Respuesta :
Answer: The discounted payback period for this project is 4.3 years. If Kathleen Danceware Co. accepts projects that have a discounted payback period of three years, the company will not accept the project.
We calculate the Discounted Value of the cash flows for each year with the following formula
[tex]\mathbf{PV_{n} = \frac{FV}{(1+r)^n}}[/tex]
where
FV represents the cash flows in each of the years from year 1 to year 5
r is the firm's cost of capital at 10%
n starts from 1 for the first year ans increases sequentially until year 5
For eg, the PV of cash flows in year 3 will be
[tex]\mathbf{PV_{3} = \frac{375,000}{(1.1)^3}} = 2,81,743.05[/tex]
The following table gives us the Discounted cash flows and cumulative discounted cash flows. The cumulative discounted cash flows column help us determining the payback period.
Total Investment $1250000
Year Cash Flow Discounted Cash Flow at 10% Cumulative Cash Flows
1 375000 3,40,909.09 3,40,909.09
2 375000 3,09,917.36 6,50,826.45
3 375000 2,81,743.05 9,32,569.50
4 375000 2,56,130.05 11,88,699.54
5 375000 2,32,845.50 14,21,545.04
We calculate Cumulative Cash flows by adding the previous year's or years' total discounted cash flows to current year's cash flows.
For e.g. [tex]Cumulative Cash Flows_{2} = Cash flow _{1} + Cash Flow_{2}}[/tex]
Substituting the values we get,
[tex]6,50,826.45 = 3,40,909.09 + 3,09,917.36}[/tex]
We calculate the cumulative cash flows for each of the following years in the same manner
From the table, we see that the project will recover its investment between 4 and 5 years.
We can find the exact time as follows:
[tex]Discounted Payback Period = 4 + \frac{1250000 - 11,88,699.54}{2,32,845.50}[/tex]
[tex]Discounted Payback Period = 4 + \frac{61,300.46}{2,32,845.50}[/tex]
[tex]Discounted Payback Period = 4.263266667[/tex]
