Question

An investment project has annual cash inflows of $2,800, $3,700, $5,100, and $4,300, for the next four years, respectively. The discount rate is 11 percent. a. What is the discounted payback period for these cash flows if the initial cost is $5,200? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is the discounted payback period for these cash flows if the initial cost is $6,400? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What is the discounted payback period for these cash flows if the initial cost is $10,400? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Results are below.

Step-by-step explanation:

Giving the following information:

Cash flows:

Cf1= $2,800

Cf2= $3,700

Cf3= $5,100

Cf4= $4,300

Discount rate= 11%

The payback period is the time required to cover the initial investment. We need to use the following formula on each cash flow:

PV= Cf / (1+d)^n

d= discount rate

A) Initial investment= $5,200

Year 1= 2,800 / 1.11 - 5,200= -2,677.47

Year 2= 3,700 / 1.11^2 - 2,677.47= 325.53

To be more specific:

(2,677.47 / 3,003)= 0.89*365= 325

The payback period is 1 year and 325 days.

B) Initial investment= $6,400

Year 1= 2,522.52 - 6,400= -3,877.48

Year 2= 3,003 - 3,877.48= -874.48

Year 3= 5,100 / 1.11^3 - 874.48= 2,854.6

To be more specific:

(874.48 / 3,729.1)= 0.23*365= 84

The payback period is 2 years and 84 days.

C) Initial investment= $10,400

Year 1= 2,522.52 - 10,400= -7,877.48

Year 2= 3,003 - 7,877.48= -4,874.48

Year 3= 3,729.1 - 4,874.48= -1,145.38

Year 4= 4,300 / 1.11^4 - 1,145.38= 1,687.16

To be more specific:

(1,145.38 / 2,832.54)= 0.40*365= 146

The payback period is 3 years and 146 days.