Question

The city council of Morristown is considering the purchase of one new fire truck. The options are Truck X and Truck Y. The purchase is to be financed by money borrowed at 12% per year. The appropriate financial data are as follows:

	Truck X	Truck Y
Capital Investment	53,533	62,366
Maintenance cost per year	6,284	5,160
Useful life	5	5
Reduction in fire damage per year	21,569	24,633
Salvage value at the end of useful life	10,140	13,256

Use conventional benefit cost ratio analysis. Write the incremental benefit cost ratio for the trucks

Answer 1

For Truck X:

Annual worth of Investment = 53533*(A/P, 12%, 5) = 53533*.2774 = $14850.05

Annual worth of the salvage benefit = 10140*(A/F, 12%, 5) = 10140*.1574 = $1596.04

So,

Conventional B/C ratio = Annual benefits / (AW of initial cost + Annual O&M cost – AW of salvage value)

Conventional B/C ratio = 21569/(14850.05+6284-1596.04)

Conventional B/C ratio = 1.104

For Truck Y:

Annual worth of Investment = 62366*(A/P, 12%, 5) = 62366*.2774 = $17300.33

Annual worth of the salvage benefit = 13256*(A/F, 12%, 5) = 13256*.1574 = $2086.5

So,

Conventional B/C ratio = Annual benefits / (AW of initial cost + Annual O&M cost – AW of salvage value)

Conventional B/C ratio = 24633/(17300.33+5160-2086.5)

Conventional B/C ratio = 1.21

As a part of incremental conventional B/C ratio analysis,

Incremental annual investment = 17300.33-14850.05 = $2450.28

Incremental annual benefit =24633-21569 = $3064

Incremental annual M&O cost = 5160-6284 = -$1124

Incremental AW of salvage benefits = 2086.5 - 1596.04 = $490.46

Incremental conventional B/C ratio = 3064/(2450.28-$1124-490.46)

Incremental conventional B/C ratio = 3.66

Since convention B/C ratio of truck Y is higher than that of truck X and incremental conventional B/C ratio of truck Y over X is also very high to these individual values, then truck Y should be selected for purchase.