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 $107,000 and is expected to generate an additional $43,000 in cash flows for five years. A bank will make a $107,000 loan to the company at a 15% interest rate for this equipment’s purchase. Compute the recovery time for both the payback period and break-even time. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.) Chart Values are Based on:
10%
Cumulative Cash Inflow Present Value of Inflow Year Present Value PV Factor (Outflow) (Outflow)
(91,000) x 1.0000- (91,000) $ (91,000) 36,000 x 36,000 x 2.5 years

Payback period = 2.49 years

Break-even time = 3.36 years

Explanation:

a. Calculation of payback period

The payback period can be described as the amount of time it will take a firm recover its cost on a project or an investment.

The payback period can be calculated as follows:

Equipment cost = $107,000

Annual cash flow = $43,000

Payback period = Equipment cost / Annual cash flow = $107,000 / $43,000 = 2.49 years

b. Calculation of break-even time

Note: See the attached excel file for the computation of the cumulative present value of inflow (outflow).

In the attached excel, the present value (PV) factor is calculated using the following formula:

PV factor = 1/(1 + r)^n (1)

Where;

r = interest rate = 15%

n = a particular year from 1 to 5.

Break even time can be described as the amount of time that is needed for both the discounted cash flows and the initial cost of a project to be equal.

The break-even time is calculated using the following formula:

Break-even time = X + (Y / Z) (2)    

X = Last year with a negative cumulative cash flow = 3

Y = Absolute value of cumulative cash flow at the end of period X = $8,821.32

Z = Present value of cash inflow for the period following X = $24,585.39  

Break-even time = 3 + ($8,821.32 / $24,585.39) = 3 + 0.36 = 3.36 years

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