MGT 470 Springl 2016 Test 1 Problem Solutions 1 4. You are considering leasing a car that cost $28,999. The lease will be for 5 years and requires monthly payments of $ Somewhere on the lease paperwork you notice a statement to the affect that you will be charged an APR of %. 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, Solution Option 2: Set BGN, P/Y=12, N=60, I/Y=4.26, PV=28999, PMT= -280; CPT FV: $17, Diamond Jim’s Corp. borrowed $500,000 today at an annual interest rate of %, compounded monthly. Interest begins to accrue immediately. However, Diamond Jim’s will not start paying off the loan until three years from now. The payment plan calls for monthly payments over a four year period. What will be the amount of each of these payments? Step 1: Find the value of the loan three years from now P/Y=12, N=36, I/Y=6.24, PV=500000; CPT FV, FV = $602, Step 2: Find PMT P/Y=12, N=48, I/Y=6.24, PV= $602,641.84; CPT PMY, PMT = $14, Today you open a new investment account for your company with a $8,000 deposit. The account has had an average yield of % 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 = $ OR Convert the weekly rate into a quarterly rate then solve for FV 2nd, ICONV, 9.48, ENTER, ↓, 4, ENTER, ↓, ↓, CPT: EFF% = % ↓, 12, ENTER. ↓, CPT: NOM% = % Set BGN, P/Y=12, N=78, I/Y=9.4061, PMT=8000; CPT,FV: FV = $ On 7 March 2015 you bought a $1,000 face value BB+ bond which has a coupon rate of % and pays semiannual coupons. At the time you bought this bond, it was selling at par. You sold this bond on 7 March 2016 when its YTM was %. The bond matures on 1 March What is this bond’s holding period return? Step 1: Find the sales price of the bond in 2016 SDT = CPN = 4.96 RDT = YLD = PRI = % V B = 10 x % = $ Step 2: Find capital gains yield Capital gains yield = (New – Old) / Old = ($ $ ) / $ = % Step 4: Find EAR of the coupon rate EAR r coupon : Use ICONV: NOM=4.96, C/Y=2, CPT EFF; EAR = % Step 5: Add capital gains yield and EAR r coupon : % % = % PMT = $ PV = $28,999 5 yrs m=12, T=5; n = m x T = 12 x 5 = 60 0 Turn-in Value = ? PV = $500,000 0 FV = ? PMT = ? PV = ? mos PMT = $8,000 FV = ? 0

MGT 470 Springl 2016 Test 1 Problem Solutions Today is Morgana's 30 th birthday. Five years ago, Morgana opened a brokerage account when her grandmother gave her $25,000 for her 25 th birthday. She added $5,000 to this account each subsequent year on her birthday (i.e. she added $5,000 on her 26 th, 27 th, 28 th, 29 th and 30 th birthdays). Morgana's goal is to have $500,000 in the account by her 40 th birthday. Morgana plans to continue contributing a fixed amount to the account each year on her birthday. She believes the upcoming fixed amount will be something other than $5,000. She will make 10 contributions with the first one occurring on her 31" birthday and the last one occurring on her 40 th birthday. Complicating things somewhat is the fact that Morgana plans to withdraw $20,000 from the account on her 35 th birthday for a down payment on a home. How large does each of the 10 contributions have to be for Morgana to reach her goal? Assume that the account has earned and will continue to earn 8% APR.