Question

A project has annual cash flows of $4,000 for the next 10 years and then $6,000 each year for the following 10 years. The IRR of this 20-year project is 12.26%. If the firm's WACC is 11%, what is the project's NPV? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

IRR = 12.26%

Cash Flow for Year 1-10 = $ 4,000

Cash Flow for Year 11-20 = $ 6,000

WACC = 11 %

IRR( Internal Rate of Return) is the rate at which all the future cash flows adjusted with initial investment has a present value of 0.

= 4000 / (1 + 0.1226)¹ + 4000 / (1 + 0.1226)² + 4000 / (1 + 0.1226)³ + 4000 / (1 + 0.1226)⁴ + 4000 / (1 + 0.1226)⁵

+ 4000 / (1 + 0.1226)⁶ + 4000 / (1 + 0.1226)⁷ + 4000 / (1 + 0.1226)⁸ + 4000 / (1 + 0.1226)⁹ + 4000 / (1 + 0.1226)¹⁰

+ 6000 / (1 + 0.1226)¹¹ + 6000 / (1 + 0.1226)¹² + 6000 / (1 + 0.1226)¹³ + 6000 / (1 + 0.1226)¹⁴

+ 6000 / (1 + 0.1226)¹⁵ + 6000 / (1 + 0.1226)¹⁶ + 6000 / (1 + 0.1226)¹⁷ + 6000 / (1 + 0.1226)¹⁸

+ 6000 / (1 + 0.1226)¹⁹ + 6000 / (1 + 0.1226)²⁰ - Initial Outlay

= $ 32,914.95 - Initial Outlay

Equating the above equation to 0, we get

Initial Outlay = $ 32914.95

= 4000 / (1 + 0.11)¹ + 4000 / (1 + 0.11)² + 4000 / (1 + 0.11)³ + 4000 / (1 + 0.11)⁴ + 4000 / (1 + 0.11)⁵

+ 4000 / (1 + 0.11)⁶ + 4000 / (1 + 0.11)⁷ + 4000 / (1 + 0.11)⁸ + 4000 / (1 + 0.11)⁹ + 4000 / (1 + 0.11)¹⁰

+ 6000 / (1 + 0.11)¹¹ + 6000 / (1 + 0.11)¹² + 6000 / (1 + 0.11)¹³ + 6000 / (1 + 0.11)¹⁴ + 6000 / (1 + 0.11)¹⁵

+ 6000 / (1 + 0.11)¹⁶ + 6000 / (1 + 0.11)¹⁷ + 6000 / (1 + 0.11)¹⁸ + 6000 / (1 + 0.11)¹⁹ + 6000 / (1 + 0.11)²⁰ - 32914.95

= $ 36,001.5 - $ 32,914.95

= $ 3086.56

= $ 3087