A project has annual cash flows of $4,500 for the next 10 years and then $9,500 each year for the following 10 years. The IRR of this 20-year project is 13.04%. If the firm's WACC is 10%, what is the project's NPV? Round your answer to the nearest cent.
Project's NPV is $ 10,668.89
Step-1:Calculation of cost of project | ||||||||
IRR is the rate at which present value of cash inflows is equal to its cost. | ||||||||
Present value of annuity of 1 for 10 years | = | (1-(1+i)^-n)/i | Where, | |||||
= | (1-(1+0.1304)^-10)/0.1304 | i | = | 13.04% | ||||
= | 5.41757987 | n | = | 10 | ||||
Present value of 1 | = | (1+i)^-n | ||||||
= | (1+0.1304)^-10 | |||||||
= | 0.29354758 | |||||||
Present value of cash flows of first 10 years | = | $ 4,500.00 | * | 5.41758 | = | $ 24,379.11 | ||
Present value of cash flows of next 10 years | = | $ 9,500.00 | * | 5.41758 | * | 0.293548 | = | $ 15,108.02 |
Present value of cash flows of next 20 years | $ 39,487.13 | |||||||
So, cost of project is | $ 39,487.13 | |||||||
Step-2:Calculation of present value of project's cash inflows at WACC that is discounted rate | ||||||||
Present value of annuity of 1 for 10 years | = | (1-(1+i)^-n)/i | Where, | |||||
= | (1-(1+0.10)^-10)/0.10 | i | = | 10.00% | ||||
= | 6.14456711 | n | = | 10 | ||||
Present value of 1 | = | (1+i)^-n | ||||||
= | (1+0.10)^-10 | |||||||
= | 0.38554329 | |||||||
Present value of cash flows of first 10 years | = | $ 4,500.00 | * | 6.144567 | = | $ 27,650.55 | ||
Present value of cash flows of next 10 years | = | $ 9,500.00 | * | 6.144567 | * | 0.385543 | = | $ 22,505.47 |
Present value of cash flows of next 20 years | $ 50,156.02 | |||||||
Step-3:Calculation of project's NPV | ||||||||
Present value of cash inflow | $ 50,156.02 | |||||||
Less cost of project | $ 39,487.13 | |||||||
Project's NPV | $ 10,668.89 |
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