Question

​(IRR calculation​) Determine the IRR on the following​ projects:

a. An initial outlay of ​$12,000 resulting in a single free cash flow of ​$16,842 after 6 years

b. An initial outlay of ​$12,000 resulting in a single free cash flow of ​$54,127 after 10 years

c. An initial outlay of ​$12,000 resulting in a single free cash flow of ​$108,856 after 24 years

d. An initial outlay of ​$12,000 resulting in a single free cash flow of ​$14,336 after 4 years

What is the IRR of a project with an initial outlay of ​$12,000 resulting in a single free cash flow of ​$16,842 after 6 ​years?

Answer 1

Let irr be x%
At irr,present value of inflows=present value of outflows.

a.

12000=16,842/1.0x^6

1.0x^6=(16,842/12000)

1.0x=(16,842/12000)^(1/6)

x=1.0581-1

=5.81%(Approx).

b.

12000=54,127/1.0x^10

1.0x^10=(54,127/12000)

1.0x=(54,127/12000)^(1/10)

x=1.1626-1

=16.26%(Approx).

c.

12000=108,856/1.0x^24

1.0x^24=(108,856/12000)

1.0x=(108,856/12000)^(1/24)

x=1.0962-1

=9.62%(Approx).

d.

12000=14,336/1.0x^4

1.0x^4=(14,336/12000)

1.0x=(14,336/12000)^(1/4)

x=1.0455-1

=4.55%(Approx).