Question

Aikman Company has an opportunity to invest in one of two projects. Project A requires a \(240,000 investment for new machinery with a four-year life and no salvage value. Project B also requires a \)240,000 investment for new machinery with a three-year life and no salvage value. The two projects yield the following predicted annual results. The company uses straight-line depreciation, and cash flows occur evenly throughout each year. Company

Project A Project B

Sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \(250,000 \)200,000

Expenses Direct materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35,000 25,000

Direct labor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50,000 30,000

Overhead including depreciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90,000 90,000

Selling and administrative expenses . . . . . . . . . . . . . . . . . . . . . . . . . 18,000 18,000

Total expenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193,000 163,000

Pretax income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57,000 37,000

Income taxes (30%) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17,100 11,100

Net income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \( 39,900 \) 25,900

Required

1. Compute each project’s annual expected net cash flows. (Round net cash flows to the nearest dollar.)

2. Determine each project’s payback period. (Round the payback period to two decimals.)

3. Compute each project’s accounting rate of return. (Round the percentage return to one decimal.)

4. Determine each project’s net present value using 8% as the discount rate. For part 4 only, assume that cash flows occur at each year-end. (Round net present values to the nearest dollar.)

Analysis Component

5. Identify the project you would recommend to management and explain your choice.

Short answer

Project Y has a net cash flow of $143,500, the payback period is 2.44 years, the accounting rate of return is 32% and NPV is $125,286. Project Z has a net cash flow of $153,067, the payback period is 2.29 years, the accounting rate of return is 20.8% and NPV is $44,469. Project Y should be recommended.

Step-by-step solution

Step-by-Step SolutionStep 1: Computation of each project’s annual expected cash flows

$$\begin{gathered} \mathbf{Depreciation}\mathbf{}\mathbf{for}\mathbf{}\mathbf{project}\mathbf{}\mathbf{A}\mathbf{=}\frac{\mathrm{Cost}}{\mathrm{Number}\mathrm{of}\mathrm{years}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$240,000}{4} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000} \end{gathered}$$

$\begin{array}{c}\mathbf{Depreciation}\mathbf{}\mathbf{for}\mathbf{}\mathbf{project}\mathbf{}\mathbf{B}\mathbf{=}\frac{\mathrm{Cost}}{\mathrm{Number}\mathrm{of}\mathrm{years}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$240,000}{3}\\ =\$80,000\end{array}$

	Project A	Project B
Net Income	$39,900	$25,900
Depreciation expense	60,000	80,000
Expected net cash flows	$99,900	$105,900

Computation of payback period

$$\begin{gathered} \mathbf{Payback}\mathbf{}\mathbf{Period}\mathbf{}\mathbf{of}\mathbf{}\mathbf{projectA}\mathbf{=}\frac{\mathrm{Cost}\mathrm{of}\mathrm{Investment}}{\mathrm{Annual}\mathrm{net}\mathrm{cashflow}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$240,000}{\$99,900} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{40}\mathbf{years} \end{gathered}$$

$$\begin{gathered} \mathbf{Payback}\mathbf{}\mathbf{Period}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Project}\mathbf{}\mathbf{B}\mathbf{=}\frac{\mathrm{Cost}\mathrm{of}\mathrm{Investment}}{\mathrm{Annual}\mathrm{netcash}\mathrm{flow}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$240,000}{\$105,900} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{27}\mathbf{years} \end{gathered}$$

Computation of accounting rate of return

$$\begin{gathered} \mathbf{Accounting}\mathbf{}\mathbf{rate}\mathbf{}\mathbf{of}\mathbf{}\mathbf{return}\mathbf{}\mathbf{of}\mathbf{}\mathbf{project}\mathbf{}\mathbf{Y}\mathbf{=}\frac{\mathrm{Annual}\mathrm{after}-\mathrm{tax}\mathrm{net}\mathrm{income}}{\mathrm{Annual}\mathrm{average}\mathrm{investment}}\mathbf{\times }\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$39,900}{\$120,000}\mathbf{\times }\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{33}\mathbf{.}\mathbf{25}\mathbf{\%} \end{gathered}$$

$$\begin{gathered} \mathbf{Accounting}\mathbf{}\mathbf{rate}\mathbf{}\mathbf{of}\mathbf{}\mathbf{return}\mathbf{}\mathbf{of}\mathbf{}\mathbf{project}\mathbf{}\mathbf{Z}\mathbf{=}\frac{\mathrm{Annual}\mathrm{after}-\mathrm{tax}\mathrm{net}\mathrm{income}}{\mathrm{Annual}\mathrm{average}\mathrm{investment}}\mathbf{\times }\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$25,900}{\$120,000}\mathbf{\times }\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{21}\mathbf{.}\mathbf{58}\mathbf{\%} \end{gathered}$$

Calculation of net present value using 8% as the discount rate

Project Y

Chart values are based on:
N = 4 I = 8%
Select chart	Amount x	PV Factor =	Present Value
Present value of an annuity of 1	$99,900	3.3121	$330,879
Present Value of cash inflows			$330,879
Present value of cash outflows			240,000
Net Present value			$90,879

Project Z

Chart values are based on:
N = 3 I = 8%
Select chart	Amount x	PV Factor =	Present Value
Present value of an annuity of 1	$105,900	2.5771	$272,915
Present Value of cash inflows			$272,915
Present value of cash outflows			240,000
Net Present value			$32,915

Comparison

Project A must be recommended over project B as it has a higher accounting rate of return and a higher net present value.