A small strip-mining coal company is trying to decide whether it should purchase

Question

A small strip-mining coal company is trying to decide whether it should purchase or lease a new clamshell. If purchased, the “shell” will cost $150,000 and is expected to have a $55,000 salvage value after 6 years. Alternatively, the company can lease a clamshell for only $18,000 per year, but the lease payment will have to be made at the beginning of each year. If the clamshell is purchased, it will be leased to other strip-mining companies whenever possible, an activity that is expected to yield revenues of $14,000 per year. If the company’s MARR is 16% per year, should the clamshell be purchased or leased on the basis of a future worth analysis? Assume the annual M&O cost is the same for both options.

The future worth when purchased is $ .

The future worth when leased is $ .

Explanation / Answer

CASE 1 - Calmshell is purchased

Cost of shell = $150,000

Salvage value = $55,000

MARR = 16%

Time period = 6 years

Calculate the future worth when clamshell is purchased -

FW = -$150,000(F/P, 16%, 6) + $55,000

FW = (-$150,000 * 2.4363) + $55,000

FW = -$365,445 + $55,000 = -$310,445

The future worth when clamshell is purchased is -$310,445.

CASE 2 - Clamshell is leased

Lease payment = $18,000 per year

Revenue = $14,000 per year

MARR = 16%

Time period = 6 years

Calculate the future worth when clamshell is leased -

FW = -$18,000(F/A, 16%, 6) + $14,000(F/A, 16%, 6)

FW = (-$18,000 * 8.9774) + ($14,000 * 8.9774)

FW = -$161,593.2 + $125,683.6

FW = -$35,909.6

The future worth of clamshell when leased is -$35,909.6

The future worth is numerically higher when clamshell is leased.

So,

The clamshell shoulld be leased.

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