Investments, tenth edition

  After-Tax Returns 

 The tax authorities recognize that the “built-in” price appreciation on original-issue dis-

count (OID) bonds such as zero-coupon bonds represents an implicit interest payment to 

the holder of the security. The IRS, therefore, calculates a price appreciation schedule to 

impute taxable interest income for the built-in appreciation during a tax year, even if the 

asset is not sold or does not mature until a future year. Any additional gains or losses that 

arise from changes in market interest rates are treated as capital gains or losses if the OID 

bond is sold during the tax year. 

Maturity

Date

Today

Time (years)

Price ($)

1,000

900

800

700

600

500

400

300

200

100

0

3

0

6

9

12

15

18

21

24

27

30

 Figure 14.7 

The price of a 30-year zero-coupon bond 

over time at a yield to maturity of 10%. Price equals 

1,000/(1.10) 

 T 

 , where  T  is time until maturity.  

 If the interest rate originally is 10%, the 30-year zero would be issued at a price of 

$1,000/(1.10) 

30

5

  $57.31. The following year, the IRS calculates what the bond price 

would be if the yield were still 10%. This is $1,000/(1.10) 

29

5

  $63.04. Therefore, the 

IRS imputes interest income of $63.04  2  $57.31  5  $5.73. This amount is subject to tax. 

Notice that the  imputed  interest income is based on a “constant yield method” that 

ignores any changes in market interest rates. 

 If interest rates actually fall, let’s say to 9.9%, the bond price will be $1,000/(1.099) 

29

5

$64.72. If the bond is sold, then the difference between $64.72 and $63.04 is treated 

as capital gains income and taxed at the capital gains tax rate. If the bond is not sold, 

then the price difference is an unrealized capital gain and does not result in taxes in that 

year. In either case, the investor must pay taxes on the $5.73 of imputed interest at the 

rate on ordinary income.