Question

A project cost $600,000 today and will peoduce a single, one time affter tax cash flow of $1,500,000 in the future. What is the IRR of this project under each of the following scenarios

A, The future cash flow occurs in 5 years
B ..... in 10 years
C..... in 15 years
D...... in 20 years

Please show formula.

Answer 1

IRR is the rate of return that will equate investment at time 0 to PV of future cashflows.

In our case-

Initial Investment = (One time CF)/(1+r)ⁿ

=> (1+r)ⁿ = (CF)/(Initial Investment)

=> 1+r = [(CF)/(Initial Investment)]^1/n

=> r = [(CF)/(Initial Investment)]^1/n - 1 ...(1)

(A) n=5

600000 = 1500000/(1+r)⁵

r = (1500000/600000)^1/5-1 {same as in formula (1)}

r = 20.1124%

(B) n=10

r = (1500000/600000)^1/10-1 {same as in formula (1)}

r = 9.5958%

(C) n=15

r = (1500000/600000)^1/15-1 {same as in formula (1)}

r = 6.2990%

(D) n=20

r = (1500000/600000)^1/20-1 {same as in formula (1)}

r = 4.6880%