Question

Heels, a shoe manufacturer, is evaluating the costs and benefits of new equipment that would custom fit each pair of athletic shoes. The customer would have his or her foot scanned by digital computer equipment; this information would be used to cut the raw materials to provide the customer a perfect fit. The new equipment costs \(90,000 and is expected to generate an additional \)35,000 in cash flows for five years. A bank will make a \(90,000 loan to the company at a 10% interest rate for this equipment’s purchase. Use the following table to determine the break-even time for this equipment. (Round the present value of cash flows to the nearest dollar.)

Present Value Present Value Cumulative Present Value

Year Cash Flows* of 1 at 10% of Cash Flows of Cash Flows

0 \)(90,000) 1.0000

1 35,000 0.9091

2 35,000 0.8264

3 35,000 0.7513

4 35,000 0.6830

5 35,000 0.6209

Short answer

The break-even point for the project is 3.1 years.

Step-by-step solution

Step-by-Step SolutionStep 1: Preparation of table

Year	Cash inflow (outflow)	Table factor	Present value of cash flows	Cumulative present value of cash flows
0	-$90,000	1.0000	-$90,000	-$90,000
1	35,000	0.9091	31,818	-58,182
2	35,000	0.8264	28,924	-29,258
3	35,000	0.7513	26,295	-2,963
4	35,000	0.6830	23,905	20,942
5	35,000	0.6209	$21,731	$42,673
	$85,000

Computation of break-even time

Break-even time occurs between year: 3 and the year 4

$$\begin{gathered} \mathbf{Remaining}\mathbf{}\mathbf{period}\mathbf{=}\frac{\mathrm{Numerator}\mathrm{for}\mathrm{partial}\mathrm{year}}{\mathrm{Denominator}\mathrm{for}\mathrm{partial}\mathrm{year}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\$2,963}{\$23,905} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{years} \end{gathered}$$

Break-even time = 3.1 years