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	52,061	62,756
Maintenance cost per year	6,313	5,106
Useful life	7	7
Reduction in fire damage per year	21,188	24,102
Salvage value at the end of useful life	10,833	13,229

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

Answer 1

R = 12%

n = 7 years

For Truck X:

Annual worth of Investment = 52061*(A/P, 12%, 7) = 52061*.2191 = $11406.57

Annual worth of the salvage benefit = 10833*(A/F, 12%, 7) = 10833*.0991 = $1073.55

So,

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

Conventional B/C ratio = 21188/(11406.57+6313 -1073.55)

Conventional B/C ratio = 1.27

For Truck Y:

Annual worth of Investment = 62756*(A/P, 12%, 7) = 62756*.2191 = $13749.84

Annual worth of the salvage benefit = 13229*(A/F, 12%, 7) = 13229*.0991 = $1311

So,

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

Conventional B/C ratio = 24102/(13749.84+5106 -1311)

Conventional B/C ratio = 1.37

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

Incremental annual investment = 13749.84-11406.57= $2343.27

Incremental annual benefit =24102-21188 = $2914

Incremental annual M&O cost = 5106-6313 = -$1207

Incremental AW of salvage benefits = 1311- 1073.55 = $237.45

Incremental conventional B/C ratio = 2914/(2343.27-1207-237.45)

Incremental conventional B/C ratio = 3.24

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.