Question

Aster Company is considering an investment in technology to improve its operations. The investment will require an initial outlay of \(800,000 and yield the following expected cash flows. Management requires investments to have a payback period of two years, and it requires a 10% return on its investments.

Period Cash Flow

1 . . . . . . . . . . . . \)300,000

2 . . . . . . . . . . . . 350,000

3 . . . . . . . . . . . . 400,000

4 . . . . . . . . . . . . 450,000

Required

1. Determine the payback period for this investment.

2. Determine the break-even time for this investment.

3. Determine the net present value for this investment.

Analysis Component

4. Should management invest in this project? Explain.

Short answer

The payback period is 2.4 years and the break-even time is 2.8 years and the net present value is $369,840.

Step-by-step solution

Step-by-Step SolutionStep 1: Computation of payback period

Year	Cash Inflow (outflow)	Cumulative net cash inflow (outflow)
0	-$800,000	-$800,000
1	300,000	-500,000
2	350,000	-150,000
3	400,000	250,000
4	450,000	600,000

Calculation of the payback period:
Payback occurs between years:	2	And year	3
Calculate the portion of the year:

$$\begin{gathered} \mathbf{Remaining}\mathbf{}\mathbf{period}\mathbf{=}\frac{\mathrm{Numerator}\mathrm{for}\mathrm{partial}\mathrm{year}}{\mathrm{Denominator}\mathrm{for}\mathrm{partial}\mathrm{year}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$150,000}{\$400,000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{4}\mathbf{years} \end{gathered}$$

The payback period will be 2.4 years.

Break-even time for the investment

Year	Cash inflow (outflow)	Table factor	Present value of cash flows	Cumulative present value of cash flows
0	-$800,000	1.0000	-$800,000	-$800,000
1	300,000	0.9091	272,730	-527,270
2	350,000	0.8264	289,240	-238,030
3	400,000	0.7513	300,520	62,490
4	450,000	0.6830	307,350	369,840

Break-even time occurs between year: 2 and the year 3

$$\begin{gathered} \mathbf{Remaining}\mathbf{}\mathbf{period}\mathbf{=}\frac{\mathrm{Numerator}\mathrm{for}\mathrm{partial}\mathrm{year}}{\mathrm{Denominator}\mathrm{for}\mathrm{partial}\mathrm{year}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$238,030}{\$300,520} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{8}\mathbf{years} \end{gathered}$$

Break-even time = 2.8 years

The net present value of this investment

$$\begin{gathered} \mathbf{Net}\mathbf{}\mathbf{present}\mathbf{}\mathbf{value}\mathbf{=}\mathbf{Cash}\mathbf{}\mathbf{inflow}\mathbf{\times }\mathbf{Table}\mathbf{}\mathbf{factor}\mathbf{+}\mathbf{Cumulative}\mathbf{}\mathbf{cashflow} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{400}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{7513}\mathbf{+}\mathbf{238}\mathbf{,}\mathbf{030} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{369}\mathbf{,}\mathbf{840} \end{gathered}$$

Should be invested

The management should invest in the project as the project has a net present value of $369,840 and the break-even time is 2.8 years.