Question

A process for producing the mosquito repellant Deet has an initial investment of $185,000 with annual costs of $47,000. Income is expected to be $90,000 per year.

What is the payback period at i = 0% per year? At i = 12% per year? (Note: Round your answers to the nearest integer.)

The payback period at i = 0% is determined to be ........years.

The payback period at i = 12% is determined to be ........ years.

Answer 1

Initial Cost = 185,000

Annual Cost = 47,000

Annual Income = 90,000

Net Annual Income = 90,000 – 47,000 = 43,000

If the interest rate = 0%, the payback period will be similar to simple payback period.

Simple payback period = Initial Cost / Net Annual Revenue

Simple payback period = 185,000 / 43,000 = 4.3 years or 4 years (rounding off)

a. The payback period at i = 0% is determined to be 4.3 years.

b. The payback period at i = 12% is determined to be ........ years.

Calculate the discounted payback period.

Year	CF	PV Factor	DCF	CCF
0	$-185,000	1	$-185,000	$-185,000
1	$43,000	0.89	$38,392.86	$-146,607.14
2	$43,000	0.8	$34,279.34	$-112,327.81
3	$43,000	0.71	$30,606.55	$-81,721.26
4	$43,000	0.64	$27,327.28	$-54,393.98
5	$43,000	0.57	$24,399.35	$-29,994.62
6	$43,000	0.51	$21,785.14	$-8,209.49
7	$43,000	0.45	$19,451.02	$11,241.53

Payback Period = 6 + [-8209.49 – 0 ÷ -8209.49 – (11,241.53)]*1 = 6.42 years

The payback period at i = 12% is determined to be 6.42 years.