Oxygen Optimization just bought a new filtration system for 234,700 dollars. To
ID: 2728076 • Letter: O
Question
Oxygen Optimization just bought a new filtration system for 234,700 dollars. To pay for the filtration system, the company took out a loan that requires Oxygen Optimization to pay the bank a special payment of 109,700 dollars in 2 year(s) and also make regular annual payments forever. The first regular payment is expected in 1 year and is expected to be 1,700 dollars. All subsequent regular payments are expected to increase by a constant rate each year forever. The interest rate on the loan is 11.36 percent per year. What is the annual growth rate of the regular payments expected to be? Answer as an annual rate in decimal format so that 12.34% would be entered as .1234 and 0.98% would be entered as .0098.
Explanation / Answer
PRESENT VALUE OF THE SPECIAL PAYMENT
= $109700 * PVIF 11.36%, 2 PERIODS
= $109700 * 0.8064
= $$88462.08
BALANCE AMOUNT TO BE PAID IN PERPETUITY
= $234700 - $88462.08
= $146237.92
PRESENT VALUE OF GROWING PERPETUITY
= PERIODIC PAYMENT / (RATE - GROWTH)
$146237.92 = $1700 / (11.36% - GROWTH)
$146237.92 (11.36% - GROWTH) = $1700
$16612.63 - GROWTH * $146237.92 = $1700
GROWTH * $146237.92 = $14912.63
GROWTH = $14912.63 / $146237.92
= 10.20% OR 0.10197
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