# 40 a vending machine is expected to produce cash

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40. A vending machine is expected to produce cash flows of \$1,570 per month with the first monthly cash flow expected later today and the last monthly cash flow expected in 7 months from today. The cost of capital for the vending machine is 8.28 percent per year. What is the value of the vending machine? (Spring 2012, test 2, question 2) (Spring 2017, test 2, question 5) (Spring 2017, final, question 6) Timeline tip for FNAN 303: t he cash flows reflect an annuity due with monthly payments, so the relevant period is for 1 month. From the timeline, we can see that the cash flows reflect an 8-period annuity due with monthly payments of \$1,570. Even though the last regular cash flow is expected in 7 months, it would be the 8 th regular payment. Time 0 1 2 3 4 5 6 7 Pmt number 1 2 3 4 5 6 7 8 CF amt 1,570 1,570 1,570 1,570 1,570 1,570 1,570 1,570 The cash flows take place monthly, so we need to use the periodic rate, which is the monthly rate Periodic rate = APR / number of periods in a year = .0828 / 12 months per year = .0069 = 0.69 percent per month PV of an 8-period annuity due BEGIN Mode Enter 8 0.69 1,570 0 N I% PV PMT FV Solve for -12,263 The vending machine is worth \$12,263
41. Amena just borrowed \$8,600 from the bank. She plans to repay this loan by making equal quarterly payments for 9 years. If the interest rate on the loan is 9.20 percent per year and she makes her first quarterly payment in 3 months from today, then how much must Amena pay to the bank each quarter? This is a problem where we need to find the payment amount associated with the present value of an annuity Time 0y0q 0y1q 0y2q 8y2q 8y03q 9y0q Time 0 1 2 ... 34 35 36 Payment # 0 1 2 34 35 36 Cash flow 0 C C C C C Present value -\$8,600 We want the quarterly rate There are 36 periods, because N = 9 years × 4 quarters per year = 36 quarters The rate of 9.20 percent for the year is assumed to be an APR, so the quarterly rate = 9.20 percent ÷ number of quarters in a year = 9.20 percent ÷ 4 = 2.30 percent = .0230 END mode Enter 36 2.30 8,600 0 N I% PV PMT FV Solve for -353.87 Amena must make quarterly payments of \$353.87
42. Kaka just borrowed \$4,630 from the bank. He plans to repay this loan by making equal semi- annual payments for 24 half years. If the interest rate on the loan is 5.46 percent per year and he makes his first semi-annual payment later today, then how much must Kaka pay to the bank each half year? (Fall 2016, test 2, question 4) This is a problem where we need to find the payment amount associated with the present value of an annuity due Time 0 1 2 ... 22 23 24 Payment # 1 2 3 23 24 Cash flow C C C C C Present value -\$4,630 We want the semi-annual rate The rate of 5.46 percent for the year is assumed to be an APR So the semi-annual rate = 5.46 percent ÷ number of half years in a year = 5.46 percent ÷ 2 = 2.73 percent = .0273 BEGIN mode Enter 24 2.73 4,630 0 N I% PV PMT FV Solve for -258.44 Kaka must make semi-annual payments of \$258.44
43. Yu-Na must borrow \$657 from the bank to pay her phone bill. She plans to repay this loan by making monthly payments to the bank of \$31 per month. If the annual interest rate on the loan is 10.68 percent and she makes her first \$31 payment in 1 month from today, then how many payments must Yu-Na make?