Question

Project L requires an initial outlay at t = 0 of $40,000, its expected cash inflows are $9,000 per year for 9 years, and its WACC is 11%. What is the project's discounted payback? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

• Project L requires initial outlay at t equals to zero of $40,000
• expected cash inflows are $9,000 per year for 9 years .
• WACC is 11%

• so , the discounted pay back period is 6.44 years .
• Calculations are given below With its theoretical view.

Pay back period helps to determine length of time needed to recover initial cash outlay in the project .

discounted pay back period ( DPP ) is the amount of time that takes for initial cost of a project to equal to discounted value of expected cash flows. thus , its the period in which cumulative net present value of a project equalize to zero .

• its formula :
• DPP = year before DPP occurs + ( cumulative discounted cash flow in year before its recovery / discounted cash flow in year after recovery )

• if DPP is less than its use full life , the project is accepted .

• otherwise , project is rejected .

• if mutually exclusive projects , as the project with shorter DPP is accepted .

Calculations are ,

Step 1 =

To calculate the discounted pay back period , firstly we needs to calculate the present value of the cash flows using ( PVIF ) Present Value Interest Factor

Present Value = PVIF * cash flow amount

PVIF = ( 1 + r ) - n

where ,

PVIF is present value interest factor

r is the discounting rate .

n is the time period

table :

Period	Cash flows	PVIF = ( 1+ 0.11 ) - n	Present Value
1	9,000	0.9009	8,108.1
2	9,000	0.8116	7,304.4
3	9,000	0.7312	6,580.8
4	9,000	0.6587	5,928.3
5	9,000	0.5935	5,341.5
6	9,000	0.5346	4,811.4
7	9,000	0.4817	4,335.3
8	9,000	0.4339	3,905.1
9	9,000	0.3909	3,518.1

Step 2 =

using the discounted cash flows , the pay back period will be ,

40,000 - 8,108.1 = 31,891.9 ( year 1 is full )

31,891.9 - 7,304.4 = 24,587.5 ( year 2 is full )

24,587.5 - 6,580.8 = 18,006.7 ( year 3 is full )

18,006.7 - 5,928.3 = 12,078.4 ( year 4 is full )

12,078.4 - 5,341.5 = 6,736.9 ( year 5 is full )

6,736.9 - 4,811.4 = 1,925.5 ( year 6 is full )

Thus ,

6 full years and , a proportion of 7^th  year :

  = 6 + ( 1,925.5 / 4,335.3 )

= 6 + 0,44

= 6.44 years

So , discounted pay back period = 6.44 years.

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