Question

​(IRR calculation​) Determine the IRR on the following​ projects: a. An initial outlay of ​$13,000 resulting in a single free cash flow of ​$17,024 after 9 years b. An initial outlay of ​$13,000 resulting in a single free cash flow of ​$50,138 after 12 years c. An initial outlay of ​$13,000 resulting in a single free cash flow of ​$113,597 after 23 years d. An initial outlay of ​$13,000 resulting in a single free cash flow of ​$13,858 after 2 years a. What is the IRR of a project with an initial outlay of ​$13,000 resulting in a single free cash flow of ​$17,024 after 9 ​years?

Answer 1

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

a.

13000=17024/1.0x^9

1.0x^9=(17024/13000)

1.0x=(17024/13000)^(1/9)

x=1.0304-1

=3.04%(Approx)

b.

13000=50138/1.0x^12

1.0x^12=(50138/13000)

1.0x=(50138/13000)^(1/12)

x=1.1191-1

=11.91%(Approx).

c.

13000=113,597/1.0x^23

1.0x^23=(113,597/13000)

1.0x=(113,597/13000)^(1/23)

x=1.0988-1

=9.88%(Approx).

d.

13000=13,858/1.0x^2

1.0x^2=(13,858/13000)

1.0x=(13,858/13000)^(1/2)

x=1.0325-1

=3.25%(Approx)