Question

Problem 10-6
Discounted Payback

A project has an initial cost of $40,000, expected net cash inflows of $9,000 per year for 9 years, and a cost of capital of 11%. What is the project's discounted payback period? Round your answer to two decimal places.

years

Answer 1

Discounted Cashflow = Actual Cashflow / (1 + i)ⁿ   where n is the nth year & i is the discount rate.

Cost of capital (Discount Rate)  = 11% Initial Cost = $40,000 Expected net cash inflows = $9,000

Discounted Cashflow for year 1 =  $9,000 / (1+0.11)¹ = $8108.11

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Discounted Cashflow for year 9 = $9,000 / (1+0.11)⁹ = $3518.32

Period	Cash Flow	DCF	Cumulative
0	$   (40,000.0)	$      (40,000.0)	$   (40,000.0)
1	$       9,000.0	$          8,108.1	$   (31,891.9)
2	$       9,000.0	$          7,304.6	$   (24,587.3)
3	$       9,000.0	$          6,580.7	$   (18,006.6)
4	$       9,000.0	$          5,928.6	$   (12,078.0)
5	$       9,000.0	$          5,341.1	$     (6,736.9)
6	$       9,000.0	$          4,811.8	$     (1,925.2)
7	$       9,000.0	$          4,334.9	$       2,409.8
8	$       9,000.0	$          3,905.3	$       6,315.1
9	$       9,000.0	$          3,518.3	$       9,833.4

Cumulative Cashflow for year 1 = Initial Investment (Negative Cashflow) + Discounted Cashflow of the year 1

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Cumulative Cashflow for year 9 = Cumulative Cashflow for year 9 + Discounted Cashflow of the year 9

Discounted Payback Period = X + Y / Z

Where,
X = Last period with a negative 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

X = 6 as after that period discounted cumulative cash flow turns positive ( -1,925.2 -> 2,409.8 )

Y = 1,925.2 Z = 4,334.9

Discounted Payback Period = 6 + 1,925.2 / 4,334.9 = 6 + 0.444 = 6.44 Years