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 $4600 to install, has a 6-year useful life, and may be salvaged for $300. Total operating cost for all five systems is $1000 for the first year, increasing by $200 per year thereafter. a. 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 purchase price but not all of the costs given.) b. The company estimates an increased net income of $6000 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

a. 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 present value of the investment = -$4,600 x 5 = -$23,000

6 years useful life, salvage value $1,500

operating costs:

year 1 = -$1,000

year 2 = -$1,200

year 3 = -$1,400

year 4 = -$1,600

year 5 = -$1,800

year 6 = -$2,000 + $1,500 = -$500

we need to calculate the present value of the required investment (I used an excel spreadsheet or financial calculator to do this) using a 9% discount rate: PV of investment = -$26,248

now to calculate the capital recovery per year we can use an annuity factor:

$26,248 = annuity x annuity factor (9%, 6 years)

$26,248 = annuity x 4.4859

annuity = $26,248 / 4.4859 = $5,851

This means that the company needs to generate at least $5,851 of additional revenue per year to pay for this investment.

b. The company estimates an increased net income of $6000 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.

Since the $6,000 is higher than the minimum required amount to recover the investment, then we can assume that implementing the GPS system is financially viable.