Question

A small trucking company is planning to install a GPS system in each of the five trucks the company owns. Each GPS system costs $5000 to install, has a 6-year useful life, and may be salvaged for $800. Total operating cost for all five systems is $1000 for the first year, increasing by $160 per year thereafter.

1. How much new annual net income (each year for 6 years) is necessary to recover the initial investment of the five GPS systems at the annual effective interest rate of 9%? (The initial investment includes more than the purchase price but not all of the costs given.)
2. The company estimates an increased net income of $7000 per year for all five systems. This is total new income, not on top of part a. Now consider if the implementation of the GPS systems is financially viable. You should consider initial investment and maintenance costs. Use the annual effective interest rate of 9% and report the income or loss the company would experience each year.

Answer 1

Information Given:

Cost of each GPS System = $5000

Useful life = 6 years

Salvage value = $800

Number of GPS systems = 5 units

Total operational cost for all systems = $1000 for first year, $160 increase per year.

Solution:

Total Initial investment = Cost of each GPS system x number of systems

Total initial investment = 5000 x 5 = $25000

Ans a.

The total initial investment needs to be recovered in 6 years.

Therefore, Amount = $25000 / 6 = $4167 each year.

But we need to consider the annual effective interest rate of 9%.

Nt year amount = Nt-1 year’s amount x (1 + annual effective interest rate)

In order to recover the initial investment in six years, following amounts indicate minimum annual net income of the company.

Year	Calculation	Amount
1		$4167
2	$4167 x (1+0.09)	$4542
3	$4542 x (1.09)	$4951
4	$4951 x (1.09)	$5397
5	$5397 x (1.09)	$5883
6	$5883 x (1.09)	$6413

Ans b.

Estimated annual net income = $7000

Total initial investment = $25000

Costs:

Operational cost = $1000 for first year, $160 increase per year.

Annual Depreciation of each system = (Cost of installation – Salvage Value) / Useful life

Annual depreciation of each system = (5000-800) / 6 = $700

Recovery of initial investment per year = as given in Ans a.

Calculation of yearly profit or loss:

Item	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
Income ($)	7000	7000	7000	7000	7000	7000
Operational Cost ($)	1000	1160	1320	1480	1640	1800
Depreciation ($)	700	700	700	700	700	700
Recovery Amount ($)	4167	4542	4951	5397	5883	6413
Net income ($)	1133	598	29	- 577	- 1223	- 1913
Outcome	Profit	Profit	Profit	Loss	Loss	Loss