Bond question regarding relationships that can exist between capital and face value
I have a question to answer I am not sure of. Wondering if you guys could help me out.
The relationship between a security’s coupon and yield (e.g. Is the coupon less than, greater than, or equal to, the yield?) directly affects the corresponding relationship between its capital and face values. Identify and name the three (3) possible relationships that can exist between capital and face values and explain how each relates to the relationship between coupon and yield
Here a couple quick definitions
Face value: the legal quantity of nominal debt on the instrument to be paid to the bond holder at maturity Coupon: the legal interest payment on the nominal debt that is made Investment value: the market value of the debt Yield: the IRR, the total annual percentage return, etc. Premium/Discount: The difference in market price of the debt vs face value in order to embed extra/less debt in the debt instrument.
What goes on here is that if I’m a company that issues some debt - interest rates change quickly and by the time I’ve issued my debt with its underwritten fixed interest rate - or floating rate plus a credit spread - it will not equal the market interest rate when the debt actually goes out the door. As the market interest rate is what investors will demand, because maybe the yield curve changes, sentiments change, rates change, etc., my issued debt will have to have a premium or discount in order to ensure that the total interest is equal to market interest.
For example, let’s say I have a $100 bond, with a 5% coupon rate, and 2 years until maturity. That means I will get -$100 in year 0. +$5 in year one. $105 in year two if the market interest rate is 5% like the coupon but if the market rate is 10% you could get twice the interest elsewhere so for that bond to sell it must come with the discount so the market interest will be there. In this case, it should sell for at an investment / market value of $91.32. You’ll notice that this gets roughly another $10 in interest when the PV is calculated (simple bond PV formula calculator) that is missing from the coupon.
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