quantitative techniques.pdf

89 Chapter 6 Equivalent Annual Worth 6-1 While in college Ellen received $10,000 in student loans at 5% interest. She will graduate in June and is expected to begin repaying the loans in either 5 or 10 equal annual payments. Compute her yearly payments for both repayment plans. Solution 5 YEARS 10 YEARS A = P(A/P, i, n) A = P(A/P, i, n) = 10,000(A/P, 5%, 5) = 10,000(A/P, 5%, 10) = $2,310.00 = $1,295.00 6-2 Suppose you wanted to buy a $100,000 house. You have $20,000 cash to use as the down payment. The bank offers to loan you the remainder at 6% nominal interest. The term of the loan is 20 years. Compute your monthly loan payment assuming the payment is the same for all months. Solution Amount of loan: $100,000 - $20,000 = $80,000 i = 6%/12 = ?% per month n = 20 x 12 = 240 periods A = 80,000(A/P, ?%, 240) = $572.80 per month 90 Chapter 6 Equivalent Annual Worth 6-3 Lester Peabody decides to install a fuel storage system for his farm that will save him an estimated 6.5 cents/gallon on his fuel cost. He uses an estimated 20,000 gallons/year on his farm. Initial cost of the system is $10,000 and the annual maintenance is a uniform gradient amount of $25. After a period of 10 years the estimated salvage is $3,000. If money is worth 12%, is it a wise investment? Solution EAC =(10,000 - 3,000)(A/P, 12%, 10) + 3,000(.12) + 25(A/G, 12%, 10) = $1,688.63 EAB = 20,000(.065) = $1,300 EAW = -$388.63 ∴ not a wise investment 6-4 The returns for a business for five years are as follows: $8,250, $12,600, $9,750, $11,400, and $14,500. If the value of money is 12%, what is the equivalent annual benefit for the five-year period? Solution PW = 8,250(P/F, 12%, 1) + 12,600(P/F, 12%, 2) + 9,750(P/F, 12%, 3) + 11,400(P/F, 12%, 4) + 14,500(P/F, 12%, 5) = $39,823 EAB = 39,823(A/P, 12%, 5) = $11,047 6-5 The local loan shark has loaned you $1000. The interest rate you mus