A project that costs $100,000 yields a cash flow of $18,000 per year for 9 years. How much is the net present value of the project using a 16% cost of capital?

Question

Quizplus · Accepted Answer

To find the net present value (NPV), we need to discount each year's cash flow to its present value and then subtract the initial investment of $100,000. Using a discount rate of 16%, we can calculate the present value of each year's cash flow as follows:

Year 1: $18,000 / (1 + 0.16)^1 = $15,517.24
Year 2: $18,000 / (1 + 0.16)^2 = $13,390.60
Year 3: $18,000 / (1 + 0.16)^3 = $11,546.08
Year 4: $18,000 / (1 + 0.16)^4 = $9,940.66
Year 5: $18,000 / (1 + 0.16)^5 = $8,547.65
Year 6: $18,000 / (1 + 0.16)^6 = $7,344.90
Year 7: $18,000 / (1 + 0.16)^7 = $6,312.28
Year 8: $18,000 / (1 + 0.16)^8 = $5,432.72
Year 9: $18,000 / (1 + 0.16)^9 = $4,690.98

Now we can calculate the NPV as the sum of the present values of each year's cash flow minus the initial investment:

NPV = ($15,517.24 + $13,390.60 + $11,546.08 + $9,940.66 + $8,547.65 + $7,344.90 + $6,312.28 + $5,432.72 + $4,690.98) - $100,000
NPV = $72,134.01 - $100,000
NPV = ($27,865.99)

Therefore, the best choice is C, which is the net present value of the project using a 16% cost of capital. The negative NPV suggests that the project is not a good investment and may not be worth pursuing.

A Project That Costs $100,000 Yields a Cash Flow of $18,000