Question

An investment project has annual cash inflows of $5,100, $3,200, $4,400, and $3,600, for the next four years, respectively. The discount rate is 15 percent.

  

What is the discounted payback period for these cash flows if the initial cost is $5,000? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Discounted payback period

years

  

What is the discounted payback period for these cash flows if the initial cost is $7,100? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Discounted payback period

years

  

What is the discounted payback period for these cash flows if the initial cost is $10,100? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Discounted payback period

years

Answer 1

Payback period is the period which tells that in how much time that company can retain its cost of investment

First we have to find the discounted cashflows at 15% discount rate

Year1 present value factor=1/(1+15%) and then multiply it with cashflow1 to arrive at Discounted cashflow1

Year2 present value factor=1/(1+15%)^2 and then multiply it with cashflow2 to arrive at Discounted cashflow2

year3 present value factor=1/((1+15%)^3) and goes on like that.

The cashflows looks as below

	Cashflows	Present value factor@15%	Discounted cashflows
Year1	5100	0.869565217	4434.8
Year2	3200	0.756143667	2419.7
Year3	4400	0.657516232	2893.1
Year4	3600	0.571753246	2058.3

1. If the initial cost is $5,000

Company receives $4434.8 in first year and the remaining 565.2 (5000-4434.8) in 2nd year

in 2nd year=565.2/2419.7=0.23 years

The discounted payback period=1.23 years

2. If the initial cost is $7,100

Company receives 6854.4 in 2 years and the remaining 245.6 (7100-6854.4) in 3rd year

In 3rd year=245.6/2893.1=0.08

The discounted payback period=2.08 years

3. If the initial cost is $10,100

Company receives 9747.5 in 3 years and the remaining 352.5 (10100-9747.5) in 4th year

In 4th year=352.5/2058.3=0.17

The discounted payback period=3.17 years