10. The local gas company has asked the planning department of your company to h

Question

10. The local gas company has asked the planning department of your company to help them plan for future cash flows. They want your company to pay an equal amount at the end of each year for the next 5 years rather than paying the yearly amounts as they become due at the end of each year for the next 5 years. Your current annual utility bill is $150,000. If ou expect the inflation rate to average 2% per year, and that the gas company will pay you 6% interest each year for the next 5 years, what equal at the end of each year from year 1 through year 5? , annual amount should be paid Page 5

Explanation / Answer

Solution-

Let A be the fixed amount at the end of each year. Given that interest rate = 6% and inflation rate = 2% and term = 5 years. Current utility bill = 150000 must equal the present value of the cashflows. SO we must have,

150000 = A * 1.06-1 * 1.02 + A* 1.06-2 * 1.022 + ...................... + A* 1.06-5 * 1.025

150000 = A* 1.06-1 * 1.02 * ( 1 - 1.06-5 * 1.025 )/(1-1.06-1 * 1.02) {using formula of geometric progression}

150000 = A * 4.4614

SO A = 33619.9

Answer

Thanks!

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