Four mutually exclusive projects are being considered for a new two-mile jogging track. The life of the track is expected to be 80 years, and the sponsoring agency’s MARR is 12% per year. Annual benefits to the public have been estimated by an advisory committee and are shown below. Use the IRR met

Question

Four mutually exclusive projects are being considered for a new two-mile jogging track. The life of the track is expected to be 80 years, and the sponsoring agency's MARR is [latex]12 \%[/latex] per year. Annual benefits to the public have been estimated by an advisory committee and are shown below. Use the IRR method (incrementally) to select the best jogging track. (6.4)

Alternative	A	B	C	D
Initial cost	$62,000	$52,000	$150,000	$55,000
Annual benefits	$10,000	$8,000	$20,000	$9,000
Rate of return on investment	16.1%	15.4%	13.3%	16.4%

Accepted Answer

List the alternatives in increasing order of initial cost: DN, B, D, A, C.

In general, we have [latex]P=A\left(P / A, i^{\prime}, 80 ight)[/latex] which becomes [latex]i^{\prime}=A / P[/latex] when the MARR is [latex]12 \%[/latex] and [latex]N=80[/latex] years, where [latex]i^{\prime}[/latex] is the IRR of the project or the incremental cash flows. The incremental comparisons follow:

[latex]\Delta(\mathrm{B}-\mathrm{DN})=8 / 52=0.154(15.4 \%)[/latex], so select B.

[latex]\Delta(\mathrm{D}-\mathrm{B})=1 / 3=0.333[/latex] (33.3%), so select [latex]\mathrm{D}[/latex].

[latex]\Delta(\mathrm{A}-\mathrm{D})=1 / 7=0.143(14.3 \%)[/latex], so select [latex]\mathrm{A}[/latex].

[latex]\Delta(C-A)=10 / 88=0.114(11.4 \%)[/latex], so keep A

Therefore, we recommend Alternative A even though it does not have the largest IRR or the largest [latex] riangle \mathrm{IRR}[/latex].

Question 6.T-Y-S.E: Four mutually exclusive projects are being considered for a ...

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