Jane’s Auto Care is considering the purchase of a new tow truck. The garage does
ID: 2726789 • Letter: J
Question
Jane’s Auto Care is considering the purchase of a new tow truck. The garage doesn’t currently have a tow truck, and the $60,050 price tag for a new truck would represent a major expenditure. Jane Austen, owner of the garage, has compiled the estimates shown below in trying to determine whether the tow truck should be purchased.
Jane’s good friend, Rick Ryan, stopped by. He is trying to convince Jane that the tow truck will have other benefits that Jane hasn’t even considered. First, he says, cars that need towing need to be fixed. Thus, when Jane tows them to her facility, her repair revenues will increase. Second, he notes that the tow truck could have a plow mounted on it, thus saving Jane the cost of plowing her parking lot. (Rick will give her a used plow blade for free if Jane will plow Rick's driveway.) Third, he notes that the truck will generate goodwill; people who are rescued by Jane’s tow truck will feel grateful and might be more inclined to use her service station in the future or buy gas there. Fourth, the tow truck will have “Jane’s Auto Care” on its doors, hood, and back tailgate—a form of free advertising wherever the tow truck goes. Rick estimates that, at a minimum, these benefits would be worth the following.
The company’s cost of capital is 9%.Suppose Rick has been overly optimistic in his assessment of the value of the additional benefits. At a minimum, how much would the additional benefits have to be worth in order for the project to be accepted? (Round answer to 0 decimal places, e.g. 125.)
Explanation / Answer
Details Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Cost Of Truck (60,050) Overhaul Cost (5,970) Salvage value 12,010 Annual Net Cash Flow from Towing 8,010 8,010 8,010 8,010 8,010 8,010 8,010 8,010 Net Cash flows (60,050) 8,010 8,010 8,010 2,040 8,010 8,010 8,010 20,020 PV factor @9% = 1 0.917 0.842 0.772 0.708 0.650 0.596 0.547 0.502 PV of Net Cash flows (60,050) 7,349 6,742 6,185 1,445 5,206 4,776 4,382 10,047 NPV = (13,918) So the PV of min additional benefits needs to be $13918 to justify the investment. PV annuity factor @9% for 8 years= Sumof dicount factors year 1-8= 5.5348 Total PV of the Additional benefit= 13,918 Annual Benefit required=PV/Annuity factor=13918/5.5348= $ 2,514.62 So Additional Minimum Annual benefits required = $ 2,514.62
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