Sin Kei Poon Carina May 7 2013 Problem Set 4 ECN 134 Finance Economics Prof Farshid Mojaver Part A Buy or not to Buy a House 1 As a first time home buyer you can buy a home now when interest rates are low 5 5 and received the 8 000 tax credit 8 000 for a 230 000 home or you can wait and buy it next year when prices are projected to decrease another 10 But if you wait you will lose the subsidy and interest rates may increase to 6 5 What is the best decision to buy the house now or to buy it next year Part B Present Value and Bond Valuation 1 How much would you pay per 1 000 face value for a bond with a coupon rate of 4 2 per year and two semi annual payments remaining The return on assets of comparable risk is 5 5 per year 2 For a 1 year pure discount bond compute the yield to maturity if the bond s face value is 1 000 and the price is 950 3 A consol has a coupon rate of 10 paid semiannually of course If the market rate for securities of comparable risk is 9 what is the price of the consol per 1 000 of face value 4 How would you price a pure discount bond that pays 1 000 at maturity with 6 years remaining until payoff in order to yield a 9 return Part C Interest Rate Risk 1 Consider the Jan 12 Treasury note principal and interest Rate 6 250 Maturity Jan 12n 20xx Bid 114 04 Asked 114 05 Chg 10 Ask Yld 2 56 suppose the maturity date is 2 years from the day of purchase i The calculated ytm on this note n means treasury note is 2 488 What is the price of the note ii Now suppose that instantaneously the market interest rate and therefore the ytm increases 68 8 from 2 488 to 4 2 which is incidentally the level it was just two years earlier What is the price of the note now iii Using the lower note price as a base calculate the percentage change in the note price resulting from the 68 8 interest rate increase 2 Now consider the principal of a Jan 12 Treasury strip reported as Maturity Jan 12 20xx Type np Bid 89 27 Asked 89 29 Chg 8 suppose the maturity date is 2 years from the day of purchase Ask Yld 2 63 Sin Kei Poon Carina May 7 2013 i The calculated ytm for this note is 02696 it differs from the reported ytm due to the exact day on which it settles What is the price of this note ii Now suppose that instantaneously the market interest rate and therefore the ytm increase 68 8 this time from 2 696 to 4 551 What is the price of the note now iii Using the lower note price as a base calculate the percentage change in the note price resulting from the 68 8 interest rate increase 3 Suppose a consol pays annual coupons of 62 50 and has a ytm of 02488 or 2 488 i What is its price ii Now suppose that instantaneously the market interest rate and therefore the ytm increases 68 8 from 2 488 to 4 2 What is the price of the consol now iii Using the lower consol price as a base calculate the percentage change in the consol price resulting from the 68 8 interest rate increase 4 Draw a conclusion regarding the effect of coupons on interest rate risk changes in price due to change in interest rates based on comparing the result of questions 1 and 2 above 5 Briefly but succinctly draw a conclusion regarding the effect of time to maturity on interest rate risk changes in price due to changes in interest rates based on comparing the results of questions 2 and 3 above 6 Given the opportunity to invest in one of the three bonds listed below which would you purchase Assume an interest rate of 7 7 In the early 1980s the Treasury yield curve had a severe downward slope with short term yields near 20 and long term yields below 15 Explain how such a pattern might occur 8 Interest rate risk is often explained by using the concept of a teeter totter Explain interest rate risk and how it is related to the movements of a teeter totter Part D Stock Valuation 1 1 The next dividend payment by MUG Inc will be 3 10 per share The dividends are anticipated to maintain a 5 growth rate forever If MUG stock currently sells for 48 00 per share what is the required return 3 1 48 0 05 2 Warren Corporation will pay a 3 60 per share dividend next year The company pledges to increase its dividend by 4 5 percent per year indefinitely If you require a 13 percent return on your investment how much you pay for the company s stock today 3 Suppose you know that a company s stock currently sells for 70 per share and the required return on the stock is 12 You also know that the total return on the stock is evenly divided between a capital gains yield and a dividend yield If it s the company s policy to always maintain a constant growth rate in its dividends what is the current dividend per share Sin Kei Poon Carina May 7 2013