Question

1. Your company purchases a new heavy-duty truck. It has an initial cost of $50,000 and maintenance will be provided by the dealer at no additional charge for the first 3 years. At the end of year 4 maintenance cost is estimated to be $2,000 increasing at 10 percent per year thereafter for an additional 4 years. You estimate the additional revenues to the company due to the use of the new heavy-duty truck to be $8,000 end of years 1 and 2 increasing to $10,000 for end of years 3 and increasing by an additional $500 per year for end of years 4 through 8. At the end of 8 years the truck will be sold for its estimated value of $15,000. Interest rate for all 8 years is 15%.

1. Draw the cash flow diagram from the company’s perspective.
2. What is the present value at time=0 for all your estimated maintenance expenses?
3. What is the present value at time=0 for all your estimated revenues including the sell of the truck at end of year 8?
4. Based on your findings for (a) and (b) above, was purchasing the heavy-duty truck profitable to the company?
   

Answer 1

Below is the tabular presentation of the inflow and outflow of the funds.

Year	Truck	Maintenance Expense	Revenue	Net Amount	Remarks
0	($50,000)	-		($50,000)	Purrchase of Truck
1		-	$8,000	$8,000
2		-	$8,000	$8,000
3		-	$10,000	$10,000
4		($2,000)	$10,500	$8,500
5		($2,200)	$11,000	$8,800
6		($2,420)	$11,500	$9,080
7		($2,662)	$12,000	$9,338
8	$15,000	($2,928)	$12,500	$24,572	Sale of Truck

PV of Maintenance Expense at T=0

Year	Maintenance Expense	PV Factor ( Int 15%)	PV
0	-	1	$0
1	-	0.87	$0
2	-	0.76	$0
3	-	0.66	$0
4	($2,000)	0.57	($1,144)
5	($2,200)	0.50	($1,094)
6	($2,420)	0.43	($1,046)
7	($2,662)	0.38	($1,001)
8	($2,928)	0.33	($957)
Total			($5,242)

PV of All revenue at T=0

Year	Inflows	PV Factor ( Int 15%)	PV	Remarks
0	-	1	$0
1	$8,000	0.87	$6,957
2	$8,000	0.76	$6,049
3	$10,000	0.66	$6,575
4	$10,500	0.57	$6,003
5	$11,000	0.50	$5,469
6	$11,500	0.43	$4,972
7	$12,000	0.38	$4,511
8	$27,500	0.33	$8,990	Includes amount of Sale of Truck
Total			$49,526

The truck should not be purrchased basis the below calculation as the NPV is negative.

Year	Truck	Maintenance Expense	Revenue	Net Amount	PV Factor ( Int 15%)	PV	Remarks
0	($50,000)	-		($50,000)	1	($50,000)	Purrchase of Truck
1	-	-	$8,000	$8,000	0.87	$6,957
2	-	-	$8,000	$8,000	0.76	$6,049
3	-	-	$10,000	$10,000	0.66	$6,575
4	-	($2,000)	$10,500	$8,500	0.57	$4,860
5	-	($2,200)	$11,000	$8,800	0.50	$4,375
6	-	($2,420)	$11,500	$9,080	0.43	$3,926
7	-	($2,662)	$12,000	$9,338	0.38	$3,511
8	$15,000	($2,928)	$12,500	$24,572	0.33	$8,033	Sale of Truck
						($5,716)