1. MGT 326 Spring 2016 Test 1 Problem Solutions 1 7. Your company is considering borrowing $10,000,000 at a cost of debt of 4.6200 p.a. If your company pays $220,000 each month towards this debt, how many years will it take to pay off the loan? Solution Opt 1: r per = r nom /m = 4.62%/m = 1.1550 P/Y=1, I/Y=1.1550, PV=-10000000, PMT=220000: CPT, N; N = 50.0629; yrs = 50.0629/12 = 4.17 yrs Solution Option 2: P/Y=12, I/Y=4.62, PV=-10000000, PMT=220000: CPT, N; N = 50.0629; yrs = 50.0629/12 = 4.17 yrs 8. You are considering two different stock mutual funds in which to invest. Fund A offers 8.5100% p.a. rate of return with monthly reinvestment of profits. Fund B offers a 8.5600% p.a. rate of return with quarterly reinvestment of profits. Compute the Effective Annual Rate for each fund. Which fund is more profitable? Fund A: 2nd, INCONV, 8.51%, ENTER, ↓, ↓, 12, ENTER, ↓, ↓, CPT: 8.8500% Fund B: 2nd, INCONV, 8.56%, ENTER, ↓, ↓, 4, ENTER, ↓, ↓, CPT: 8.8387% 9. You are considering buying a new car which cost $24,999. You do not have that kind of cash so you must borrow the money. Your bank offers a nominal rate of 3.4200% for a 5 year amortized loan with monthly payments. You cannot afford to pay more than $440 per month. You will not make a down payment. If you borrow the money from your bank, can you afford this car? n = T x m = 5 x 12 = 60 Solution Opt 1: Find the PMT r periodic = r nominal /m = 3.42%/12 = 0.29%; P/Y=1, N=60, I/Y=0.29, PV=24999; CPT PMT: $454.55 No OR P/Y=12, N=60, I/Y=3.42, PV=24999; CPT PMT: $454.55 No Solution Option 2: Find the PV @ PMT of $440 P/Y=1, N=60, I/Y=0.29, PMT=440; CPT PV: $24,234.49 No OR P/Y=12, N=60, I/Y=3.42, PMT=440; CPT PV: $24,234.49 No Solution Option 3: Find I/Y @ PMT:$440 & PV:$24,999 P/Y=12, N=60, PV=-24999, PMT:440; CPT I/Y: 2.1665% No, the ROR to the bank will be too low 10. ) You are considering leasing a car that cost $28,999. The lease will be for 5 years and requires monthly payments of $280.00. Somewhere on the lease paperwork you notice a statement to the affect that you will be charged an APR of 4.2600%. What kind of annuity is this?___________________ What is the implied value of the car at end of the lease (i.e. what is its turn-in value)?Annuity Due Solution Opt 1: r periodic = r nominal /m = 4.26%/12 = 0.265%; Set BGN, P/Y=1, N=60, I/Y=0.265, PV=28999, PMT= -280; CPT FV: $17,116.56 Solution Option 2: Set BGN, P/Y=12, N=60, I/Y=4.26, PV=28999, PMT= -280; CPT FV: $17,116.56 11. What is the future value of an annuity in arrears yielding 9.6000% p.a. that pays semiannual payments of $900 for 2 years? (Do the math; do not use the financial functions on your calculator. Draw a cash flow diagram) FV = PV(1 + r/m) n + PV/(1 + r/m) n-1 + ………….. = 900(1 + 0.096/2) 3 + 900(1 + 0.096/2) 2 + 900(1 + 0.096/2) 1 + $900 = 900(1.0480) 3 + 900(1.0480) 2 + 900(1.0480) 1 + 900 = 900(1.1510) + 900(1.0983) + 900(1.0480) + 900 = 1,035.9203 + 988.4700 + 943.2000 + 900 = $3,867.59 12 585960 PMT = ? PV = $24,999 5 yrs 0 12 585960 PMT = $280.00 PV = $28,999 6 yrs m=12, T=6; n = m x T = 12 x 6 = 72 0 Turn-in Value = ? 4 PMT = $900 123 FV = ? 0

2. MGT 326 Spring 2016 Test 1 Problem Solutions 2 12. Today you open a new investment account for your company with an $8,000 deposit. The account has had an average yield of 9.4800% over the last four years and compounds every quarter. You plan to deposit $8,000 into this account every month at the beginning of the month. How much will you have in this account 6.5 years from now? Set BGN, P/Y=12, C/Y=4, N=78 I/Y=9.48, PMT=8000; CPT,FV: FV = $862.611.06 OR Convert the weekly rate into a quarterly rate then solve for FV 2nd, ICONV, 9.48, ENTER, ↓, 4, ENTER, ↓, ↓, CPT: EFF% = 9.8224% ↓, 12, ENTER. ↓, CPT: NOM% = 9.4061% Set BGN, P/Y=12, N=78, I/Y=9.4061, PMT=8000; CPT,FV: FV = $862.611.06 13. You are tasked with estimating the fair market value of a security that promises uneven future payments. The table below shows the quarterly payment schedule (each cash flow occurs at the end of the quarter). You consider 6.4000% APR to be the appropriate opportunity cost of capital. What is the theoretical value of this security? 12 767778 mos PMT = $8,000 FV = ? 0 123456 660 820-750300400 I/Y = r periodic = r nominal /m = 6.4%/4 = 1.6% CF, 2nd, CLR WORK (Clear Cash Flow Registers) 0, ENTER, ↓, 660, ENTER ↓, ↓, 660, ENTER ↓, ↓, 820, ENTER ↓, ↓, -750, ENTER ↓, ↓, 300, ENTER ↓, ↓, 400 ENTER NPV, 1.6, ENTER ↓, CPT = $2,007.76 14. Your company plans to sell the security described in Problem 13 (above). What would the rate of return for your company be if the sales price is $2,2000.00? ROR = (SP-FMV) / FMV = ($2,200 - $2,007.76) / $2,007.76 = 0.095748 = 9.5748% 15. Fly By Night Trucking Company is financing a new truck with an amortized loan of $100,000 to be repaid in 11 semi- annual installments of $10,500, paid at the end of each six months. What type of annuity is this? Ordinary. What is the annual cost of debt for this loan? P/Y=4, N=11, PV= - 100000, PMT=10500; CPT I/Y: I/Y = 4.9641% OR P/Y=1, N=11, PV= - 100000, PMT=10500; CPT I/Y: I/Y = 1.6231%; this is a periodic rate which must be converted to a nominal rate: r nominal = r periodic x m = 2.4820% x 2 = 4.9641%