Question

Retsa Company is considering an investment in technology to improve its operations. The investment will require an initial outlay of \(800,000 and will 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 . . . . . . . . . . . . \)450,000

2 . . . . . . . . . . . . 400,000

3 . . . . . . . . . . . . 350,000

4 . . . . . . . . . . . . 300,000

Required

1. Determine the payback period for this investment. (Round the answer to one decimal.)

2. Determine the break-even time for this investment. (Round the answer to one decimal.)

3. Determine the net present value for this investment.

Analysis Component

4. Should management invest in this project? Explain.

5. Compare your answers for parts 1 through 4 with those for Problem 24-5B. What are the causes of the differences in results and your conclusions?

Short answer

The payback period is 1.9 years and the break-even time is 2.2 years and the net present value is $407,510. This project should be accepted and the values are opposite of which are given in 24-5B.

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	450,000	-350,000
2	400,000	50,000
3	350,000	400,000
4	300,000	700,000
	$700,000

Calculation of the payback period:
Payback occurs between years:	1	And year	2
Calculate the portion of the year:

$$\begin{gathered} \mathbf{Remaining}\mathbf{}\mathbf{period}\mathbf{=}\frac{\mathrm{Numerator}\mathrm{for}\mathrm{partial}\mathrm{year}}{\mathrm{Denominator}\mathrm{for}\mathrm{partial}\mathrm{year}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$350,000}{\$400,000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{9}\mathbf{years} \end{gathered}$$

The payback period will be 1.9 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	450,000	0.9091	409,095	-390,905
2	400,000	0.8264	330,560	-60,345
3	350,000	0.7513	262,955	202,610
4	300,000	0.6830	204,900	407,510
	$700,000

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

$$\begin{gathered} \mathbf{Remaining}\mathbf{}\mathbf{period}\mathbf{=}\frac{\mathrm{Numerator}\mathrm{for}\mathrm{partial}\mathrm{year}}{\mathrm{Denominator}\mathrm{for}\mathrm{partial}\mathrm{year}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$60,345}{\$262,955} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{2}\mathbf{years} \end{gathered}$$

Break-even time = 2.2 years.

The net present value of this investment

$$\begin{gathered} \mathbf{Net}\mathbf{}\mathbf{present}\mathbf{}\mathbf{value}\mathbf{=}\mathbf{Cash}\mathbf{}\mathbf{inflow}\mathbf{\times }\mathbf{Table}\mathbf{}\mathbf{factor}\mathbf{-}\mathbf{Cumulative}\mathbf{}\mathbf{cashflow} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{300}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{6830}\mathbf{+}\mathbf{202}\mathbf{,}\mathbf{610} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{407}\mathbf{,}\mathbf{510} \end{gathered}$$

Should be invested

The management should invest in the project as the project has a net present value of $407,510 and the break-even time is 3.07 years.

Comparison

	24-5B	24-6B	Causes
1	2.4 years	1.9 years	The cash flow was higher in the beginning and lower in the ending in 24-6B and vice versa in 24-5B
2	2.8 years	2.2 years	The cash flow was higher in the beginning and lower in the ending in 24-6B and vice versa in 24-5B
3	$369,840	$407,510	The cash flow was higher in the beginning and lower in the ending in 24-6B and vice versa in 24-5B
4	Yes	Yes	Both the project should be accepted

Conclusion: In the problem, 24-5B values of cash flow are lower in the beginning and got increased but in the problem 24-6B the values are opposite of that of problem 24-5A.