Question

In: Finance

Assume you have the following information on Project X: Initial Investment -$1,000 Required rate of return...

Assume you have the following information on Project X: Initial Investment -$1,000 Required rate of return = 10%

Year

Cash Flow

Present Value of CF

Accum. Discount CF

0

-1000

-1000

-1000

1

200

182

182

2

400

331

513

3

700

526

1039

4

300

205

1244

What is the discount payback period?

Solutions

Expert Solution

Solution:
Discount payback period 2.93 Years
Working Notes:
Notes: In the given information accumulated discount cash flow is given which does not considered the initial investment which is required for calculation of discount payback period, hence we have to do again that portion.
Given
a b c= a x b
Year Cash flows PVF @ 10% Present Value of CF Accum. Discount CF
0 ($1,000) 1 -1000 -1000
1 $200 0.909090909 182 182
2 $400 0.826446281 331 513
3 $700 0.751314801 526 1039
4 $300 0.683013455 205 1244
We rework for computation of Discount payback period
a
Year Cash flows Present Value of CF Accumulated cash flow
0 ($1,000) -1000 -1000
1 $200 182 -818 [-1000+182]
2 $400 331 -487 [-818+331]
3 $700 526 39 [-487+526]
4 $300 205 244 [39+244]
Notes: Since cumulative discounted cash flow becomes positive at 3rd years means discounted payback period is between 2nd & 3rd year
Discounted Payback period = 2 year + Acc. balance of 2nd year /discounted cash flow of 3rd year
Discounted Payback period = 2 year + 487 /526
Discounted Payback period = 2 years + 0.9258555
Discounted Payback period = 2.9258555
Discounted Payback period = 2.93 years
Notes: PVF is calculated @ 10% = 1/(1+0.10)^n     where n is the period for which PVF is calculated.
Please feel free to ask if anything about above solution in comment section of the question.

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