Question

Kathleen Dancewear Co. has bought some new machinery at a cost of $1,250,000. The impact of the new machinery will be felt in the additional annual cash flows of $375,000 over the next five years. The firm's cost of capital is 10 percent. What is the discounted payback period for this project? If its acceptance period is three years, will this project be accepted? (Do not round intermediate computations. Round your answer to one decimal place.)

Answer 1

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

$\mathbf{PV_{n} = \frac{FV}{(1+r)^n}}$

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

$\mathbf{PV_{3} = \frac{375,000}{(1.1)^3}} = 2,81,743.05$

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. $Cumulative Cash Flows_{2} = Cash flow _{1} + Cash Flow_{2}}$

Substituting the values we get,

$6,50,826.45 = 3,40,909.09 + 3,09,917.36}$

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:

$Discounted Payback Period = 4 + \frac{1250000 - 11,88,699.54}{2,32,845.50}$

$Discounted Payback Period = 4 + \frac{61,300.46}{2,32,845.50}$

$Discounted Payback Period = 4.263266667$