Consider the following 4 bonds, currently being sold in the primary market pj(t)

Question

Consider the following 4 bonds, currently being sold in the primary market pj(t) $1,000.00 $890.00 S17411 $1,000.00 Bond n FVc 2 30 00 $1.000 6% $1.0000% $1,0000% $1,000 6% ? Assume that coupon payments, if any, are made annually, and at the end of the year 1 Calculate the yield to maturity on each bond, rj, j- A, B, C, D 2 Assuming interest rates do not change over the next year, first calculate the equilibrium price of each bond if sold in the secondary market in t+1 pj(t 1), j- A, B, C, D. Second, calculate the one-year rate of return, RET, for each bond, assuming that it is sold at that maximum price 3 Suppose alternatively that after one year, all market interest rates in- crease 5 percentage points (or, more precisely, 500 basis points). Redo the calculations in (1.2) for each of the 4 bonds Now consider a 5th bond (E), which is identical to bond A in terms of the following : FVE-$1,000, nE = 2, and cE-6 percent. However, it is sold in the primary market in t+1 under the tighter market conditions specified in (1.3). Without calculating pE(t 1), show 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)

Explanation / Answer

Bond n FV c P A 2 1000 6% 1000 B 2 1000 0% 890 C 30 1000 0% 174.11 D Infinite 1000 6% 1000 PV of bond = PV of coupon payment + PV of Face Value Bond A 1000 = 60/(1+r)^n + 1060/(1+r)^n+1 Assuming Yield to Maturity is 6% Discounting Factor @ 6% 60 0.943396 56.60377 1060 0.889996 943.3962 1000 Bond B Yield to Maturity of zero coupon bond = (Face Value/Current Price Bond)^(1/years to maturity)-1 (1000/890)^(1/2)-1 0.059998 5.99% Bond C Yield to Maturity of zero coupon bond = (Face Value/Current Price Bond)^(1/years to maturity)-1 ((1000/174.11)^(1/30))-1 0.0600 6% Bond D 0.06 Yield to Maturity is 6%

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