Calculate Bond Total Return

A corporation issues a bond to raise money to run a business. Government entities issue bonds to fund capital projects, such as a new highway. The bond issuer is the debtor and a bond investor is the creditor. The investor earns interest income each year and is repaid the face amount of the bond on the bond’s maturity date. In addition to earning interest, the investor may also benefit from selling the bond for a gain. If the bond is sold at a loss, the loss reduces the investor’s total return. Your total return can be adjusted for taxes and the present value of your cash inflows

Steps

Calculating the Bond Interest Earned

1. Confirm the coupon rate and dollar amount of the bond purchase. The vast majority of bonds come with a fixed rate of interest, called the coupon rate. This may be different from the current market interest rate. Whether the bond is a corporate bond or a municipal bond, you should find the coupon rate on the bond certificate.
   • Most bonds are now issued in book entry form. When you buy the bond, you will receive documentation of the bond you own. Rather than receive a physical certificate of ownership, you receive a third party document, which verifies that you own the bond. That document includes the coupon rate and the dollar amount of your purchase.
   • The interest you earn on a bond is based on the face amount of the certificate. The face amount will be in multiples of $1,000. Multiply the coupon rate by the face value of the bond.
   • Assume that you purchase a $10,000 bond with a 6% fixed rate of interest. Since the rate is fixed, this means that the bond will pay you $600 each year ($10,000 x 0.06). The interest payment is fixed, regardless of any fluctuations in the market price of the bond.
   • Discounts or premiums on bonds refer to the selling price of the bond. Discounts and premiums compensate investors for the difference between the coupon rate on the bond and the current market interest rates. If the current market interest rate is higher than the coupon rate, the bond is sold at a discount. If the current market interest rate is lower than the coupon rate, the bond is sold at a premium.
2. Add up the total interest earned on the bond. Part of your bond’s total return is the interest you earn over the life of the bond. Verify how many years you have owned the bond then calculate the annual interest earned each year.
   • Use the accrual method of accounting to calculate interest earned. The accrual method recognizes interest income when it is earned. If you own the bond during a particular month of year, you earn the bond’s interest during that period.
   • The accrual method is unrelated to the cash payments you receive. Your interest earnings are based on owning the bond, not the date of a particular interest payment.
   • Most corporate bonds pay interest twice a year. Say, for example, that your bond pays interest on February 1st and August 1st of each year. You are calculating interest earned during December. Since you owned the bond for the full month of December, you are entitled to receive the interest paid for that month. You earned an entire month of interest in December, even though the interest won’t be paid until February of the following year.
3. Determine your interest earned after you sell your bond. Bonds can be bought and sold between investors, just as stocks are traded. As an investor, you can hold you bond until the maturity date, or sell the bond before it matures. You can sell your bond on any business day.
   • If you choose to sell your bond, the sale impacts the total interest you earn on the bond. Assume, for example, that your bond pays interest on February 1st and August 1st of each year. You sell your bond on December 15th.
   • To calculate the total return, you need to know the total interest that you earned during the time you held the bond.
   • Say that your $10,000 bond has a 6% fixed rate of interest. The bond pays you $600 each year. If you held the bond for 5 full years, your total interest earned would be ($600 multiplied by 5 years = $3,000).
   • You also need to calculate the fractional year of interest. In this case, you held the bond from January 1st to December 15th of the final year of ownership. That is 11 ½ of 12 months in a year. The interest earned for the fractional year is [($600 X (11.5/12) = $575].
   • You are entitled to the interest earned for the period of your ownership even though the interest may not be paid until months later
   • Your total interest earned over 5 years and 11 ½ month is ($3,000 + $575 = $3,575).
   • Total return formulas may count the precise number of days of ownership. Those days may be based on a 360-day year, or on a 365-day year. The number of days depends on whether or not the bond is issued by a corporation or a government entity.

Computing Capital Gains or Losses

1. Note your original purchase price for the bond. A capital gain or loss is a component of a bond’s total return. If you sell a bond for more than your purchase price, you have a gain. A loss is generated when you sell a bond for less than you paid for the security. To calculate a capital gain or loss, you need to know the price that you paid for the bond.
   • When a bond is issued, it is sold for the first time from the issuing company (or government entity) to the public. An investor buys the bond, and the sale proceeds go to the issuer.
   • If you buy a bond when it is issued, you normally pay the face amount of the bond. The face amount of a bond is $1,000 or some multiple of $1,000. If you buy a $10,000 face amount bond when it is issued, for example, you pay $10,000.
   • Once a bond is issued to the public it can then be bought and sold between investors. Assume, for example, that Bob purchases an IBM corporate bond when it is originally issued. Bob pays the face amount of $10,000. Bob can choose to sell the bond at any time before the bond’s maturity. The price he receives for the bond sale may be more or less than $10,000.
   • Note that any capital gain is considered income by the IRS and you must pay taxes on the interest earned.
2. Sell a bond at a discount. A discount means that the price of the bond is less than the face amount. For example, the $10,000 bond can have a current market value of $9,800. The market indicates that investors are not willing to pay $10,000 for this bond.
   • A bond is valued at a discount if the interest rate stated on the bond is less than the interest rate on newly issued bonds. To make the comparison, consider newly issued bonds by the same issuer and with the same time until maturity.
   • Assume that IBM has a $10,000, 6% bond outstanding. The bond matures in 10 years. Interest rates increase. An investor can now buy a 7% IBM bond due in 10 years. The 6% bond is now less valuable, since it pays less interest than the 7% bond. The market price of the bond will drop to a price that is less than $10,000.
   • If an investor buys the bond for $10,000 and sells the security for $9,800, that investor has a $200 capital loss. The loss reduces the total return on the bond.
3. Trade a bond at a premium. A premium means that the price of the bond is more than the face amount. For example, the $10,000 bond may have a current market value of $10,100. The market indicates that investors are willing to pay more than $10,000 for the bond.
   • A bond is valued at a premium if the interest rate stated on the bond is more than the interest rate on newly issued bonds. To make the comparison, consider newly issued bonds by the same issuer and with the same time until maturity.
   • Assume that IBM has a $10,000, 6% bond outstanding. The bond matures in 10 years. Interest rates decrease. An investor can now buy a 5% IBM bond due in 10 years. The 6% bond is now more valuable, since it pays more interest than the 5% bond. The market price of the bond would increase to a price that is more than $10,000.
   • If an investor buys the bond for $10,000 and sells the security for $10,100, that investor has a $100 capital gain. The gain increases the total return on the bond.
   • You may incur a gain or loss by buying a bond and selling it before the maturity date. An investor may also buy a bond at a premium or discount and hold the bond until maturity. In each case, you may have a gain or a loss.

Determining A Bond’s Total Return

1. Add up your total proceeds from the bond. You can calculate your total return by adding the interest earned on the bond to the gain or loss your incur. The gain or loss may be generated based on selling the bond, or simply holding the bond until maturity.
   • Assume that you buy a $10,000 face amount. You hold the bond until maturity and receive the $10,000 principal amount. There is no gain or loss on the bond. The bond pays 6% interest, and you hold the bond for 5 year and 11 ½ months.
   • The 11 ½ of 12 months in the final year can be converted into .958. Your total interest earned over the life of the bond is [($10,000) X (6%) X (5.958 years) = $3,575]. Your total return on the bond is the interest earned ($3,575).
   • Say that you buy the same bond and own the security for the same length of time. Assume, however, that you buy the bond for $10,000 and sell the bond for $9,800. You generate a $200 loss. The total return on your bond is ($3,575 interest) - ($200 capital loss) = $3,375.
   • Assume that you buy the same bond and own the security for the same length of time. In this instance, you buy the bond for $10,000 and sell it for $10,100. You generate a $100 gain. The total return on your bond is ($3,575 interest) + ($100 capital gain) = $3,675.
2. Adjust your bond’s total return for the impact of taxes. Your interest income and any capital gain or loss will be taxed. You should consider the dollar amount of your payments after taxes are paid.
   • Assume that your interest income and a gain on a bond sale total $3,675. You pay a 20% tax on the interest income and the gain.
   • Your total return after taxes is $3,675 X 80% = $2,940.
   • Interest income is taxed as ordinary income. The tax rate for interest income is the same rate that you pay on your wages.
   • Keep in mind that the tax rates for interest income and capital gains or losses may be different.
   • It is important to note that you can declare capital losses as deductibles on your tax return. You can use your capital losses from investments to reduce your capital gains. This reduces how much you have to pay in taxes. If your capital losses are more than your capital gains, you can offset your ordinary income up to $3,000 in a single tax year. If your loss is greater than $3,000, then you can claim another $3,000 the next year, and so on until the entire amount has been deducted.
3. Calculate the impact of the market interest rate on the price of the bond. The selling price of a bond varies depending on the current interest rate in the market. If the current market interest rate goes higher than the bond’s coupon rate, then the bond is sold at a discount. Conversely, if the market interest rate falls below the bond’s coupon rate, then the bond is sold at a premium.
   • For example, suppose a company is selling $500,000, 5-year, 10 percent bonds, but the current market interest rate is 12 percent. If the current market interest rate is 12 percent, you are not going to want to invest your $1,000 in a bond that only has a 10 percent rate of return. So the company discounts the price of the bond to compensate you for the difference in the interest rate. In this example, the company would set the selling price at $463,202.
   • Conversely, suppose the current market interest rate is 8 percent. In that case, the 10 percent coupon rate of the bond is a better return than you could get elsewhere. The company knows this, so they increase the price of the bond and issue it at a premium. The company would issue the $500,000 bond for a selling price of $540,573.
   • In either case, you still receive interest payments based on the face value and coupon rate of the bond. The annual interest payments on the bond are $50,000 ($500,000 * .10 = $50,000).
   • When a bond matures, you get the face value of the bond. Whether you bought the bond at a discount or a premium, upon maturity you receive the face value. Using the example above, whether you bought the bond at a discount or a premium, you would receive $500,000 upon maturity.
4. Understand the difference between yield and interest rate. The yield is your total return on the principal of a bond. The yield is impacted by the market interest rate because the market interest rate affects the selling price of the bond. But, the yield is different from the coupon rate and the market interest rate.
   • Calculate the yield with the formula coupon amount / price.
   • Using the example above, a company issues $500,000, 5-year, 10 percent bonds, and the market interest rate is 12 percent. The company sells the bond at a discount, and the price is $463,202.
   • The annual coupon payments are $50,000.
   • The annual yield is $50,000 / $463,202 = 10.79 percent.
   • In the example where the market interest rate was 8 percent, the bond was sold at a premium, and the price was $540,573.
   • The annual yield is $50,000 / $540,573 = 9.25 percent.

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