A dozer cost $300,000 to purchase, and the machine useful life is 10 years and 10,000 operating hours. The salvage value of the equipment at the end of 10 years is 20% of the purchase price. The maintenance cost for the equipment is $30 per operating hour. A major engine repair is expected in 5 years for $30,000. if the company cost of capital rate is 10%, how much should the owner of the machine charge per hour of use if the machine is expected to operate 1,000 hours per year?

Hi, in order to find the price per hour, we need to establish the equation with all the information given, that is bringing to present value all the future cash flows, both positive and negative.

[tex]NPV(+)CF=NPV(-)CF[/tex]

that is

Cost + PV maintenance + PV major repairs = PV(Revenue) + PV Salvage Value

So, everything should look like this:

[tex]30,000+\frac{(30*1,000)((1+0.1)^{10}-1) }{0.1(1+0.1)^{10} } +\frac{30,000}{(1+0.1)^{5} } =\frac{0.2*300,000}{(1+0.1)^{10} } +\frac{A((1+0.1)^{10}-1) }{0.1(1+0.1)^{10} }[/tex]

Now, we solve for "A", which is the annual value to charge for the dozer, for 10 years.

[tex]30,000+\frac{(30*1,000)((1+0.1)^{10}-1) }{0.1(1+0.1)^{10} } +\frac{30,000}{(1+0.1)^{5} } -\frac{0.2*300,000}{(1+0.1)^{10} } =\frac{A((1+0.1)^{10}-1) }{0.1(1+0.1)^{10} }[/tex]

[tex]30,000+184,337.01 +18,627.64 -23,132.60=A(6.144567106)[/tex]

[tex]479,832.06=A(6.144567106)[/tex]

[tex]A=\frac{479,832.06}{6.144567106}[/tex]

A= $78,090.46

So, the annual revenue of the dozer would have to be $78,090.46, but since it works 1,000 hours per year, the owner would have to charge $78,090.46 / 1,000 = $78.10 (rounded so we get a little excess)

Best of luck.