Question

Suppose you invest $ 3,500 today and receive $ 9,000 in five years.

a. What is the internal rate of return​ (IRR) of this​ opportunity?

b. Suppose another investment opportunity also requires $ 3,500 ​upfront, but pays an equal amount at the end of each year for the next five years. If this investment has the same IRR as the first​ one, what is the amount you will receive each​ year?

Answer 1

The 3,500 invested today is the present value which will provide $9,000 in five years. The increase is due to the interest element
Formula to calculate present value of investment
PV = FV/(1+r)^n
Where FV = Future value of investment
PV = Investment made today
r = rate of interest
n = investment period
Using the above formula we can calculate the rate of interest from investment
Calculation of rate of interest or IRR from investment
3,500 = 9000/[(1+r)^5]
(1+r) = [9,000/3,500]^(1/5)
(1+r) = [2.57142]^(1/5)
1+r = 1.20791
r = 20.791%
The internal rate of return of this opportunity is 20.79%
Formula to calculate present value of annuity
where annuity is the series of payment made
PV = A*([1-(1+r)^-n]/r)
where PV is the present value of investment
A is the yearly payment received
r = rate of interest
n = number of years of investment
Calculation of payment received each year
3,500 = A*([1-(1+0.20791)^(-5)]/0.20791)
3,500 = 2.93930A
A = 3,500/2.93930
A = 1,190.76
The yearly amount received would be $1,190.76