?(IRR calculation?) Determine to the nearest percent the IRR on the following? p

Question

?(IRR calculation?) Determine to the nearest percent the IRR on the following? projects:

a. An initial outlay of ?$9,000 resulting in a free cash flow of ?$3,000 at the end of year? 1, ?$6 ,000 at the end of year? 2, and $8,500 at the end of year 3

b. An initial outlay of ?$9,000 resulting in a free cash flow of ?$8,500 at the end of year? 1, ?$6,000 at the end of year? 2, and $ 3,000 at the end of year 3

c. An initial outlay of ?$9,000 resulting in a free cash flow of ?$3,000 at the end of years 1 through 5 and ?$6,000 at the end of year 6

Explanation / Answer

IRR Project A 36% Project B 55% Project C 28% Working: Project A: IRR is the rate, at which net present value is zero. Net Present Value at 20% Net Present Value at 40% Year Cash flow Discount factor Present Value Year Cash flow Discount factor Present Value a b c=1.20^-a d=b*c a b c=1.40^-a d=b*c 0 $            -9,000      1.0000 $       -9,000 0 $   -9,000      1.0000 $   -9,000 1                  3,000      0.8333             2,500 1         3,000      0.7143         2,143 2                  6,000      0.6944             4,167 2         6,000      0.5102         3,061 3                  8,500      0.5787             4,919 3         8,500      0.3644         3,098 Net Present Value             2,586 Net Present Value           -698 IRR = 20%+(40%-20%)*(2586/(2586+698)) = 36% Project B: IRR is the rate, at which net present value is zero. Net Present Value at 20% Net Present Value at 60% Year Cash flow Discount factor Present Value Year Cash flow Discount factor Present Value a b c=1.20^-a d=b*c a b c=1.60^-a d=b*c 0 $            -9,000      1.0000 $       -9,000 0 $   -9,000      1.0000 $   -9,000 1                  8,500      0.8333             7,083 1         8,500      0.6250         5,313 2                  6,000      0.6944             4,167 2         6,000      0.3906         2,344 3                  3,000      0.5787             1,736 3         3,000      0.2441            732 Net Present Value             3,986 Net Present Value           -611 IRR = 20%+(60%-20%)*(3986/(3986+611)) = 55% Project C: IRR is the rate, at which net present value is zero. Net Present Value at 20% Net Present Value at 30% Year Cash flow Discount factor Present Value Year Cash flow Discount factor Present Value a b c=1.20^-a d=b*c a b c=1.30^-a d=b*c 0 $            -9,000      1.0000 $       -9,000 0 $   -9,000      1.0000 $   -9,000 1                  3,000      0.8333             2,500 1         3,000      0.7692         2,308 2                  3,000      0.6944             2,083 2         3,000      0.5917         1,775 3                  3,000      0.5787             1,736 3         3,000      0.4552         1,365 4                  3,000      0.4823             1,447 4         3,000      0.3501         1,050 5                  3,000      0.4019             1,206 5         3,000      0.2693            808 6                  6,000      0.3349             2,009 6         6,000      0.2072         1,243 Net Present Value             1,981 Net Present Value           -450 IRR = 20%+(30%-20%)*(1981/(1981+450)) = 28%

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