Question

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

a. An initial outlay of $10,000 resulting in a single free cash flow of $16,863 after 7 years

b. An initial outlay of ​$10,000 resulting in a single free cash flow of $50,003 after 14 years

c. An initial outlay of ​$10,000 resulting in a single free cash flow of $114,691 after 23 years

d. An initial outlay of $10,000 resulting in a single free cash flow of ​$14,283 after 3 years

Answer 1

We have been given an initial outlay along with a single cash flow after "n" years. Calculating IRR is simple for this as we can use the compound annual rate growth formula for solving this.

IRR = [ ( Single Cash flow / Initial Outlay ) ^ (1 / Years) ] - 1

a)

Initial Outlay = $ 10,000 , Single Cash flow = $ 16,863, Years = 7

Hence, IRR = [ (16863 / 10000) ^ ( 1 / 7) ] - 1

IRR =  ( 1.6863 ^ 0.14285) - 1

IRR = 1.0775049 - 1

IRR = 7.75%

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b)

Initial Outlay = $ 10,000 , Single Cash flow = $ 50,003 , Years = 14

Hence, IRR = [ (50003 / 10000) ^ ( 1 / 14) ] - 1

IRR =  ( 5.0003 ^ 0.0714285) - 1

IRR = 1.121833 - 1

IRR = 12.18%

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c)

Initial Outlay = $ 10,000 , Single Cash flow = $ 114,691, Years = 23

Hence, IRR = [ (114691 / 10000) ^ ( 1 / 23) ] - 1

IRR =  ( 11.4691 ^ 0.0434782) - 1

IRR = 1.1119019 - 1

IRR = 11.19%

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d)

Initial Outlay = $ 10,000 , Single Cash flow = $ 14,283 , Years = 3

Hence, IRR = [ (14283 / 10000) ^ ( 1 / 3) ] - 1

IRR =  ( 1.4283 ^ 0.333333) - 1

IRR = 1.1261765 - 1

IRR = 12.62%

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