A project is expected to create operating cash flows of $22,500 a year for three
ID: 2723537 • Letter: A
Question
A project is expected to create operating cash flows of $22,500 a year for three years. The initial cost of the fixed assets is $50,000. These assets will be worthless at the end of the project. An additional $3,000 of net working capital will be required throughout the life of the project. What is the project's net present value if the required rate of return is 10%?
A. $2,208.11
B. $2,954.17
C. $4,306.09
D. $5,208.11
E. $5,954.17
I know the answer is D, but I need a clear explanation on how to get to that answer.
Explanation / Answer
The assumptions taken as per details given in the problem
The value of asset is $ 50,000 , so the initial investment or cash out flow at year 0 is $50,000
The initial investment of investment of $3,000 will be required as working capital at year 0 for use throughout the period of 3 years
The working capital will be recovered at end of project i.e year 3
The time period of project is 3 years
The cost of capital is 10%
No we will calculate the cash flow on yearly basis is operating cash flow minus
The net present value is = Present value of cash inflows – present value of cash outflow
Now we have to calculate the present value factor of $1 receivable annually for 3 years at 10% is 2.486852
The present value factor of $1 received at end of year 3 is 0.751315
So the present value of cash inflow of $ 22,500 received annually for 3 years = $22,500 x 2.486852=55954.17
Present value of working capital of $3,000 recovered at the end of year 3 = $3,000 x 0.751315= $2253.94
Calculation of NPV of the project
Present value of operating cash inflows $ 55954.17
Present value of WC recovered $ 2253.94
Total cash inflow $58208.11
Less -:
Present value cash outflow
Value of asset $50,000
Initial investment in working capital $3,000
Total cash outflow $53,000
NPV
($ 58208.11 - $53,000) $5,208.11
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