Another helpful yeild concept for investors in fixed income investments is "after tax yeild," or ATY. This figure gives the net after tax return that an investor receives when he or she sells, exchanges or redeems a security, after taxes have been considered.

Interest income is taxed as ordinary income. Amortization of a premium is considered a capital loss while the accretion of a discount is taxed at a capital gains rate. The ATY is calculated on par, premium and discount bonds.

ATY information is helpful in allowing an investor to compare after tax returns on various taxable bonds as well as against the desirability of purchasing a tax exempt bond versus taxable bonds.

If, for example, you had a choice of purchasing a seven-year tax exempt issue that would afford you a 5 1/2 percent tax exempt return, or the Treasury 8 percent issue maturing in 1986 at a discount from par with a ATY of 5.9 percent, the choice obviously would favor the Treasury.

Finally, how is interest paid? Interest is paid in two ways. The first method is by discounting. The security is sold at a discount from par. At maturity the security is redeemed at par. The difference between your purchase price and par is your return or income.

Well known types of securities in this category would be Treasury bills, Series E. savings bonds, commercial paper (corporate IOUS) and bankers acceptances.

The yield on discount paper is computed on a bank discount basis which is the exact number of days based on a 360-day year (12 months of 30 days each). The interest that is earned is equal to the discount.

To arrive at the discount rate, the following calculations are needed. To illustrate we will use the results of the Treasury bill auction held on May 7, 1979 for the new 91-day bills that were issued May 10 and mature August 9. The average price was $97.568. From this number we can ascertain the dollar amount of discount earned (income), the discount or bill rate, and lastly the true investment yield or coupon equivalent.

First, the amount or discount (income) is: $100 -- Price = Amount of Discount (income); or $100 -- 97.568 = $2.432.

The amount of discount can be converted into an interest rate figure which will be our discount rate or bill yield.

Discount Bill Rate

100 (Amount of Discount x 360) / (Par x # days to maturity) = discount bill rate

100 (2.432 x 360) / (100 x 91) = DBR = 9.621% = discount bill rate

This method of figuring discount understates the actual new return since it assumes that the full face value ( $100) is invested rather than the actual dollar amount (97.568). In reality, less dollars are invested and to arrive at the true investment return based on the actual monies invested a slightly different formula is used. This formula is based on the actual number of days to maturity on a 365/366 day year plus the actual monies invested.

True Investment Rate -- Coupon Equivalent:

100 (Amount of Discount x 365* Days) / (price x # days to maturity) = TIR/CE

100 (2.432 x 366*) / (97. 568 x 91) = TIR/CE TIR/CE = 10.025%

*366 days if year following date of issue contains February 29th.

The investment rate is also the "coupon equivalent." The coupon equivalent enables you to compare bill yields with coupon bond yield of the type discussed earlier.

If you should have only the market discount rate and desire the true investment yield or coupon equivalent this formula may be used.

100 (365* x Discount Rate) / (360 -- Dist Rate x # days) to maturity from delivery date) = TIR/CE

100 (366 x .09621) / (360 -- (.09621 x 91) = TIR/CE TIR/CE = 10.025%

*366 days if year following date if issue contains February 29th.

This formula is used in computing returns on discount paper maturing in 182 days or less. For longer discount paper a quadratic formula is used which because of its complexity will not be included in this article. The special formula is required because interest paid on bonds and six-month paper is paid every six months. The year bill pays its interest only at maturity and so the lack of reinvestment of income at the six-month interval is taken into consideration.

The other method of paying interest is through interest bearing securities which pay their income at fixed intervals. These payments run the gamut from bonds that pay semi-annually (which most do) to Government National Mortgage Association pass throughs that pay both principal and interest monthly; to preferred stocks which pay quarterly; to certificates of deposit that pay their interest at maturity.

The interest may be calculated on 360-day year or on a 365/366-day year in the case of Treasury bonds.

For interest bearing securities the income may be paid by "clipping" the coupons and submitting them for payment. Or if the bonds are registered, the owner receives the interest by check.

Fixed income securities are bought and sold with accrued interest. For example, our Treasury bond pays $90 per year or $45 semi-annually. If you should sell the bonds three months after interest payment date, you are entitled to the interest that has accrued over those three months.

Therefore, the buyer pays you not only a principal price (based on the market value) but the three months accrued interest as well. At the next coupon payment date,The buyer will receive six months' interest and will recoup the three-month interest he paid to the seller.