Question

​(IRR calculation​) Determine the IRR on the following​ projects:
a. An initial outlay of ​$9,000 resulting in a single free cash flow of ​$17,118 after 7 years

____%
b. An initial outlay of ​$9,000 resulting in a single free cash flow of ​$46,991 after 13 years

____%
c. An initial outlay of ​$9,000 resulting in a single free cash flow of ​$109,128 after 19 years

____%
d. An initial outlay of ​$9,000 resulting in a single free cash flow of ​$13,542 after 4 years

____%

Answer 1

a)

IRR is the rate of return that makes initial investment equal to present value of cash inflow.

Initial investment = CF / (1 + r)ⁿ

9,000 = 17,118 / (1 + R)⁷

(1 + R)⁷ = 1.902

1 + R = 1.0962

R = 0.0962 or 9.62%

IRR is 9.62%

b)

IRR is the rate of return that makes initial investment equal to present value of cash inflow.

Initial investment = CF / (1 + r)ⁿ

9,000 = 46,991 / (1 + R)¹³

(1 + R)¹³ = 5.221222

1 + R = 1.1356

R = 0.1356 or 13.56%

IRR is 13.56%

c)

IRR is the rate of return that makes initial investment equal to present value of cash inflow.

Initial investment = CF / (1 + r)ⁿ

9,000 = 109,128 / (1 + R)¹⁹

(1 + R)¹⁹ = 12.125333

1 + R = 1.1403

R = 0.1403 or 14.03%

IRR is 14.03%

d)

IRR is the rate of return that makes initial investment equal to present value of cash inflow.

Initial investment = CF / (1 + r)ⁿ

9,000 = 13,542 / (1 + R)⁴

(1 + R)⁴ = 1.504667

1 + R = 1.1075

R = 0.1075 or 10.75%

IRR is 10.75%