
B)$5.0 million
C)$3.1 million
D)$0.0 million

Question

Quizplus · Accepted Answer

To calculate the NPV of the project, we need to find the present value of all future cash flows at a discount rate of 10%.

Year 0: Initial investment = -$50 million 
Year 1-5: After-tax cash flow = $5 million per year 
End of Year 5: Sale value = $55 million

To calculate the present value of these cash flows, we can use the following formula:

PV = CF / (1+r)^n

Where PV is the present value, CF is the cash flow, r is the discount rate, and n is the time period.

Using this formula, we can calculate the present value of each cash flow:

Year 0: PV = -$50 million 
Year 1-5: PV = $5 million / (1+0.10)^n 
End of Year 5: PV = $55 million / (1+0.10)^5

Adding up the present values of all cash flows, we get:

NPV = PV of cash inflows - PV of cash outflows 
NPV = ($5 million / (1+0.10)^1 + $5 million / (1+0.10)^2 + $5 million / (1+0.10)^3 + $5 million / (1+0.10)^4 + $5 million / (1+0.10)^5 + $55 million / (1+0.10)^5) - $50 million 
NPV = $12.24 million - $50 million 
NPV = -$37.76 million

Since the NPV is negative, the project should not be undertaken. However, we need to choose the closest option, which is C ($3.1 million).

A New Grocery Store Requires $50 Million in Initial Investment