what is the IRR for the Electric Barriers and the incremental IRR The migration

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what is the IRR for the Electric Barriers and the incremental IRR

The migration of Asian carp into the Great Lakes must be stopped. Two mutually exclusive alternatives with a useful life of three years have been proposed to keep the carp from travelling further north. If the MARR is 10%, which alternative should be chosen if it is specified that the internal rate-of-return method must be utilized? Assume repeatability. Fish Nets $1,100,000 $580,000 (EOY 1) 5640,000 (EOY 2) Electric Barriers $2,570,000 $860,000 (EOY 1) $3,140,000 (EOY 2) Initial investment Annual benefits less expenses 550,000 (EOY 3) S0 (EOY 3) (Round to one The IRR for the Fish Nets is 28.9 %, so this alternative is acceptable decimal place.) . (Round to one The IRR for the Electric Barriers is 28.5 %, so this alternative is acceptable decimal place.) The incremental IRR is 28.6%, so one should choose the Electric Barriers alternative. (Round to one decimal place.)

Explanation / Answer

For electric barriers investment,

Let, IRR = R

Then,

2570000 = 860000/(1+R) + 3140000/(1+R)^2 + 0/(1+R)^3

At R = 28%

Present value of cash inflows = $2588379

At R = 29%

Present value of cash inflows = $2553573

By method of interpolation,

R = 28% + ((PV of cash inflows – 2570000)/( PV of cash inflows- PV of cash outflows))*(29%-28%)

R = 28% + ((2588379 - 2570000)/( 2588379 - 2553573))*(29%-28%)

R = 28.528% or 28.5%

Though, the IRR of electric barrier alternative has higher IRR than the 10%, but it is lower than the IRR of Fish Nets, then the fishnet investment should be preferred over the electric barrier alternative.

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For incremental IRR

in electric barrier over Fishnets investment,

Incremental investment = 2570000 – 1100000 = $1470000

Incremental net benefits in year 1 = 860000 – 580000 = $280000

Incremental net benefits in year 2 = 3140000 – 640000 = $2500000

Incremental net benefits in year 3 = 0 – 550000 = -$550000

Let, K = incremental IRR

then,

1470000 = 280000/(1+K) + 2500000/(1+K)^2 – 550000/(1+K)^3

At K = 28%

Present value of Incremental cash inflows = $1482368

At K = 29%

Present value of Incremental cash inflows = $1463159

By the method of interpolation,

K = 28% + ((1482368-1470000)/( 1482368-1463159))*(29%-28%)

K = 28.643% or 28.6%

The incremental IRR is also lower than the IRR of Fish net alternative, hence Fishnet alternative should be selected.

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