3530-_A1-F2011-Solutions

# 3530-_A1-F2011-Solutions - Assignment 1 SOLUTIONS Question...

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Assignment 1 - SOLUTIONS Question 1 -TVM (15 marks) John and Jane are analyzing promises from political candidates about reducing the cost of attending university. Their daughter, Jane Jr., plans to attend the University of Southern Ontario for four years, starting one year from now. Tuition at USO is currently \$6000 per year, paid at the beginning of each year. Tuition is expected to rise by \$400 each year. Use an annual interest rate of 5%. (a) The Red Party promises to freeze tuition, so that it will stay at \$6000 for each of the four years that Jane Jr. attends USO. What is the value today of the Red Party’s plan? (5 marks) (b) The Yellow Party promises to give scholarships of \$1000 per year, awarded at the beginning of each school year. What is the value today of Jane Jr.’s scholarship? (5 marks) (c) The Blue Party promises to give Jane Jr. a tax credit after she graduates. At the end of the first year after she graduates, and continuing each year afterwards, her income taxes will be reduced by \$200. What is the value today of the Blue Party’s tax credit? Assume she lives forever. (5 marks) Solution: a) Compared to the previous expectation of \$400 increases, Jane Jr. will save \$400, \$800, \$1200, and \$1600 in her four years. The value today is PV = 400/(1 + .05) + 800/(1 + .05) 2 + 1200/(1 + .05) 3 + 1600/(1 + .05) 4 = \$3,459.51 b) This can be valued as a standard 4-year annuity. Even though the scholarship is awarded at the beginning of the year, we don’t need to value this as an annuity due, because it will be one year until Jane Jr. starts school. PV = 1000 x PVA(5%, 4) = 1000 x (1/.05 – 1/(.05)(1+.05) 4 ) = \$3,545.95 c) The PV of a perpetuity is C/r, or 200/.05 = \$4000. But the annual cash flow starts at the end of year 6, so the perpetuity calculation gives the value at the end of year 5. This must be discounted by 5 years to get the value today. PV = 4000/(1 + .05) 5 = \$3134.10

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Question 2 - TVM (15 marks) You are thinking of buying a used car that costs \$6000 and has an expected zero resale value at the end of 4 years. Both Campus Cars and Deals on Wheels are offering special low-rate car loans to York students. Campus Cars will loan you the \$6000 and charge you a 10.25% EAR and want the loan repaid in 48 equal monthly payments, with the first payment due immediately. Deals on Wheels will loan you the purchase price of the car at a 9.8% APR with the first of 48 payments starting in one month’s time. Your estimated costs of operating the car, including insurance, are \$215.00 per month, payable at the end of each month and increasing at a rate of 6% (APR) each year. a) What is the monthly payment for the Campus Cars loan? (5 marks) b) What is the monthly payment for the Wheels on Deals loan? (5 marks) c) What is the present value of your operating costs if your opportunity cost of funds is 9% (APR)? (5 marks) Solution : (a) Campus Cars loan This loan is an annuity due : Monthly Interest rate (i m ) = (1.1025) 1/12 = .008165 = .8165%
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3530-_A1-F2011-Solutions - Assignment 1 SOLUTIONS Question...

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