LOS c: Calculate accrual equivalent after-tax returns.

Q1. An investor deposited $33,000 in a zero coupon bond position 20 years ago. It consisted of 100 zero coupon bonds each with a face value of $1,000 and 20 years to maturity. Over the years he has sold portions of the position to pay income taxes on the position as it grew in value. The investor’s current marginal tax rate is 30%. At maturity, and after all taxes have been paid, the value of the position is $84,500. Compute the accrual equivalent after-tax return.

A)   4.81%.

B)   4.33%.

C)   3.99%.

Q2. You compute that an investment with a current value and basis equal to $20,000 will have an annual return after realized taxes equal to 10% for the next 12 years until it is sold. The effective capital gains rate will be 15%. What will be the accrual equivalent after-tax return?

A)   8.50%.

B)   9.02%.

C)   12.50%.

LOS c: Calculate accrual equivalent after-tax returns. fficeffice" />

Q1. An investor deposited $ffice:smarttags" />33,000 in a zero coupon bond position 20 years ago. It consisted of 100 zero coupon bonds each with a face value of $1,000 and 20 years to maturity. Over the years he has sold portions of the position to pay income taxes on the position as it grew in value. The investor’s current marginal tax rate is 30%. At maturity, and after all taxes have been paid, the value of the position is $84,500. Compute the accrual equivalent after-tax return.

A)   4.81%.

B)   4.33%.

C)   3.99%.

Correct answer is A)

The accrual equivalent after-tax return = 4.81% = ($84,500 / $33,000)^(1/20) ? 1. The current marginal tax rate is not relevant to solving the problem.

Q2. You compute that an investment with a current value and basis equal to $20,000 will have an annual return after realized taxes equal to 10% for the next 12 years until it is sold. The effective capital gains rate will be 15%. What will be the accrual equivalent after-tax return?

A)   8.50%.

B)   9.02%.

C)   12.50%.

Correct answer is B)

The balance in the account after payment of all taxes in 12 years uses the future value interest factor after all taxes:

Future value = $20,000 × [((1.1)¹²) × (1 ? 0.15) + 0.15] = $56,353

The accrual equivalent after-tax return is then ($56,353 / $20,000)^1/12 ? 1 = 9.02%.