Question

) A public school district is investigating whether to purchase a new school bus to take over the rural-most route in the district. They have two options:

A modern, eco-friendly bus complete with seat belts and air conditioning, will have a first cost of $95,000, cost savings (in terms of fuel efficiency and maintenance costs) of $20,000/year the first year, and decreasing by $1000 per year thereafter (so $19,000 the second year, 18,000 the third year, etc…). It’s estimated that the salvage value will be $8,000 at the end of its 20 year life.

A more basic bus will have a first cost $70,000, cost savings of $14,000 per year decreasing by $500 per year each year thereafter (so $13,500 the second year, $13,000 the third year, etc.).It is estimated that the salvage value will be $5000 at the end of its 20-year life.

Assume that the school district also has the option to stay with their current fleet (so the do nothing option is also available).

A) Use Benefits to Costs analysis to determine which of the options, if any, would be most economical for the school district if their MARR is 5%.

B) Compute the value of X- i.e., the first cost of the modern bus- that makes the two alternatives in this example equally desirable:

	Modern	Basic
Cost	X	$70,000
Uniform annual benefit	$20,000 in year 1, decreasing by $1000/year thereafter	$14,000 in year 1, decreasing by $500/year thereafter
Salvage value	$8000	$5000

C) In this problem only the economic consequences were evaluated. Do you think this type of decision is only economic, or are there other factors that could/would/should be considered? Briefly discuss…

(if using excel please post code)

Answer 1

Modern Bus

Year	Cash Inflow	PVF @ 5%	Present Value
0	-95000.00	1	-95000.00
1	20000.00	0.952	19040.00
2	19000.00	0.907	17233.00
3	18000.00	0.864	15552.00
4	17000.00	0.823	13991.00
5	16000.00	0.784	12544.00
6	15000.00	0.748	11220.00
7	14000.00	0.711	9954.00
8	13000.00	0.677	8801.00
9	12000.00	0.645	7740.00
10	11000.00	0.614	6754.00
11	10000.00	0.585	5850.00
12	9000.00	0.557	5013.00
13	8000.00	0.530	4240.00
14	7000.00	0.505	3535.00
15	6000.00	0.481	2886.00
16	5000.00	0.458	2290.00
17	4000.00	0.436	1744.00
18	3000.00	0.416	1248.00
19	2000.00	0.396	792.00
20	9000.00	0.377	3393.00
		NPV	58820.00

Note: Cash inflow at the end of year 20 = 1000 and 8000 salvage value

Basic bus

Year	Cash Inflow	PVF @ 5%	Present Value
0	-70000.00	1	-70000.00
1	14000.00	0.952	13328.00
2	13500.00	0.907	12244.50
3	13000.00	0.864	11232.00
4	12500.00	0.823	10287.50
5	12000.00	0.784	9408.00
6	11500.00	0.748	8602.00
7	11000.00	0.711	7821.00
8	10500.00	0.677	7108.50
9	10000.00	0.645	6450.00
10	9500.00	0.614	5833.00
11	9000.00	0.585	5265.00
12	8500.00	0.557	4734.50
13	8000.00	0.530	4240.00
14	7500.00	0.505	3787.50
15	7000.00	0.481	3367.00
16	6500.00	0.458	2977.00
17	6000.00	0.436	2616.00
18	5500.00	0.416	2288.00
19	5000.00	0.396	1980.00
20	9500.00	0.377	3581.50
		NPV	57151.00

Similarly, 4500 and 5000 salvage value

B.

In order to make both the alternatives equally desirable, the Net Present Value(NPV) from the alternatives should be equal Modern    Present value of cash inflow - PV of Cash outflow    Basic Present value of cash inflow - PV of Cash outflow 153820-X = 57151 X = 96669 Hence, if the first cost of the modern bus equals $96669 then the both alternatives would be equally desirable i.e. they will provide equal NPV.