Question

Tom wants to start a new project. A project requires a start up cost of $11000 today and 20 annual cost of $4500 starting in one year. Starting at the end of the 21th year, the project returns 10 annual payments of $Y. Find Y so that the project yields an annual effective rate of 5% over the 30 years.

PLZ by hand and not excel

Answer 1

-4500 -4500 +Y +Y

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0 1 2 3 20 21 22 30

-11000 -4500 -4500 +Y

The above is the representation of how the cashflows will be present. At year 0, today, we have cash outflow of 11000, from year 1 to year 20 we have annual cash out flow of 4500. From 21st year till 30th year we get cash inflow of Y. The annual effective rate of 5% is the IRR. The equation we need to solve is NPV=0 as that rate gives us IRR.

The equation to find Y is as under

-11000 - [4500/1.05 + 4500/1.05^2 + ..... 4500/1.05^20] + [ Y/1.05^21 + Y/1.05^22 + ..... Y/1.05^30] =0 --------(1)

The values under bracket are in Geometric Progression.

The sum of GP formula is a*(1-r^n)/(1-r)

(4500/1.05) * (1-(1/1.05)^20) / (1-(1/1.05)) = 56079.95

(Y/1.05^21) * (1-(1/1.05)^10) / (1-(1/1.05)) = 2.91Y

From (1), -11000-56079.95 + 2.91Y = 0

2.91Y = 67079.95

Y = $ 23051.53