Question

Suppose that you are reviewing a price sheet for bonds and see the following prices (per $100 par value) reported. You observe what seem to be several errors. Without (!) calculating the price of each bond, indicate which bonds seem to be reported incorrectly and explain why.

Bond	Price	Coupon Rate (%)	Yield (%)
U	90	6	9
V	96	9	8
W	110	8	6
X	105	0	5
Y	107	7	9
Z	100	6	6

Answer 1

Bond price is obtained by discounting of the future cash flows and these cash flows are discounted with present yield. If the yield is higher the price will be the lower than the par value or face value and if the yield is lower than the price will be higher than the par value. This happens due to yield is discounting factor. Higher the discounting factor results in lower present value of the cash flows and lower the discounting factor results in higher present value of the cash flows. This logic we will apply in each case.

Bond	Price	Coupon Rate (%)	Yield (%)	Correct / incorrect	Comment / Reason
U	90	6	9	Correctly priced	When coupon rate is less than yield then the bond price is lower than face value of the bond
V	96	9	8	Incorrectly priced	As coupon rate is higher than the yield this implies the bond price should be more than the par value of the bond i.e more than 100. The price should have been more than par value and which is not the case here.
W	110	8	6	Correctly priced	As coupon rate is higher than the yield this implies the bond price should be more than the par value of the bond i.e more than 100 and here price is more than 100 therefore correctly priced.
X	105	0	5	Incorrectly priced	As this seems to be zero coupon bond and zero-coupon bond cannot trade above the face value or par value of the bond because coupon rate is always lower than the present yield.
Y	107	7	9	Incorrectly priced	As coupon rate is lower than the yield therefore, the price of the bond cannot be higher than the par value or face value of the bond i.e cannot be higher than 100
Z	100	6	6	Correctly priced	If yield and coupon are equal then bonds trade at par value that is 100

*In all above cases we don’t know the maturity period
**Assuming face value or par value as 100