Bond Yields and Prices using the Yield curve/Spot yield curve

Hi John,

Just a bit confused around using the yield curve to value debt, if you can help please.

In his technical article “Bond Valuation & Bond Yields”, the examiner introduces the term structure of interest rates & the yield curve, and describes how a normal upward sloping yield curve could have an organisation for example having to pay interest (i.e. the required yield) of 3.5% each year for a 2 year debt issue, or 4.2 % each year for a 3 year debt issue. The key word here is “each” year, as I come to my confusion below.

He then proceeds to value bonds using the yield curve, using a bond to be issued with redemption in 4 years @ Par $100; with a 5% annual coupon.

The spot yield curve rates, for a bond with the same risk class, are

One-year 3.5%
Two-year 4.0%
Three-year 4.7%
Four-year 5.5%

I thought, from reading the first piece above, that a bond with 4 year maturity (and with same risk class, so no risk-premium spread required in this case) will have to pay average interest of 5.5% each year for the 4 years, and so each annual coupon could be discounted at 5.5% to calculate the bond’s total Present Value. However in his solution he takes each annual coupon and discounts each of these at that year’s yield curve rate (3.5% for fist 5$ coupon, 4% for second year’s coupon, etc). This seems to me to be inconsistent with the first principal above of paying interest/coupon “each year” at the one overall yield curve rate of the bond’s maturity?

Sorry if I’m not articulating well.

One possible explanation from my research is that the yield curve he is using here is for zero-coupon bonds, strictly called a “zero curve” – in which case we treat each year’s coupon as having the same yield (plus any risk premium) as a zero-coupon bond maturing in the same time period, and it is then appropriate to treat a coupon paying bond with 4 years to maturity of being made up of 4 x zero coupon paying bonds.. in which case using the yield curve like he does above may make sense. But I’m not sure why he would not call out the yield curve as being specifically a “zero curve” if this is what he is using…

Sorry if this doesn’t make sense or if i’m indeed over thinking or complicating.. i’ve come back to this in my revision and keep getting muddled on it 🙂