Question

1. A 100-year corporate bond has a coupon rate of 9% 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 9%, and a par value of $1000.

3. A taxable bond has a yield of 9% and a municipal bond has a yield of 4.6%. If you are in a 23% tax bracket, which bond do you prefer?

Answer 1

1. FV = 1,000

N = 100 * 2 = 200 Semi-annual payments

PMT = 1,000 * 0.09/2 = 45

PV = -400

CPT I/Y

I/Y = 11.25%

Yield to maturity = 11.25% * 2

Yield to maturity = 22.5%

2. PV = FV/(1 + r)^n

PV = 1000/(1 + 0.09)^30

PV = $75.371136128

We would pay $75.371136128 for this zero-coupon government bond

3. Income from Municipal bond is tax-free

After-tax yield from municipal bond = 4.6%

After-tax yield from the taxable bond = 9% * (1 - 0.23)

After-tax yield from the taxable bond = 0.0693

After-tax yield from the taxable bond = 6.93%

We would prefer the taxable bond because it has a higher yield even after paying taxes