Question

Payback Period Each of the following scenarios is independent. Assume that all cash flows are after-tax cash flows.

a. Colby Hepworth has just invested $550,000 in a book and video store. She expects to receive a cash income of $120,000 per year from the investment.

b. Kylie Sorensen has just invested $1,560,000 in a new biomedical technology. She expects to receive the following cash flows over the next 5 years: $350,000, $490,000, $780,000, $490,000, and $290,000.

c. Carsen Nabors invested in a project that has a payback period of 4 years. The project brings in $960,000 per year.

d. Rahn Booth invested $1,300,000 in a project that pays him an even amount per year for 5 years. The payback period is 2.5 years.

Required:

1. What is the payback period for Colby? Round your answer to two decimal places. years

2. What is the payback period for Kylie? Round your answer to one decimal place. years

3. How much did Carsen invest in the project? $

4. How much cash does Rahn receive each year? $ per year

Answer 1

1.

Payback period refers to the time in which initial investment in the project is recovered.

Payback period = Initial investment/Annual cash inflow

= 550,000/120,000

= 4.58 years

2.

Payback period = A + B/C

where,

A = years full recovery

B = unrecovered cost at the begining of the last year

C = cash flows in the following year

Initial investment = $1,560,000

Cash flows over the next 5 years: $350,000, $490,000, $780,000, $490,000, and $290,000.

Total cash inflows in 2 years = 350,000 + 490,000

= $840,000

Remaining cash inflows required in the 3rd year = 1,560,000 - 840,000

= $720,000

Payback period = 2 + 720,000/780,000

= 2 + 0.92

= 2.92 years

3.

Payback period = 4 years

Annual cash flow = $960,000

Investment in the project = ?

Payback period = Initial investment/Annual cash inflow

4 = Initial investment/960,000

Hence, initial investment = $3,840,000

4.

Initial investment = $1,300,000

Payback period = 2.5 years

Payback period = Initial investment/Annual cash inflow

2.5 = 1,300,000/Annual cash inflow

Annual cash inflow = $520,000

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