Question

ABC Company has gathered the following information related
to an investment in new equipment:

annual net cash inflows .......................   $ 46,000
initial investment ............................      ???
life of new equipment .........................   10 years
working capital needed now ....................   $ 37,000
cost of capital ...............................   10%
income tax rate ...............................   30%

Assume the working capital needed now will be released for
investment elsewhere at the end of the project. The after-tax
net present value of the project was calculated as $24,740.

Calculate the amount of the initial investment.

To answer this question use the present value table factors
given below. No credit will be awarded for this question
using a means other than the table factors given below to
answer this question.

Factors from the present value of a lump sum table for:

i = 10%
n = 6       n = 7       n = 8       n = 9       n = 10 
0.565       0.513       0.467       0.424       0.385


Factors from the present value of an annuity table for:

i = 10%
n = 6       n = 7       n = 8       n = 9       n = 10
4.355       4.868       5.335       5.759       6.500

Answer 1

Compute the present value of cash inflows, using the equation as shown below:

Present value = Annual cash flows*Present value annuity factor10%, 10 years

                      = $46,000*6.50

                      = $299,000

Hence, the present value of cash flows is $299,000.

Compute the present value of working capital refund, using the equation as shown below:

Present value = Working capital*Present value factor10%, 10 years

                      = $37,000*0.385

                      = $14,245

Hence, the present value of the working capital refund is $14,245.

Compute the amount of initial investment, using the equation as shown below:

Net present value = Present value of cash inflows + Present value of working capital refund – Initial investment – Working capital

               $24,740 = $299,000 + $14,245 – Initial investment - $37,000

                $24,740 = $276,245 – Initial investment

Rearrange the above-mentioned equation to determine the initial investment as follows:

Initial investment = $276,245 - $24,740

                             = $251,505

Hence, the initial investment is $251,505.