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 provide code)

Answer 1

A)

Steps:

I) Discount the value of each cost and benefit/savings using Net Present value (NPV) Formula i.e. cost/savings/(1+i)^n (where i=discounting factor/rate of return and n=time period)

II) Arrive at the total Present Value (PV) of cost and PV of savings

III) Divide PV of savings by PV of cost. If the value is less than 1, then the benefit-cost analysis is negative and the option is to be rejected.

OPTION 1: Modern Bus

I) NPV of cost : $95,000 (Initial cost so n=0)

NPV of savings :

Rate (r)	5%
Time Periods (n)	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Savings & Salvage Value	20,000	19,000	18,000	17,000	16,000	15,000	14,000	13,000	12,000	11,000	10,000	9,000	8,000	7,000	6,000	5,000	4,000	3,000	2,000	9,000
NPV	$153,770.91

*Salvage value of $ 8000 is included in Year 20

* In excel insert function =NPV (Discount rate cell, Value1:Value20)

III) Benefit Cost Analysis : 153,771/95,000 = 1.62

OPTION 2: Basic Bus

I) NPV of cost : $70,000 (Initial cost so n=0)

NPV of savings :

Rate (r)	5%
Time Periods (n)	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Savings & Salvage Value	14,000	13,500	13,000	12,500	12,000	11,500	11,000	10,500	10,000	9,500	9,000	8,500	8,000	7,500	7,000	6,500	6,000	5,500	5,000	9,500
NPV	$127,111.19

*Salvage value of $5000 is included in Year 20

III) Benefit Cost Analysis : 127,111/70,000 = 1.82

Considering that the Benfit-Cost ratio of Option 2 is higher, the school should purchase the Basic Bus. (If the Benfit-Cost ratio of both options would have been less than 1, the school could have continued with their current fleet.)

B) To make both options equally desirable,

Benefit Cost Ratio of Option 1 = Benefit Cost ratio of Option 2

PV of savings of option1 / Cost of Modern Bus (X) = PV of Savings of option 2 / Cost of Basic Bus

153,771 / X = 127,111/70,000

X= (153,771 * 70,000) / 127,111

X= $ 84,682

The cost of the modern bus should be $84,682 to make it equally desirable as Option 2

C) There are many factors that should be considered while buying a school bus besides the economic aspects. These include Safety, Size, Comfort, Engine type etc. The modern bus with safety belts, air conditioning and an engine type which is eco-friendly, scores higher than the Basic bus when these other factors are taken into consideration. Even economically, the benefit-cost ratio of the Modern bus is not negative and only slightly less as compared to the Basic Bus. Adding in the other amenities that the Modern Bus provides, it might be desirable to opt for Option1 i.e. the Modern Bus.