53.7
7a. Write down a cash flow diagram for the cash flows for a 5%
coupon bond with semi-annual coupons and 5 ½ years to maturity.
[6 pts]
5% coupon means that 5% of par (recall, this is always $1000 if not mentioned), or $50 in this case, is paid annually. Semi-annual coupons means that the $50 is split into 2 equal payments of $25, once every 6 months. We get the par value back at the end.
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 25 25 25 25 25 25 25 25 25 25 1025
7b. Assume that the term structure shows that the interest rate for 6-month maturities is 5.75% and the interest rate for 5 ½ year maturities is 6.25%. Interest rates increase by an increment of 0.05% for each 6-month interval in between, so that the average for the 11 rates is 6.00%. If you use 6% as your single discount rate to compute the PV of the package of cash flows from part a, will you underestimate, overestimate, or correctly value the bond? EXPLAIN. YOU SHOULD NOT DO ANY CALCULATIONS FOR THIS QUESTION. [6 pts]
This is a YTM question. We know that if we have to pick one rate when multiple rates are appropriate, the only single rate that will give us the correct value of the bond is the YTM. We also know that we can think about the YTM as a weighted average of the spot rates, where the weights are approximately proportional to the size of the cash flows to which they are attached. Given that, we know that the YTM for this bond will be above 6% because the largest cash flow occurs at the end, where the spot rate is 6.25%. Thus, if we use 6%, we will be using too low of a discount rate, which will result in too high of a present value (price) for the bond. So, the answer is that we will overestimate the price of the bond.