Question

You are offered the following two bonds.

	Bond C	Bond D
Maturity	5 years	10 years
Bond rating	AAA	AAA
Coupon	2%	3%
YTM	2%	4%
Par value	100	100

Assume the yield curve is flat.
Suppose Bond C is correctly priced. Analyse Bond D to determine whether it is consistently priced in relation to Bond C.

Answer 1

Calculation showing price of Bond C

YTM (yield to maturity) = 2%, Coupon rate = 2%, Maturity = 5years, Face value = Rs. 100

Note : If coupon rate of bond and yield to maturity of Bond are equal in the market then the bond is traded in the market at par value or face value.

In the given case the coupon rate = 2% and YTM = 2% hence the bond will be valued at par or face value i.e the price of bond will be Rs. 100/-.

Calculation showing price of Bond D

YTM (yield to maturity) = 4%, Coupon rate = 3%, Maturity = 10years, Face value = Rs. 100

Price of bond = C/(1+ytm)1+ C/(1+ytm)2 + ....C/(1+ytm)10 +FV/(1+ytm)10

Annuity value of 4% for 10 years = 8.111

Present value factor of 4% for 10th years = 0.676

Since the coupon rate are samwe can find the value by multiplying the coupon rate for annuity valuee for all the 10 years

Price of bond = 3*8.111 + 100*0.676

=24.333 + 67.6

Price of Bond D= Rs.91.93/-

Since the YTM is higher than the coupon rate then the bond will be traded at discount in the market.

As it is given in the question that the we have to assume that the yield curve for both the bond is flat which means that the yield on short term and long term bond will be approximately similar and holding the bond for long term duration also not given higher yield in regards to risk associated with time.

In the given case Bond C is traded at par and it is correctly priced however the bond D having long term maturity of 10 years and its yield is higher than Bond C by 2% even being having a flatten yield curve and traded at discount so it can be concluded that Bond D is not consistently priced  in relation to bond C.