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A project has annual cash flows of $3,000 for the next 10 years and then $6,500...

A project has annual cash flows of $3,000 for the next 10 years and then $6,500 each year for the following 10 years. The IRR of this 20-year project is 13.95%. If the firm's WACC is 12%, what is the project's NPV? Round your answer to the nearest cent.

Thanks!!!

Solutions

Expert Solution

Project's NPV is $ 2,481.51

Working:

Step-1:Calculation of initial cost of project
IRR is the rate at which present value of cash inflows become equal to initial cost.
So, initial cost is the present value of cash inflows at IRR rate
Present Value of annuity of 1 = (1-(1+i)^-n)/i Where,
= (1-(1+0.1395)^-10)/0.1395 i 13.95%
=                 5.226310 n 10
Present value of annual cash inflows of first 10 years = Annual Cash inflows * Present value of annuity of 1
= $             3,000.00 *       5.226310
= $           15,678.93
Present value of annual cash inflows of next 10 years = Annual Cash inflows * Present value of annuity of 1*Present value of 1 to be recived in year 10
= $             3,000.00 *       5.226310 * (1.1395^-10)
= $             3,000.00 *       5.226310 * 0.27093
= $             4,247.89
Present value of all cash inflows = $           15,678.93 + $   4,247.89
= $           19,926.82
So, initial cost of project is $           19,926.82
Step-2:Calculation of project's NPV
Present Value of annuity of 1 = (1-(1+i)^-n)/i Where,
= (1-(1+0.12)^-10)/0.12 i 12.00%
= 5.650223 n 10
Present value of annual cash inflows of first 10 years = Annual Cash inflows * Present value of annuity of 1
= $             3,000.00 *       5.650223
= $           16,950.67
Present value of annual cash inflows of next 10 years = Annual Cash inflows * Present value of annuity of 1*Present value of 1 to be recived in year 10
= $             3,000.00 *       5.650223 * (1.12^-10)
= $             3,000.00 *       5.650223 * 0.321973
= $             5,457.66
Present value of all cash inflows = $           16,950.67 + $   5,457.66
= $           22,408.33
Present value of annual cash inflows $           22,408.33
Less initial cost of project $           19,926.82
Project's NPV $             2,481.51

jeff jeffy answered 1 year ago
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