Question

The M2 Corporation is considering expanding its ergonomics consulting business. To do so, several pieces of equipment for performing a given analysis technique must be purchased. The CEO estimates that it will cost $155,000 to expand the business, resulting in $31,000 in revenues per year, $12,000 in expenses per year, and a salvage value of $3000. If the useful life of the expansion is expected to be 15 years, and the Corporation’s MARR is 15%.

a. Should they undertake the expansion? You must use the Benefit/Cost Ratio to receive ANY credit.

b. What would the break-even point be for annual revenues for this problem?

Answer 1

Particulars	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Intial Investment	($155,000.00)
Revenues		31,000	31,000	31,000	31,000	31,000	31,000	31,000	31,000	31,000	31,000	31,000	31,000	31,000	31,000
Expenses	-	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000
Salvage Value															3000
Total Cash flows	($155,000.00)	$19,000.00	$19,000.00	$19,000.00	$19,000.00	$19,000.00	$19,000.00	$19,000.00	$19,000.00	$19,000.00	$19,000.00	$19,000.00	$19,000.00	$19,000.00	$22,000.00
Rate	15%	19000/1.15^2	19000/1.15^3	19000/1.15^4	19000/1.15^5	19000/1.15^6	19000/1.15^7	19000/1.15^8	19000/1.15^9	19000/1.15^10	19000/1.15^11	19000/1.15^12	19000/1.15^13	19000/1.15^14	22000/1.15^15
	($155,000.00)	$14,366.73	$12,492.81	$10,863.31	$9,446.36	$8,214.22	$7,142.80	$6,211.13	$5,400.99	$4,696.51	$4,083.92	$3,551.24	$3,088.03	$2,685.24	$2,703.68
NPV(Sum of Present Value of all The cash flows)	($39,835.63)
Benefit(Sum of Cash flows Present Value)	$94,946.98
Benefit/Cost	0.61

Clearly, benefit/cost is less than 1 and hence the investment is not worthy with given revenues.

For break even, we need to increase our revenue. Currently the sum of cash flows(Present Value) is 94946 and we want to equate it to 155000. The yearly net cash flow is 19000 when we have BCR 0.61. Hence we need to what will be cash flow for BCR to be 1?

That will be given by 19000/BCR = 19000/0.61 = 31200. And hence we need to increase our revenues by 31200 - 19000 = 12,200.

Now have a look at the cash flows, after the break even revenues

Intial Investment	($155,000.00)
Revenues		43,200	43,200	43,200	43,200	43,200	43,200	43,200	43,200	43,200	43,200	43,200	43,200	43,200	43,200
Expenses	-	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000	-12,000
Salvage Value															3000
Total Cash flows	($155,000.00)	$31,200.00	$31,200.00	$31,200.00	$31,200.00	$31,200.00	$31,200.00	$31,200.00	$31,200.00	$31,200.00	$31,200.00	$31,200.00	$31,200.00	$31,200.00	$34,200.00
Rate	15%	31,200/1.15^2	31,200/1.15^3	31,200/1.15^4	31,200/1.15^5	31,200/1.15^6	31,200/1.15^7	31,200/1.15^8	31,200/1.15^9	31,200/1.15^10	31,200/1.15^11	31,200/1.15^12	31,200/1.15^13	31,200/1.15^14	34,200/1.15^15
	($155,000.00)	$23,591.68	$20,514.51	$17,838.70	$15,511.91	$13,488.62	$11,729.24	$10,199.34	$8,868.99	$7,712.16	$6,706.23	$5,831.50	$5,070.87	$4,409.45	$4,202.99
NPV(Sum of Present Value of all The cash flows)	$20,893.59
Benefit(Sum of Cash flows Present Value)	$155,676.20
Benefit/Cost	1.00

Hope this helps. Please ask in the comment section, if you have any doubt.