Question

Consider the following par bond (ie coupon rate-yield): Maturity: 12345 VTM: 4.5%;4.0%;3.75%;3.5%;3.375%

Q1a. Calculate discount factor for all 5 years
Q1b.Calculate spot rates for all 5 years
Q1c.Calculate forward rates for all 5 years
Q1d. Price a 5 year 10% coupon bond. What is the YTM for the bond
Q1e. You manage 100 million dollar floating rate loan that is indexed to one year spot rate plus 2.5% spread (margin). You want to convert it to a 5-year fixed rate loan using a swap contract with notional value of 100 million. What is the breakeven five year fixed rate?

Answer 1

To determine a bond's present value, future cash flows are discounted back to their present value using the market discount rate. A bond with a coupon rate below the market interest rate will be priced below par value. The bond's price adjusts inversely with the market interest rate to provide a comparable yield.

Step-by-step explanation:

The calculation of a bond's present value, also known as the discount factor, is critical to understanding its worth compared to current market conditions. When a bond's coupon rate is less than the market interest rate, it generally sells for less than its par value. The calculation relies on discounting the bond's future cash flows, which include periodic interest payments and the principal repayment at maturity, back to their present value using the prevailing market interest rate.

For example, consider a simple two-year bond with a principal of $3,000 and an interest rate of 8%, paying $240 annually. If the market discount rate is 8%, the bond's price equals its face value, as the coupon rate matches the market rate. However, if market rates rise to 11%, the bond's price would decrease since the fixed coupon payments are less attractive compared to newer bonds with higher rates. Thus, you wouldn't pay more than the present value of the bond's future cash flows, discounted at the new market rate.