Making Money, Inc. is considering the purchase of a new truck so it can make mor
ID: 2792678 • Letter: M
Question
Making Money, Inc. is considering the purchase of a new truck so it can make more money. The truck costs $120,000.
Making Money, Inc. had been renting the truck every week for $500 per week plus $1.20 per mile. On average, the truck is traveling 75 miles per week.
If Making Money, Inc. purchases the truck, it will only have to pay for diesel fuel and maintenance, at about $.50 per mile. Insurance costs for the new truck are $5,000 per year.
The truck will probably be worth $20,000 (in real terms) after six years, when the company would be looking to sell the truck.
Assume a nominal discount rate of 10% and a forecasted inflation rate of 2.5%. The tax code is rapidly changing, so we are going to ignore taxes for now.
WHAT IS THE NPV of BUYING vs RENTING? (round to nearest whole dollar)
Hint: All numbers given in the questions are in real terms. Assume CF at end of year, for simplicity.
Hint #2:
Step 1: list assumptions
Step 2: calc real interest rate
Step 3: Calc cost (NPV) to rent
Step 4: Calc cost (NPV) to buy
Step 5: subtract NPVs
Explanation / Answer
Before finding the NPV let us find the real interest rate = Nominal interest rate - inflation rate
= 10% - 2.5% = 7.5%
Computation of NPV for buying and renting:
yearly fixed cost for buying = 5,000+ 75miles*$0.5*52weeks = 5,000+ 1,950 = 6,950
yearly fixed cost for renting =500*52 weeks + $1.20per mile*75miles*52weeks = 26,000+4,680 = 30,680
Cash flows
Discounting factor
PV of cash flows
Years
Buying the truck
Renting
at 7.5%
Buying the truck
Renting
0
120,000.00
-
1
120000
0
1
6,950.00
30,680.00
0.930233
6,465.12
28,539.53
2
6,950.00
30,680.00
0.865333
6,014.06
26,548.40
3
6,950.00
30,680.00
0.804961
5,594.48
24,696.19
4
6,950.00
30,680.00
0.748801
5,204.16
22,973.20
5
6,950.00
30,680.00
0.696559
4,841.08
21,370.42
6
(13,050.00)
30,680.00
0.647962
(8,455.90)
19,879.46
NPV
139,663.00
144,007.21
From the above NPV's it is better to buy the truck since it has less cost compare to renting by $4,344.21
Cash flows
Discounting factor
PV of cash flows
Years
Buying the truck
Renting
at 7.5%
Buying the truck
Renting
0
120,000.00
-
1
120000
0
1
6,950.00
30,680.00
0.930233
6,465.12
28,539.53
2
6,950.00
30,680.00
0.865333
6,014.06
26,548.40
3
6,950.00
30,680.00
0.804961
5,594.48
24,696.19
4
6,950.00
30,680.00
0.748801
5,204.16
22,973.20
5
6,950.00
30,680.00
0.696559
4,841.08
21,370.42
6
(13,050.00)
30,680.00
0.647962
(8,455.90)
19,879.46
NPV
139,663.00
144,007.21
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