ARE 171a Fall 2010 Homework 2 M. Whitney Due Monday, Oct. 25, in class 1. For each set of cash flows below, find the present value given the…

1. For each set of cash flows below, find the present value given the following annual discount rates: 3%, 6%, and 9%a. An ordinary annuity that pays $400 per month, for 5 years.b. A lump sum of $400,000, that you will inherit at the end of 20 years.c. An apartment building that is expected to generate the following annual cash flows (at the end of each year)The first year shows a loss, due to costs of renovating the property.1 2 3 4 5 6 7-60,000 20,000 20800 21600 22500 23400 700000d. A British consol bond (a perpetuity) that pays $25 per year, at the end of each year, forever.2. Margaret plans to buy a new car a year from now. Its price will be $20,000 at that time. She has $6000 in cashon hand today. How much will she need to deposit at the end of each month in order to afford this car?First assume that her savings earn a 3% annual rate, then assume they earn a 12% annual rate.3. Donte plans to purchase a home that costs $400,000. He will pay 20% in cash as a downpayment, and finance the rest.a. One option he is considering is a 30 year fully amortized mortgage, with an annual rate of 4.8%How much is his payment? Show the first 2 lines of his amortization schedule. If he buys the home late in the year, suchthat only Nov and Dec.’s payments are made in 2010, how much interest will he be able to claim as a deduction on his2010 taxes? What will his ending balance be after these first 2 payments?b. Repeat part a, but assume he instead chooses a 15 year mortgage with an annual rate of 4.56%4. Mrs. Sheridan wants to make a gift of $800,000 today (Fall 2010), to be shared by her two grown children, Thomas and Brad.However, she wants to take into account the value of other gifts she has given each of them in the past, so that the total valueof the two boy’s gifts is equal.Thomas received an annual payment of $30,000 in the fall of 2002, 2003, and 2004, to attend graduate schoolHe also received $50,000 in cash in the fall of 2008, to help with the purchase of a home.Brad was given a new car with a value of $25,000 in the fall of 2007.How much of today’s $800,000 cash gift should each son receive? Assume the discount rate is 6%5. Suppose that a 30 year treasury bond purchased in Oct. 1990 had a coupon rate of 8%, semiannual payments anda par value of $1000. Today, the bond has 10 years remaining till maturity.a. What is its value today, if new 10 year treasuries pay 2%?b. What would it have been worth today, if instead of falling to their current low levels,rates had risen sharply, such that new 10 year T-bonds yielded 14%?6. A corporate bond has 3 years remaining to maturity. It has a par value of $1000 and a coupon rate of 9%a. Find its present value, if the current required rate of return is 4%b. How might your answer to a. differ, if the bond is callable? (verbal answer only)c. What is this bond’s duration, if purchased today at the value in part a?

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