In Wednesday's article we saw that current yield on fixed income investments considered the coupon return and the price paid to receive that return. Whether or not the price paid was at a discount (below par), par to at a premium (above par) was not considered.

Another bit of investment terminology is "yield to maturity," or YTM which considers various aspects of the purchase price. YTM shows the effect of the capital gain or capital loss from paying a discount or a premiun at the time of purchase. YTM takes into consideration the time to maturity, the price paid and the coupon income.

Consider a 20-year Treasury issue with a 9 percent coupon purcahsed at 90. The investor will receive \$1,000 at maturity, which is \$100 more than was purchase price and the par value (100) must be taken into consideration. This appreciation to par is called accumulation or accretion and is factored into the YTM.

Consider the same Treasury bond where the market value of the bond was 8 percent and the dollar value of the bond was \$1125.00. The premium ( \$125) or depreciation mist be taken into account when YTM is calculated, since the owner receives \$1,000 at maturity. This depreciation is called amortization.

By using bond tables or a computer, we arrive at the YTMS is our examples.

First, the YTM of the 9 percent Treasury selling at 100 is 9 perent. Secondly the Ytm of the same bond selling at 90 (discount) is 10.18 percent, and when the bond is selling at 112 1/2 (premium) the YTM is 7:76 percent.

Putting the current yield and YTM in perspective, we see that when a bond sells at a premium over the par value the current yield is larger than the YTM because current yield ignores the capital loss. When it sells at a discount from par value, the current yield is smaller than the YTM because it ignores the capital gain. When purchased at par, both are the same.

Another aspect of YTM that is often overlooked is that YTM assumes that the coupon income is reinvested at the purchase yield semiannually and compound over the life of the bond. Therefore if investors are able to reinvest their coupon income and compound their return, YTM will be more important than current yield.

It the coupon income is reinvested at a higher yield than the purchase yield, then the YTM will be greater than the original yield.

Conversely, if the future rates of reinvestment are made at yield lower than the purchase yield, the YTM will be less than the YTM at the time of the original purchase.

The question is often asked, Why do bonds sell at premiums and discounts? The correct answer would be that outstanding bonds are adjusting to the changing levels of interest rates in the marketplace. To understand how this works, let us suppose that three years have passed and our 20-year Treasury bond now has 17 years until maturity. The interest rate level has risen to 10 percent, and new bonds are being sold at that level. I can purchase a bond with a 10 percent coupon for \$1,000. For my original bond to stay competitive, it must decline in dollar value so that it too will yield close to 10 percent on the Ytm basis.

Now let us supposes that the interst rate levels dropped to 8 percent. New bonds would sell to return 8 percent or \$80 of income per \$1,000 par value. Investors would then bid up the price of our old Treasury to a premium until they could purchase our old bonds at the same YTM as tey could purchase a new bond. The YTM would become 8 percent while the current yield woukd be 8.33 percent. The price becomes the requalating factor for the old bonds to adjust to the new market levels.

Another feature to be considered are bonds that may be redeemed, or "called" from their holders before they mature. This is especially important in times of high interest rates with unusally high cupons. Some municipal bonds are callable and most long Treasuy bonds are callable during the five-years period to their maturing.

In essence, new bonds have a period during which the issuer cannot redeem the loan at lower interest rates. For utility issues that period is five years, for industrials it is generally ten years.

However, once that time has elapsed, the issuer may redeem and pay off the loan at the fixed dollar price which declines every six months once the bonds are issued.

The call feature becomes important to the bond holder during periods of low interest rates and once the "no-call" feature has elapsed.

To illustrate, suppose we have a 9 percent General Moters bond that will be called for redemption in the tenth year of its existence at a dollar price of 105 (\$1,050) per bond. Depending on where the bond is selling in the open market, we are able to calculate its YTM or at what yield we must reinvest the bond proceeds, should we sell the bond, to come out ahead.

We must decide whether to use the call date or the maturity date in calculating the YTM. Since the bonds may be redeemed at the discretion of the issuer after the tenth year, they would be redeemed, or called, when the time is favorable to the issuer.

When the bond is selling below its call price (105), the final maturity date is used in calculating the YTM. This is true because it is cheaper for the issuer to buy the securities in the open market at a price lower than the higher call price.

But when the bond is selling above the call price, the call date is when the call price, is the sate is then used to compute the YTM and will be designated the "yield to call." Obviously it will be cheaper for the issuer to redeem his bonds at 105 rather than to pay the higher market price.

The logic for redemption on the part of General Motors is, that if the bonds are selling above par when the call protection expires, then the yield is less than the face yield and it would be cheaper to pay off the high-coupon bonds by issuing new low-coupon bonds.