A software company that installs systems for inventory control using RFID technology spent $760,000 per year for the past 3 years in developing their latest product. The company optimistically hopes to recover its investment in 5 years on a single contract beginning immediately (year 0). The company is negotiating a contract that will pay $280,000 now and a to-be-agreed-upon annual increase of a constant amount each year through year 5. How much must the income increase (an arithmetic gradient) each year if the company wants to realize a return of 9% per year

$2,096,924.50

Explanation:

Present value of an investment and cash inflows is measured at present time means year 0. Gradient is also valued at present time.

$760,000 each year at 9% for next 3 years is annuity payment and its Present value can be calculated as follow

PV of Annuity = P + P x ( 1 - ( 1 + r )^-(n-1) / r

Where

P = $760,000

r = 9%

n = 3 years

Placing values in the formula

PV of Annuity = $760,000 + $760,000 x ( 1 - ( 1 + 9% )^-(3-1) / 9%

PV of Annuity = $760,000 + $760,000 x 1.759111  

PV of Annuity = $760,000 + $1,336,924.50  

PV of Annuity = $2,096,924.50

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