Provide computations and answers to four following problems. Be sure to show all of your work, as partial credit will be given for incomplete or incorrect answers. Type your answers.
(1) The city has won a court judgment against a local firm for polluting a stream. The firm has been ordered to make annual payments at the end of the next three years of $100,000 each. The city wishes to begin cleanup of the stream immediately, however. Estimated cleanup costs are estimated at $260,000. A bank has offered the city to buy the rights to receive the judgement at a discount, for around $250,000. If the interest rate on the city’s other accounts is 4%, should the city take the deal with the bank? Show computations to support your recommendation.
(2) The City of Monroe has a loan outstanding. It requires making three annual payments at the end of the next three years of $1000 each. The bank has offered the city the option of forgoing making the next two payments in lieu of one large payment at the end of the loan, which is in 3 years’ time. If the interest rate on the loan is 5%, what final payment will the bank require the city to make so that it is indifferent between the two forms of payment?
(3) A city issued 25-year general obligation (G.O.) $5,000 face value bonds ten years ago, with a coupon rate of 8 percent, payable semiannually. The current market rate of interest on similar bonds is 10 percent. Answer the following questions.
(a) What was the market price of the bonds on the day they were issued?
(b) What is the market price of the bond today?
(c) What will be the bonds’ current yield (C.Y.) and capital gain yield (C.G.Y.) in the eleventh year of its life?
(d) What price will the bond sell for the day before the issue matures?
(4) Sometimes the coupon rate on a bond is slightly different from the market rate, because the market rate changes just days before the bond is to be sold. For example, suppose that a certain city issued a 10-year bond with a face value of $1000, and a coupon rate of 7% (assuming annual payments). The yield to maturity on this bond on the day that it was issued was 6%.
a.) What was the price of this bond when it was issued?
b.) Assuming the investor’s yield remains constant, what is the price of the bond immediately before and after it makes its first coupon payment? [Hint: What would be the present value of a coupon payment on the day that it is to be paid?]