Question

A1 Company is considering three long-term capital investment. Relevant data on each project are as follows: Capital Investment Project X Project Y Project Z $110,000 $170,000 $210,000 Annual net income Year Project X Project Y Project Z 1 $12,000 $21,000 $23,000 2 $12,000 $17,000 $18,000 3 $12,000 $11,000 $21,000 4 $12,000 $12,000 $23,000 5 $12,000 $14,000 $17,000 Assumptions: Depreciation is computed by straight-line method with no salvage value The company's cost of capital is 14% Cash flows occur evenly throught the year Instructions: a. Compute the cash payback period for each project (rounded to two decimals) b. Compute the net present value for each project (rounded to nearest dollar) c. Compute the annual rate of return for each project d. Rank the projects on each of the above bases e. Which of the project would your group recommend and why?

Answer 1

Project Y is the optimal choice, boasting the shortest payback period, highest net present value, and a competitive annual rate of return. It promises the best return on investment.

a. Compute the cash payback period for each project:

Project X: $110,000 ÷ $12,000 = 9.17 years

Project Y: $170,000 ÷ $21,000 = 8.10 years

Project Z: $210,000 ÷ $23,000 = 9.13 years

b. Compute the net present value for each project:

To calculate the net present value (NPV) for each project, we need to discount the cash flows to their present value and subtract the initial capital investment. We'll use the formula: NPV = (Cash Flow / (1 + Cost of Capital)^n) - Initial Investment

Project X NPV = ($12,000 / (1 + 0.14)^1) + ($12,000 / (1 + 0.14)^2) + ($12,000 / (1 + 0.14)^3) + ($12,000 / (1 + 0.14)^4) + ($12,000 / (1 + 0.14)^5) - $110,000 = $10,625.49

Project Y NPV = ($21,000 / (1 + 0.14)^1) + ($17,000 / (1 + 0.14)^2) + ($11,000 / (1 + 0.14)^3) + ($12,000 / (1 + 0.14)^4) + ($14,000 / (1 + 0.14)^5) - $170,000 = $28,564.86

Project Z NPV = ($23,000 / (1 + 0.14)^1) + ($18,000 / (1 + 0.14)^2) + ($21,000 / (1 + 0.14)^3) + ($23,000 / (1 + 0.14)^4) + ($17,000 / (1 + 0.14)^5) - $210,000 = $17,761.43

c. Compute the annual rate of return for each project:

To calculate the annual rate of return (ARR) for each project, we need to divide the average net income by the average investment and express it as a percentage.

Project X ARR = ($12,000 + $12,000 + $12,000 + $12,000 + $12,000) ÷ ($110,000 ÷ 2) = 54.55%

Project Y ARR = ($21,000 + $17,000 + $11,000 + $12,000 + $14,000) ÷ ($170,000 ÷ 2) = 52.35%

Project Z ARR = ($23,000 + $18,000 + $21,000 + $23,000 + $17,000) ÷ ($210,000 ÷ 2) = 52.38%

d. Rank the projects on each of the above bases:

- Cash Payback Period: Project Y (8.10 years), Project Z (9.13 years), Project X (9.17 years)

- Net Present Value: Project Y ($28,564.86), Project Z ($17,761.43), Project X ($10,625.49)

- Annual Rate of Return: Project X (54.55%), Project Y (52.35%), Project Z (52.38%)

e. Which project would you recommend and why?

Based on the analysis, I would recommend Project Y because it has the shortest cash payback period, the highest net present value, and a competitive annual rate of return. This project is likely to generate the highest return on investment in the shortest timeframe.