Question

A project has annual cash flows of $4,000 for the next 10 years and then $6,500 each year for the following 10 years. The IRR of this 20-year project is 13.97%. If the firm's WACC is 10%, what is the project's NPV? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Answer : Project 's NPV is $ 9907.39

Calculation of Project,s NPV

Given that the IRR of the Project is 13.97 %

IRR is the rate at which present value of cash inflow is equal to present value of cash outflow.

Therefore we need to first calculate the present value of cash inflows

Present Value of cash inflow = (Annual Cashflow * Present Value annuity for 0-10 years @ 13.97%)+[Annual Cashflow*(Present Value annuity for 0-20 years @ 13.97%) - (Present Value annuity Factor 0-10 years @ 13.97% ]

= 4,000 * 5.22222841675 + 6500 * (6.6346045847 - 5.22222841675)

= 4000 * 5.22222841675 + 6500 * 1.41237616795

= 20888.913667 + 9180.4451

= 30069.358767

Therefore Present Value of Cash Inflow = $ 30069.358767

At IRR ,Present Value of cash inflow = Present value of Cash outflow

Present Value of cash outflow = $ 30069.358767

Calculation of NPV of the project when WACC = 10%

NPV = Present Value of cash inflow - Present Value of cash outflow

Present Value of cash outflow ( Already calculated above) = $ 30069.358767

WACC = 10 %

Present Value of Cash Inflow = (Annual Cashflow * Present Value annuity for 0-10 years @ 10%)+[Annual Cashflow*(Present Value annuity for 0-20 years @ 10%) - (Present Value annuity Factor 0-10 years @ 10% ]

= 4,000 * 6.14456710558 + [6500 * (8.51356371927 - 6.14456710558)]

= 4,000 * 6.14456710558 + 6500 * 2.36899661369

= 24578.2684223 + 15398.4779889

= 39976.7464112

NPV = Present Value of Cash Inflow - Present Value of cash outflow

= 39976.7464112 - 30069.358767

= 9907.3876442 or 9907.39