Suppose your firm is considering investing in a project with the cash flows show

Question

Suppose your firm is considering investing in a project with the cash flows shown below, that the required rate of return on projects of this risk class is 11 percent, and that the maximum allowable payback and discounted payback statistics for yout company are 2.5 and 3.0 years, respectively Time Cash flow 3 5 -$231,000 $65,400 $83,600 $140,600 $121,600 $80,800 Use the discounted payback calculations. Round your final answer to 2 decimal places.) k decision rule to evaluate this project. (Do not round intermediate Discounted payback years

Explanation / Answer

In order to calculate the discounted payback period, we first need to calculate the discounted cashflows at time t = 0, discounted at 11%.

Time

Cash flow

Discounted Cash flow

0

-231,000

= -231000/(1 + 0.11)^0 = (231,000.00)

1

65,400

= 65400/(1 + 0.11)^1 = 58,918.92

2

83,600

= 83600/(1 + 0.11)^2 = 67,851.64

3

140,600

= 140600/(1 + 0.11)^3 = 102,805.51

4

121,600

= 121600/(1 + 0.11)^4 = 80,101.69

5

80,800

= 80800/(1 + 0.11)^5 = 47,950.87

Payback period is the time taken for the cash inflows to re-earn the invested amount. Discounted payback, on same lines, is the time taken for the discounted cash inflows to re-earn the invested amount.

Now, we need to calculate the amount of taken by discounted cash inflows to re-earn invested amount of $231,000.

Till year 3, total cash infows (discounted) = 58,918.92 + 67,851.64 + 102,805.51 = $229,576.06

Amount left to completely re-earn invested amount = $231,000 - $229,576.06 = $1,423.94

Butm the amount of cashflow in year 4 is more than the required amount.

Fraction of year = 1,423.94/80,101.69 = 0.0178 year

Total discounted payback = 3 Years + 0.0178 year = 3.0178 Years = 3.02 years

Time

Cash flow

Discounted Cash flow

0

-231,000

= -231000/(1 + 0.11)^0 = (231,000.00)

1

65,400

= 65400/(1 + 0.11)^1 = 58,918.92

2

83,600

= 83600/(1 + 0.11)^2 = 67,851.64

3

140,600

= 140600/(1 + 0.11)^3 = 102,805.51

4

121,600

= 121600/(1 + 0.11)^4 = 80,101.69

5

80,800

= 80800/(1 + 0.11)^5 = 47,950.87

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