Question

"The initial investment for a project is $135,000. The project will last for 7 years and can be salvaged for $22,950 at the end of 7 years. The annual expenses for the project are $7,500 in year 1 and increase at an annual rate of 7% in each year of the project. Assume the annual revenue remains the same in each of the 7 years. What does the annual revenue need to be in order for the internal rate of return of the project to equal 22.4%? "

Answer 1

Assuming all the values are after tax

At IRR, NPV=0
Let annual revenue be x

Hence, 0=
-135000+22950/(1+IRR)^7+(x-7500)/(1+IRR)+(x-7500*1.07)/(1+IRR)^2+(x-7500*1.07^2)/(1+IRR)^3+(x-7500*1.07^3)/(1+IRR)^4+(x-7500*1.07^4)/(1+IRR)^5+(x-7500*1.07^5)/(1+IRR)^6+(x-7500*1.07^6)/(1+IRR)^7

0=-135000+22950/(1+22.4%)^7+(x-7500)/(1+22.4%)+(x-7500*1.07)/(1+22.4%)^2+(x-7500*1.07^2)/(1+22.4%)^3+(x-7500*1.07^3)/(1+22.4%)^4+(x-7500*1.07^4)/(1+22.4%)^5+(x-7500*1.07^5)/(1+22.4%)^6+(x-7500*1.07^6)/(1+22.4%)^7

=>x=47083.295284