Question

four mutually exclusive projects are being considered for a new 2 - mile jogging track. the life of the track is expected to be 80 years, and the sponsoring agencys marr is 11% per year. annual benefits to the public have been estimated by an advisory committee and are shown below. use the b - c method (incrementally) to select the best jogging track. perform the incremental b - c analysis. fill - in the table below. (round to two decimal places.)

Explanation:

Step1: Calculate incremental B - C ratio for D vs C

First, find incremental cost and incremental benefit.
Incremental cost \( \Delta C=160000 - 61000=\$99000\)
Incremental benefit \( \Delta B=19000 - 10500=\$8500\)
Since the life \(n = 80\) years and \(i=11\%\), the capital - recovery factor \(CRF=\frac{i(1 + i)^{n}}{(1 + i)^{n}-1}\approx\frac{0.11(1 + 0.11)^{80}}{(1 + 0.11)^{80}-1}\approx0.11\) (because for large \(n\), \(CRF\approx i\) when \(i\) is in decimal)
Incremental B - C ratio \(=\frac{\Delta B}{\Delta C\times CRF}=\frac{8500}{99000\times0.11}=\frac{8500}{10890}\approx0.78\)

Answer:

Alternative	Inc. B - C ratio	Is the alternative acceptable?
A	6.82	Yes
C	1.52	Yes
D	0.78	No

Since the incremental B - C ratio of D vs C is less than 1, D is not acceptable. Among A, B and C (where all have B - C ratio > 1 and incremental B - C ratios (A vs B, C vs A) also > 1), the best alternative is C.