Question

Par value is 1000

1) A 100-year corporate bond has a coupon rate of 10% with semi-annual payments. If the current value of the bond in the marketplace is $400, then what is the Yield-to-Maturity (YTM)?

2) How much do you pay for a zero coupon government bond that has a term of 30 years, an interest rate of 10%, and a par value of $1000.

3) A taxable bond has a yield of 10% and a municipal bond has a yield of 4.6%. If you are in a 23% tax bracket, which bond do you prefer?

4) A taxable bond has a yield of 8% and a municipal bond has a yield of 10%. If you are in a 23% tax bracket, which bond do you prefer?

Answer 1

1) Par Value = 1000

Market price of bond= $400

Coupon rate = 10% with semi annual payments

YTM = ?

Yield to maturity is the discount rate at which the sum of all future cash flows from the bond (coupons and principal) is equal to the current price of the bond.

In this question, we need to calculate YTM, but coupon rate is semi-annually given -

Semi-annual YTM = Coupon payment +(Face value - Price)/Years to maturity

(Face Value+Price)/2

where coupon payment = Face VAlue* coupon rate/2

1000*10%/2 = $100/2 =$50

and number of years will be = 100 years*2 = 200 years

= 50+(1000-400)/200

(1000+400)/2

=50+3

700

= .075714

YTM = 2* Semi annual YTM

= 2*0.75714

= .151429 or, 15.14 %

2) No. of years = 30 years

Interest Rate = 10%

FAce Value = $1000

Zero Coupon bond value = 1000

(1+.10)raised to the power 30

= $ 57.31