Question

14. A project has annual cash flows of $7,500 for the next 10 years and then $8,000 each year for the following 10 years. The IRR of this 20-year project is 12.21%. If the firm's WACC is 12%, what is the project's NPV? Do not round intermediate calculations. Round your answer to the nearest cent.

$

Answer 1

in a project at an IRR the NPV will be zero that means present value of cash flow at IRR will be the cost of the project

Cost of the project = Cash flow * PVAF (R , N) where R is discounting rate and N is years

= 7500 * PVAF (12.21%,10) + 8000*PVAF( 12.21%,10-20)

PVAF(12.21%,10) = 1/1.1221^1 + ..........1/1.1221^10 = 5.6019

PVAF(12.21%,10-20)= PVAF(12.21%,20) - PVAF(12.21%,10) = 7.3721 - 5.6019 = 1.7702

Cost of the project = 7500* 5.6019 + 8000*1.7702

= 42014.250+14161.60 = $ 56175.850

Calculation of NPV:

NPV = PV of cash inflow- cost of product

= [ 7500 * PVAF (12%,10) + 8000*PVAF( 12%,10-20) ] - 56175.850

= 7500*5.6502 + 8000*1.8192 ] - 56175.850

= 56930.10- 56175.850

= $ 754.250

Note ;

PVAF(12.%,10) = 1/1.12^1 + ..........1/1.12^10 = 5.6502

PVAF(12%,10-20)= PVAF(12%,20) - PVAF(12%,10) = 7.4694-5.6502 = 1.8192