Question

A track dozer cost $165,500 to purchase. Fuel, oil, grease, and minor maintenance are estimated to cost $35.00 per operating hour. A major engine repair costing $26,000 will probably be required after 7,200 hr of use. The expected resale price (salvage value) is 21% of the original purchase price. The machine is expected to have a useful life of 10,800 hr. How much should the owner of the machine charge per hour of use, if it is expected that the machine will operate 1,800 hr per year? The company's cost- of-capital rate is 7.3%.

Answer 1

Answer:

It will charge 54.22 per hour to obtain a yield of 7.3% on the track dozer.

Explanation:

purchase cost 165,500

repair costing 26,000 at year 4

annual cost: 1,800 x 35 = 63,000

salvage value at end of useful life:

21% of purchase cost :

21% of 165,500 = 34,755

We will calculate the present value of the salvage value and the overhaul, to know how much does the company need to generate per year:

165,000 + pv of overhaul + pv of salvage value  = present value of the cash inflow

pv of the overhaul

$\frac{overhaul}{(1 + rate)^{time} } = PV$

overhaul: 26,000

time   4

rate 0.073

$\frac{26000}{(1 + 0.073)^{4} } = PV$

PV  $19,614.3744

Then, the PV of the salvage value:

$\frac{salvage}{(1 + rate)^{time} } = PV$

salvage 34,755

time 6

rate 0.073

$\frac{34755}{(1 + 0.073)^{6} } = PV$

PV  $22,772.9326

165,500 + 19,614.3744-22,772.9326 = 163,341.4418

The present value of the contribution per hour at 7.3% discount rate should equal this amount

So we will set up the formula for the cuota of an annuity:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $163,341.44

time 6

rate 0.073

$-34586.3538411519 \div \frac{1-(1+0.073)^{-6} }{0.073} = PV$

C 34,586.35

The contribution per year should be 34,586.35

each hour contribution should be: 34,586.35/1,800 = 19.2146

After the operating cost it should net 19.2146

hourly rate - 35 = 19.2146

hourly rate = 19.2146 + 35 = 54.2146 = 54.22