Question

Part 2:  Problem Solving

Show all computations where necessary. Partial credit will only be given if work is shown.

Solve the following problem using the formula.

1. Wells Fargo issued a 10 percent zero coupon bond with 10 years to maturity. What is the yield to maturity of this bond if it is sold at 111% of par? ( This problem should be done using the formula only, show all your work.

Answer 1

Solution :

The Yield to Maturity of a zero coupon bond can be calculated using the following formula

YTM = (Face value / Current Price)^{(1/ Years to maturity )} - 1

As per the Information given in the question we have

Let the Face value of the bond = $ 1000

Current price of the bond = 111 % of par = $ 1000 * 111 % = $ 1110

Years to maturity = 10 years

Applying the above values in the formula we have

= ( 1000 / 1110 ) ^{( 1/ 10)} – 1

= ( 0.9009 ) ^{( 0.10 )} – 1

= 0.9896 – 1 = - 0.0104

Thus the YTM of the zero coupon bond = - 1.04 % ( when rounded off to two decimal places )

Note : ( 0.9009 ) ^{( 0.10)} = 0.9896 is calculated using the excel formula =POWER(Number,Power)

=POWER(0.9009,0.10)