Question

Four mutually exclusive projects are being considered for a new​ 2-mile jogging track. The life of the track is expected to be 75 years, and the sponsoring​ agency's MARR is 9​% 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.

                                                                                                                         

	Alternative
	A		B		C		D
Initial cost	​$54,000		​$55,000		​$62,000		​$145,000
Annual benefits	​$7,000		​$8,500		​$10,000		​$19,000
​B-C ratio	1.44		1.71		1.79		1.45

Perform the incremental​ B-C Analysis.​ Fill-in the table below. ​(Round to two decimal​ places.)

Alternative	Inc.​ B-C ratio	Is the alternative​ acceptable?
A	1.44	Yes
D C B

what is the most reasonable alternative?

Answer 1

While doing incremental analysis, we look at the alternative with the highest B/C ratio, and then check it against the next highest provided such next highest has an investment requirement greater than that of the highest. For instance, in this case:

C has the highest B/C ratio and the next highest is B. If we do incremental analysis between C and B, it is not of much value since C has higher investment than B and also a higher B/C ratio so the incremental (C-B) will obviously have a high (higher than even C) B/C ratio.

Similarly we don't need to do incremental analysis between C and A.

That leaves us with C and D and we should do this since D has a higher investment but lower B/C ratio than C.

D: Investment 145,000 and B/C ratio = 1.45, hence Benefits (PV of them) = 1.45*145,000 = 210250

C: Investment 62,000 and B/C ratio = 1.79, hence Benefits (PV) = 1.79*62000 = 110980

D-C: Investment 145000-62000 = 83000, Benefits (PV) = 210250-110980 = 99270, hence B/C ratio = 99270/83000 = 1.196

Since D-C has a positive B/C ratio, we should go for D.