6 A construction firm is considering buying a backhoe since

6. A construction firm is considering buying a backhoe, since it pays $50/h to rent one, and it needs to use a backhoe for 150 hours per month. Assuming a backhoe lasts 5 years, and has monthly maintenance of $2,000 and a salvage value of $15,000, what\'s the most the company should pay for this backhoe? (Use a 6% discount rate). (2 pt)

Solution

Consider the given problem here the construction firm have 2 choices either to hire it and pay “$50/h” or to buy it.

Now, if the firm hire it then the firm have to pay “$50/h” and it needs to use 150hours per month, the firm have to pay “$50*150=$7,500” per month. In a year there are 12 months, => in 5 month, there are 5*12=60 months.

So, the present value of all these cash flow is given below.

=> $7,500*[(1.06^60 - 1) / 0.06*1.06^60] = $7,500*[31.9877 / 1.9793] = $7,500*16.1611 = $121,208.25.

Now, if the firm will purchase it then the firm have to incur maintenance cost of “$2000” per month and the salvage value is “$15,000”. Let’s assume that the price that the firm should pay is “$X”.

So, given this the present value of all the cost if the firm buy the backhoe is mentioned below.

=> $X + $2,000*[(1.06^60 - 1) / 0.06*1.06^60] - $15,000/(1+i)^60.

=> $X + $2,000*[31.9877 / 1.9793] - $15,000/(1+0.06)^60.

=> $X + $2,000*16.1611 - $454.7151 = $X + $32,322.2 - $454.7151 = $X + $31,867.4849.

So, now the firm should buy the backhoe is “present value of cost when the firm will purchase the backhoe” is less than the “present value of cost when the firm will hire the backhoe”.

=> $X + $31,867.4849 $121,208.25, => $X $121,208.25 - $31,867.4849 = $89,340.7651 = $89,341.

So, if “$X $89,341, the firm should pay maximum “$89,341” for the backhoe.