1. Consider the following 4 bonds, each with a face value of F = $10, 000, currently being sold in the primary market:
A: a 2 year coupon bond with a coupon rate of cA = 5 percent and priced at PA(t) = $10, 000.
B: a 2-year discount bond, priced at PB (t) = $9, 070.29.
C: a 30-year discount bond, priced at PC (t) = $2, 313.77.
D: a console with an annual coupon payment of $500 and priced at
PD(t) = $10, 000.
(a) Calculate the yield to maturity on each bond, ij , j = A, B, C, D.
(b) Suppose that market conditions remain unchanged over the next year, so that interest rates remain where they were when the bonds were initially sold in the primary market. First, calculate the max- imum value that others would be willing to pay for each bond in the secondary market, Pj (t + 1), j = A, B, C, D. Second, calculate the one-year rate of return, retj , for each bond, assuming that it is sold at that maximum price, Pj (t + 1).
(c) Suppose alternatively that after one year, all market interest rates increase by 5 percentage points. Redo the calculations in (b), for each of the 4 bonds.
(d) Now consider a 5th bond (E). It is identical to bond A in terms of the following payout features: FE = $10, 000, nE = 2, and cE = 5 percent. However, it is sold in the primary market in t + 1 under the tighter market conditions specified in (c). Without calculating PE (t + 1), prove that, under these tighter market conditions, bond E would sell in the primary market at a lower price than did bond A, PE (t + 1) < PA(t). You should also be able to verify that, if these tighter market conditions were to persist into the next year, the price of this bond would rise (i.e., PE (t +2) > PE (t +1)). [Again it is not necessary to do any numerical calculations.]
2. You are offered a one-year subscription to the Economist for $55, or a two-year subscription for $105. Assume that you plan to get the periodi- cal for at least the next two years. (a) If the current market interest rate is 5 percent, would you subscribe today for one or two years? (b) What is highest market interest rate which makes the two-year subscription a better deal? (c) Would your answer to part b necessarily change, if you were to expect inflation over the next year?