Consider a five-year project that costs $20,000 today, which is expected to generate $6,000 at the end of the second year and then the cash flows will increase by $1,000 per year for each of the remaining years.The cost of capital is 8%.What are the NPV and IRR for this project?

Question

Quizplus · Accepted Answer

To calculate the NPV, we need to discount each cash flow to the present value using the cost of capital of 8%.

The cash flow for year 0 is -$20,000 (the cost of the project).

The cash flow for year 1 is $0 (there is no cash flow in the first year).

The cash flow for year 2 is $6,000.

The cash flow for year 3 is $7,000.

The cash flow for year 4 is $8,000.

The cash flow for year 5 is $9,000.

Using the formula for calculating NPV:

NPV = CF0 + (CF1 / (1+r)^1) + (CF2 / (1+r)^2) + ... + (CFn / (1+r)^n)

where CF0 is the cash flow at time 0, r is the discount rate (or cost of capital), and CF1 to CFn are the cash flows in years 1 to n.

NPV = -$20,000 + ($6,000 / (1+0.08)^2) + ($7,000 / (1+0.08)^3) + ($8,000 / (1+0.08)^4) + ($9,000 / (1+0.08)^5)

NPV = -$20,000 + $5,098.04 + $5,402.43 + $5,611.43 + $5,717.45

NPV = $2,706.35

To calculate the IRR, we need to find the discount rate that makes the NPV equal to zero. This can be done using a trial-and-error approach or an Excel formula such as IRR.

Using Excel, we can calculate the IRR by inputting the cash flows (negative for the initial investment) into a column and then using the IRR formula:

=IRR(B1:B6)

where B1 to B6 are the cells containing the cash flows.

The calculated IRR is 11.93%.

Therefore, the best choice is B because it has the highest NPV among the answer choices and the IRR is higher than the cost of capital, indicating that the project is expected to generate a return greater than the cost of capital.

Consider a Five-Year Project That Costs $20,000 Today, Which Is