Services United is considering a new project that requires an initial cash investment of $78,000. The project will generate cash inflows of $29,500, $32,700, $18,500, and $10,000 over each of the next four years, respectively. How long will it take to recover the initial investment

2.85 years

Explanation:

The time taken to recover initial investment is known as payback period. It is calculated in years. It is the time taken for the total inflows to be equal to the initial outflow.

Year Inflow Outflow Balance

0 - $78,000 ($78,000)

1 $29,500 - ($48,500)

2 $32,700 - ($15,800)

3 $18,500 - $2,700

4 $10,000 - $12,700

The fractional year

= 15800/18500

= 0.85

Period required = 2.85 years

2.85405 years

Explanation:

Cash Flows

Year 0 ($78,000)

Year 1 $29,500

Year 2 $32,700

Year 3 $18,500

Year 4 $10,000

Services United would receive $29,500 in year 1 therefore remaining balance is = 78,000 - 29,500 = 48,500

Services United would receive $32,700 in year 2 therefore remaining balance is = 48,500 - 32,700 = 15,800

Services United would receive $18,500 in year 3 therefore remaining balance is = 15,800 - 18,500 = - 2700

We observe that the company would recover the initial amount somewhere in year 3

15800 / 18500 = 0.85405 years

Total payback period = 2 years + 0.85405 years = 2.85405 years