determine the IRR on the following projects: a. an initial outlay of $10,000 res

Question

determine the IRR on the following projects: a. an initial outlay of $10,000 resulting in a single free cash flow of $1,993 at the end of each year for the next 10 years. b. an initial outlay of $10,000 resulting in a single free cash flow of $2,054 at the end of each year for the next 20 years. c. an initial outlay of $10,000 resulting in a single free cash flow of $1,193 at the end of each years for the next 12 years. d. an initial outlay of $10,000 resulting in a single free cash flow of $2,843 at the end of each year for the next 5 years.

Explanation / Answer

For IRR we make NPV = 0

a)      NPV = -10000 + (1993/(1+r)1) + (1993/(1+r)2) + (1993/(1+r)3) + (1993/(1+r)4) + (1993/(1+r)5) + (1993/(1+r)6) + (1993/(1+r)7) + (1993/(1+r)8) + (1993/(1+r)9) + (1993/(1+r)10)

10000 = (1993/(1+r)1) + (1993/(1+r)2) + (1993/(1+r)3) + (1993/(1+r)4) + (1993/(1+r)5) + (1993/(1+r)6) + (1993/(1+r)7) + (1993/(1+r)8) + (1993/(1+r)9) + (1993/(1+r)10)

Solving this we get

r = 15%

IRR = 15%

b)      NPV = -10000 + (2054/(1+r)1) + (2054/(1+r)2) + (2054/(1+r)3) + (2054/(1+r)4) + (2054/(1+r)5) + (2054/(1+r)6) + (2054/(1+r)7) + (2054/(1+r)8) + (2054/(1+r)9) + (2054/(1+r)10) + (2054/(1+r)11) + (2054/(1+r)12) + (2054/(1+r)13) + (2054/(1+r)14) + (2054/(1+r)15) + (2054/(1+r)16) + (2054/(1+r)17) + (2054/(1+r)18) + (2054/(1+r)19) + (2054/(1+r)20)

10000 = (2054/(1+r)1) + (2054/(1+r)2) + (2054/(1+r)3) + (2054/(1+r)4) + (2054/(1+r)5) + (2054/(1+r)6) + (2054/(1+r)7) + (2054/(1+r)8) + (2054/(1+r)9) + (2054/(1+r)10) + (2054/(1+r)11) + (2054/(1+r)12) + (2054/(1+r)13) + (2054/(1+r)14) + (2054/(1+r)15) + (2054/(1+r)16) + (2054/(1+r)17) + (2054/(1+r)18) + (2054/(1+r)19) + (2054/(1+r)20)

Solving this we get

r = 20 %

IRR = 20%

c)      NPV = -10000 + (1193/(1+r)1) + (1193/(1+r)2) + (1193/(1+r)3) + (1193/(1+r)4) + (1193/(1+r)5) + (1193/(1+r)6) + (1193/(1+r)7) + (1193/(1+r)8) + (1193/(1+r)9) + (1193/(1+r)10) + (1193/(1+r)11) + (1193/(1+r)12)

10000 = (1193/(1+r)1) + (1193/(1+r)2) + (1193/(1+r)3) + (1193/(1+r)4) + (1193/(1+r)5) + (1193/(1+r)6) + (1193/(1+r)7) + (1193/(1+r)8) + (1193/(1+r)9) + (1193/(1+r)10) + (1193/(1+r)11) + (1193/(1+r)12)

Solving this we get

r = 6%

IRR = 6%

d) NPV = -10000 + (2843/(1+r)1) + (2843/(1+r)2) + (2843/(1+r)3) + (2843/(1+r)4) + (2843/(1+r)5)

10000 = (2843/(1+r)1) + (2843/(1+r)2) + (2843/(1+r)3) + (2843/(1+r)4) + (2843/(1+r)5)

Solving this we get

r = 13%

IRR = 13%

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