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PMT = 1000

7.   Your company is considering borrowing $3,000,000 at a cost of debt of 3.4400% p.a. If your company pays $180,000 each quarter towards this debt, how many years will it take to pay off the loan? Solution Opt 1:

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PMT = 1000

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  1. MGT 326/526 Summer 2014 Test 1 Problem Solutions 7.   Your company is considering borrowing $3,000,000 at a cost of debt of 3.4400% p.a. If your company pays $180,000 each quarter towards this debt, how many years will it take to pay off the loan? Solution Opt 1: P/Y=1, I/Y=0.86, PV=-3000000, PMT=180000: CPT, N; N =18.07; yrs = 18.07 / 4 = 4.52yrs Solution Option 2: P/Y=4, I/Y=3.44, PV=-3000000, PMT=180000: CPT, N; N =18.07; yrs = 18.07 / 4 = 4.52yrs 8. 14 months from now your company will receive $350,000 as payment for services rendered. How much is this payment worth today? Your company has a line of credit at a local bank that charges 4.7500% compounded weekly. There are 52 weeks per year. n = T x m = 14/12 x 52 = 60.6667 Solution Opt 1: rperiodic = rnominal/m = 4.75%/52 = 0.09135%; P/Y=1, N=60.6667, I/Y=0.09135, FV=350000; CPT PV: $331,140.18 Solution Option 2: P/Y=52, N=60.6667, I/Y=4.75, FV=350000; CPT PV: $331,140.18 9. What is the present value of an annuity due yielding 8.6400% APR that pays quarterly payments of $1,000 for 1 year? (Do the math; do not use the financial functions on your calculator. Draw a cash flow diagram) PV = FV/(1 + r/m)n + FV/(1 + r/m)n-1 + ………….. = 1000 + 1000/(1 + 0.0864/4)1 + 1000/(1 + 0.0864/4)2 + 1000/(1 + 0.0864/4)1\3 = 1000 + 1000/(1.0216)1 + 1000/(1.0216)2+ 1000(1.0216)3 = 1000 + 1000/(1.0216) + 1000/(1.04367)+ 1000/(1.06621) = 1,000 + 978.86 + 958.16 + 937.90 = $3,874.92 10. You are considering two different stock mutual funds in which to invest. Fund A offers 5.2550% APR rate of return with quarterly reinvestment of profits. Fund B offers a 5.0128% APR rate of return with monthly reinvestment of profits. Compute the Effective Annual Rate for each fund. Which fund is more profitable? Fund A: 2nd, INCONV, 5.2550%, ENTER, ↓, ↓, 4, ENTER, ↓, ↓, CPT: 5.3595% Fund B: 2nd, INCONV, 5.0128%, ENTER, ↓, ↓, 12, ENTER, ↓, ↓, CPT: 5.1296% 11. You are considering leasing a car that cost $29,999.00. The lease will be for 5 years and requires monthly payments of $345.00. Somewhere on the lease paperwork you notice a statement to the affect that you will be charged an APR of 4.8000%. What kind of annuity is this?___________________ How much will the car be worth at the end of the lease (i.e. what is its salvage value)? Annuity Due Solution Opt 1: rperiodic = rnominal/m = 4.8%/12 = 0.4% Set BGN, P/Y=1, N=60, I/Y=0.4, PV=-29999, PMT=345; CPT FV: $14,681.82 Solution Option 2: Set BGN, P/Y=12, N=60, I/Y=4.8, PV=-29999, PMT=345; CPT FV: $14,681.82 12. Today you open a new investment account for your company that pays 7.5000% compounded daily. You plan to deposit $40,000 into this account at the end of every quarter, starting at the end of this quarter. How much will you have in this account 3 years from now? There are 365 days in a year. P/Y=4, C/Y=365, N=12 I/Y=7.55, PMT=40000; CPT,FV: FV= $533,251.9 OR Convert the dailly rate into a quarterly rate then solve for FV 2nd , ICONV, 7.5, ENTER, ↓, 365, ENTER, ↓, ↓, CPT: EFF% = 7.78758% ↓, 4, ENTER. ↓, CPT: NOM% = 7.56997% P/Y=4, N=12, I/Y=7.56997, PMT=40000; CPT,FV: FV = $533,251.90 PV = ? 0 4 1 2 3 PMT = 1000 PV = $29,999 m=12, T=5; n = m x T = 12 x 5 = 60 6 yrs 58 59 60 0 1 2 FV = ? PMT = $345.00 FV = ? 154 155 156 wks 0 1 2 PMT = $15,000

  2. MGT 326/526 Summer 2014 Test 1 Problem Solutions 13.A $1,000 face value Diamond Jim’s Corporation bond matures 1 Sept 2025. It has a 5.7850% coupon rate and pays coupons semiannually. Its YTM as of 3 July 2014 was 5.4200%. What is this bond’s retail price as of 3 July 2014? (Show all calculator inputs; work in at least 4 decimal places) SDT = 7.0314 CPN = 5.785 RDT = 9.0125 YLD = 5.42 PRI = 103.01877; VB = 10 x 103.01877 = $1030.19 16. ) At the beginning of the year a $1,000 face value bond paying a coupon rate of 7.4200% APR with semiannual payments and 8.5 years maturity was selling at par (excluding fees and transaction costs). At the end of the year the bond's YTM was 6.8660%. What is the bond’s total yield for the year? EARCPN = NOM=7.42, C/Y=2; EFF = 7.5576% VB,0 = $1,000 VB,1: T=7.5, m=2; n = 15; PMT = $1,000(0.0742/2) = $37.10 P/Y=2, N=15, I/Y=6.866, PMT=37.1, FV=1000; CPT, PV: VB,1 = $1,032.0558 Cap Gain Yield = ($1,032.0558 -$1,000)/$1,000 = 3.2056% Total Yield = 7.5576% + 3.2056% = 10.7632%

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