Question

Currently a three-year zero-coupon treasury bond is traded at a price of $70.38. The Treasury plans to issue a three-year annual coupon bond, with a coupon rate of 10%. The face value of all treasury annual coupon bonds is $100.

(a) What is the yield to maturity of the three-year zero-coupon bond?

(b) At what price should the three-year coupon bond be selling for?

(c) A bond analyst comments that without calculation, he can infer whether the bond will sell above its face value or not. How can he do this? Provide a brief explanation.

(d) If two bonds have the same term to maturity, the same yield to maturity, and the same level of risk, the bonds should sell for the same price." Do you agree that this is correct? Provide a brief explanation.

(e) Lily manages a bond portfolio with the following Treasury bonds:

• 3 year zero-coupon bonds
• 3 year 10% coupon bonds
• 10 year zero-coupon bonds
• 10 year 10% coupon bonds

She believes that market interest rates are going to increase over the next several months. Accordingly, she is suggested to do the following. Comment on each suggestion and make your recommendations to Lily (e.g., whether or not to adopt the suggestion).

1. Sell the 3 year zero coupon bonds and buy the 10 year zero coupon bonds
2. Buy the 10 year zero coupon bonds and sell the 10 year 10% coupon bonds

Answer 1

a) Yield to Maturity (YTM) :

Formula for YTM = [ C + (FV - PV) / T] / [(FV + PV) / 2], Where

C = Interest or Coupon payment, here C = 10% of $100 = $10

FV = Face Value of Bond, here FV = $100

PV = Present Value of Similar Bond, here PV = $70.38

T = Time period to Maturity, here T = 3 years

Therefore required YTM = [ C + (FV - PV) / T] / [(FV + PV) / 2

= [$10 + ($100 - $70.38) / 3] / [($100 + $70.38) / 2]

= [$10 + (29.62 / 3)] / [$170.38 / 2]

=[$10 + $9.87] / $85.19

=$19.87 / 85.19

= 0.2332 OR 23.32%

Hence, Yield To Maturity of the Three Year Zero Coupon Bond is 23.32%

b) At what price should the three-year coupon bond be selling for :

PV = FV / (1 + r)^t

Where PV = Present Value

FV = Face Value, here FV = $100

r = Rate of interest or Coupon Rate, here r = 10% or 0.1

t = Time period to maturity, here t = 3 years

Therefore, PV = FV / (1 + r)^t

= $100 / (1 + 0.10)³

= $100 / 1.1³

= $100 / 1.331

= $ 75.13

Hence, the price at which three year coupon bond will be selling is $74.13 per bond.

c) Bond valuation is a way to determine the theoretical fair value or par value of a particular bond. A bond's present value is calculated basis expected future coupon payments and the face value of the bond, Face value of a bond is the amount to be paid on maturity. Bond valuation helps the investors to understand whether investing in a particular bond is worthy or not. So without proper calculation it is not possible to infer whether a bond will sell at or above face value. Hence, the claim made by the Bond Analyst, that he can infer whether the bond will sell at or above the face value without making any calculation, is not correct.

d) Mathematically, the statement "If two bonds have the same term to maturity, the same yield to maturity, and the same level of risk, the bonds should sell for the same price" is correct. However, there are certain factors other than Term to Maturity, Yield to Maturity and level of Risk, which influence the value of the bond. Such factors are -

1. Financial Health of the issuer, 2. Creditworthiness of the issuer.

Creditworthiness of the issuer affects the bond price in the secondary market. If the issuer is financially strong, investors are will to pay more for the bond, since they are confident that the investor will be able to paying interest as well as pay off the bond on maturity. but if the issuer is not financially strong and if any of the credit rating agency has downgraded the issuer of the bond, then investors looses their confidence on the issuer and as a result price of the bond is likely to fall. Also inflationary conditions lead to discrimination in bond price at secondary market depending on the time issue.

Hence, it can not be said the "If two bonds have the same term to maturity, the same yield to maturity, and the same level of risk, the bonds should sell for the same price".