Question

An investment project has annual cash inflows of $4,300, $4,000, $5,200, and $4,400, for the next four years, respectively. The discount rate is 13 percent. a. What is the discounted payback period for these cash flows if the initial cost is $5,800? (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 $7,900? (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 $10,900? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

1.64 years

2.27 years

3.13 years

Explanation:

Discounted payback calculates the amount of time it takes to recover the amount invested in a project from it cumulative discounted cash flows

Present value of cash flow in year 1 = 4300 / 1.13 = 3805.31

Amount recovered in year 1  = -5800 + 3805.31 = -1994.69

Present value of cash flow in year 2 = 4000 / (1.13^2) = 3132.59

Amount recovered in year 2 =-1994.69 + 3132.59 = 1137.90

Payback period = 1 + 1994.69/3132.59 = 1.64 years

B

Present value of cash flow in year 1 = 4300 / 1.13 = 3805.31

Amount recovered in year 1  = -7900 + 3805.31 = -4094.69

Present value of cash flow in year 2 = 4000 / (1.13^2) = 3132.59

Amount recovered in year 2  = -4094.69 + 3132.59 = -962.10

Present value of cash flow in year 3 = 5200 / (1.13^3) = 3603.86

Amount recovered in year 3  = -962.10 + 3603.86 = 2641.76

Payback period = 2 years + -962.10 / 3603.86 = 2.27 years

C

Present value of cash flow in year 1 = 4300 / 1.13 = 3805.31

Amount recovered in year 1  = -10900 + 3805.31 = -7094.69

Present value of cash flow in year 2 = 4000 / (1.13^2) = 3132.59

Amount recovered in year 2  = -7094.69 + 3132.59 = -3962.10

Present value of cash flow in year 3 = 5200 / (1.13^3) = 3603.86

Amount recovered in year 3  = -3962.10 + 3603.86 = -358.24

Present value in year 4 =  4400 / (1.13^4) = 2698.60

Amount recovered in year 4  = -358.24 + 2698.60 = 2340.36

Payback period = 3 years + 358.24 + 2698.60 = 3.13 years