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1 Kenan-Flagler Business School The University of North Carolina MBA 772 / MAC718 Introductory Finance Week 1 Homework: Problem Set 1 Weekly problem sets are to be submitted in a well-organized set of calculations with clearly visible (suggest circled) answers PRIOR TO your synchronous session. You may submit in Excel, Word, PDF, hand-written or typed. Homework may be done in groups up to no more than 4 students, but assignments must be individually submitted and a student’s own work (i.e. you cannot simply copy group work). If you work in a group, all students names must be identified on your submission file. 1. You are considering various retirement plans. Your goal is to have a lump sum of $3,000,000 available (‘in the bank’) when you retire at age 67. The various plans, with their payment schedules, are listed below. In each case, calculate the payment(s) that must be made into the plan to ensure that you have the $3,000,000 available. For each plan, you may assume that your opportunity cost of funds is 6% per year; for each plan, you may assume that the phrase “at age XX” means the same thing as “on your XX’th birthday”. Plan 1: Single lump sum at age 25 Plan 2: Single lump sum at age 50 Plan 3: Equal annual payments, commencing at age 31 and ending at age 67 Plan 4: Equal annual payments, commencing at age 51 and ending at age 67 Plan 5: Equal annual panicky payments, commencing at age 60 and ending at age 67 2. You have just taken out a mortgage for $575,000, at a fixed rate of 4.75% per year, compounded monthly, and a term of 30 years. a) Calculate the monthly payments b) For the first six months’ payments, calculate the portion that is interest and the portion that is principal c) Immediately after the sixth payment, what is the balance remaining on the mortgage? d) If you design the mortgage so that the payments will grow at 0.20% per month, what will be the first payment on the mortgage? 3. You are saving for your child’s college education. Your child will start college in 16 years, and college tuition is due at the beginning of the year (i.e., the first tuition payment will occur at t=16). Average college tuition at a private school this year is $38,500 per year. You may assume that your opportunity cost of funds is 6.0% per year, compounded monthly. a) Calculate the value, at t=16, of four years’ worth of college tuition if tuition charges grow at the general inflation rate of 2.4% per year, compounded monthly. b) Calculate the value, at t=16, of four years’ worth of college tuition if tuition charges grow at the recent education inflation rate of 6.4% per year, compounded monthly. c) Calculate the single payment you must make into the child’s college account to pay for the entire college experience, if you make the payment now. Assume the education inflation rate of 6.4%, compounded monthly. d) Calculate the monthly payment you must make into your child’s college account to pay for four years of college under the assumption that tuition will grow at the general inflation rate; you may assume that the first payment into the college account comes in one month’s time and the last payment will come one month prior to the first college tuition payment. e) Calculate the monthly payment you must make into your child’s college account to pay for four years of college under the assumption that tuition will grow at the education inflation rate; you may assume that the first payment into the college account comes in one month’s time and the last payment will come one month prior to the first college tuition payment. 4. You have been offered the following opportunity: receive a tax ‘forbearance’ credit of $10,000 today, and in return, you must make higher tax payments of $1,000 per year for 15 years. The first of the annual payments will come in one year’s time. What is the internal rate of return on this investment? 5. A recent graduate of the university has gotten into a little more credit card debt than he had anticipated. He currently owes $22,000; the credit card company charges him 1.5% per month on this debt. a) If he wishes to pay off his credit card bill in 5 years of equal monthly installments, promises to make the first payment next month and not use the credit card again, what monthly payments must he make? You may assume that there are no additional fees or charges related to the card, and that the credit card interest rate is not expected to change. b) After solving for the payment in a), the graduate realizes that he can’t afford the first payments, given the salary of his new job. He wishes his payment to start small, then increase; the first payment will still come in one month’s time. If he wishes his payments to grow at, say, 0.50% per month and still let him pay off the credit card debt in 5 years of monthly payments, what must the first payment be? c) The graduate’s parents hear of his plight. They offer to extend him a loan to pay off the debt, with the interest rate charged equal to 8% per year, compounded monthly. The student wishes to know the incremental value of this new borrowing opportunity (relative to the credit card debt) today (so that he can go shopping.) That is, he wishes to know how much he can spend today and still have the same monthly payments as in p art a). What can he spend on today’s shopping trip? 6. Your opportunity cost of funds can be expressed as 6% per year, compounded quarterly. a) You have been offered a three-month internship. If the internship pays $24,000 at the end of the three month period, what is the value today of that salary? b) Assume now that the internship pays $8,000 per month (paid at the end of the month.) What is the value today of the salary? 7. Spot rates over three different horizons are given below. Each of the rates is expressed as a ‘per annum’ rate, which assumes monthly compounding. One-month 0.18% Two-month 0.24% Three-month 0.375% What is the value today of an investment that pays $100 at the end of each of the next 3 months? Week 1 Homework: Problem Set 1