Suppose you are the owner of a zero- coupon bond maturing in 30 years. Suppose further that the current applicable discount rate is 10% (and for simplicity treat this zero as an annual bond. Note that in the US, Zero-coupon bonds are treated as semi-annual bonds). Calculate the current market price of the zero and, if the applicable tax rate is 20%, the taxes owed at the end of the next three years (assume the interest rates remain the same and that the par value of the STRIPS= 1000).

The current market price of the zero-coupon bond = $53.54

The tax owed at the end of the first year = $1.10

The tax owed at the end of the second year = $1.21

The tax owed at the end of the third year = $1.33

Step-by-step explanation

Calculate the current market price of the zero-coupon bond

Semiannual rate r = 5% » 10% / 2

Maturity n = 60 » 30 * 2

Face value = $1,000

Market price today P₀ = Face value * (1 + r)^-n

= $1,000 * (1 + 5%)^-60

= $53.54

The current market price of the zero-coupon bond is $53.54

Calculate the taxes owed at the end of the next three years

Tax rate = 20%

Market price in 1 year P₁ = Face value * (1 + r)^-(n-2)

= $1,000 * (1 + 5%)^-58

= $59.02

Tax owed = (P₁ - P₀) * Tax rate

= ($59.02- $53.54) * 20%

= $1.10

The tax owed at the end of the first year is $1.10

Market price in 2 years P₂ = Face value * (1 + r)^-(n-4)

= $1,000 * (1 + 5%)^-56

= $65.07

Tax owed = (P₂ - P₁) * Tax rate

= ($65.07 - $59.02) * 20%

= $1.21

The tax owed at the end of the second year is $1.21

Market price in 3 years P₃ = Face value * (1 + r)^-(n-6)

= $1,000 * (1 + 5%)^-54

= $71.74

Tax owed = (P₃ - P₂) * Tax rate

= ($71.74 - $65.07) * 20%

= $1.33

The tax owed at the end of the third year is $1.33