A project has annual cash flows of $4,000 for the next 10 years and then $6,500...

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 10.13%. 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.

Solutions

Expert Solution

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

Cash Flow for year 11-20 = $ 6,500

IRR = 10.13 %

WACC = 10%

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

= 4000 / ( 1+ 0.1013)¹ + 4000 / ( 1+ 0.1013)² + 4000 / ( 1+ 0.1013)³ + 4000 / ( 1+ 0.1013)⁴ + 4000 / ( 1+ 0.1013)⁵ +

4000 / ( 1+ 0.1013)⁶ + 4000 / ( 1+ 0.1013)⁷ + 4000 / ( 1+ 0.1013)⁸ + 4000 / ( 1+ 0.1013)⁹ + 4000 / ( 1+ 0.1013)¹⁰ +

6500 / ( 1+ 0.1013)¹¹ + 6500 / ( 1+ 0.1013)¹² + 6500 / ( 1+ 0.1013)¹³ + 6500 / ( 1+ 0.1013)¹⁴ + 6500 / ( 1+ 0.1013)¹⁵ +

6500 / ( 1+ 0.1013)¹⁶ + 6500 / ( 1+ 0.1013)¹⁷ + 6500 / ( 1+ 0.1013)¹⁸ + 6500 / ( 1+ 0.1013)¹⁹ + 6500 / ( 1+ 0.1013)²⁰ - Initial Outlay

= $ 39,574.66 - Initial Outlay

Equating the above equation to 0, we get

Initial Outlay = $ 39,574.66

= 4000 / ( 1+ 0.10)¹ + 4000 / ( 1+ 0.10)² + 4000 / ( 1+ 0.10)³ + 4000 / ( 1+ 0.10)⁴ + 4000 / ( 1+ 0.10)⁵ +

4000 / ( 1+ 0.10)⁶ + 4000 / ( 1+ 0.10)⁷ + 4000 / ( 1+ 0.10)⁸ + 4000 / ( 1+ 0.10)⁹ + 4000 / ( 1+ 0.10)¹⁰ +

6500 / ( 1+ 0.10)¹¹ + 6500 / ( 1+ 0.10)¹² + 6500 / ( 1+ 0.10)¹³ + 6500 / ( 1+ 0.10)¹⁴ + 6500 / ( 1+ 0.10)¹⁵ +

6500 / ( 1+ 0.10)¹⁶ + 6500 / ( 1+ 0.10)¹⁷ + 6500 / ( 1+ 0.10)¹⁸ + 6500 / ( 1+ 0.10)¹⁹ + 6500 / ( 1+ 0.10)²⁰ - $ 39,574.66

= $ 37,038.55 - $ 39,574.66

= - $ 2,536.11 (negative NPV)

= - $ 2,536 (negative NPV)

jeff jeffy answered 1 year ago

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