An investment project has annual cash inflows of $4,700, $3,600, $4,800, and $4,

Question

An investment project has annual cash inflows of $4,700, $3,600, $4,800, and $4,000, and a discount rate of 14 percent.

What is the discounted payback period for these cash flows if the initial cost is $5,400? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What is the discounted payback period for these cash flows if the initial cost is $7,500? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What is the discounted payback period for these cash flows if the initial cost is $10,500? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

An investment project has annual cash inflows of $4,700, $3,600, $4,800, and $4,000, and a discount rate of 14 percent.

Explanation / Answer

Rate = 14%

i = 0.14

The discounted payback period = X + (Y/Z)

Where,
X = The last period with a -ve discounted cumulative cash flow
Y = Absolute value of discounted cumulative cash flow at the end of the period X
Z = Discounted cash flow during the period after X

1)

Discounted Payback Period = 1 + |-1277.192981| / 2770.083102 = 1.46 years

2)

Discounted Payback Period = 2 + |-607.10988| / 3239.863278 = 2.19 years

3)

Year Cash flow PV factor = 1/(1+i)^n Discounted cash flow Cumulative discounted cash flow 0 -5400 1 -5400 -5400 1 4700 0.877192982 4122.807018 -1277.192982 2 3600 0.769467528 2770.083102 1492.89012 3 4800 0.674971516 3239.863278 4732.753398 4 4000 0.592080277 2368.321109 7101.074507

Discounted Payback Period = 1 + |-1277.192981| / 2770.083102 = 1.46 years

2)

Year Cash flow PV factor = 1/(1+i)^n Discounted cash flow Cumulative discounted cash flow 0 -7500 1 -7500 -7500 1 4700 0.877192982 4122.807018 -3377.192982 2 3600 0.769467528 2770.083102 -607.10988 3 4800 0.674971516 3239.863278 2632.753398 4 4000 0.592080277 2368.321109 5001.074507

Discounted Payback Period = 2 + |-607.10988| / 3239.863278 = 2.19 years

3)

Year Cash flow PV factor = 1/(1+i)^n Discounted cash flow Cumulative discounted cash flow 0 -10500 1 -10500 -10500 1 4700 0.877192982 4122.807018 -6377.192982 2 3600 0.769467528 2770.083102 -3607.10988 3 4800 0.674971516 3239.863278 -367.2466022 4 4000 0.592080277 2368.321109 2001.074507 Discounted Payback Period = 3 + |-367.2466| / 2368.3211 = 3.15 years

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