15.2 How households supply financial capital  (Page 4/43)

Calculating the bond yield

You have bought a $1,000 bond whose coupon rate is 8%. To calculate your return or yield, follow these steps:

1. Assume the following:
   Face value of a bond: $1,000
   Coupon rate: 8 %
   Annual payment: $80 per year
2. Consider the risk of the bond. If this bond carries no risk, then it would be safe to assume that the bond will sell for $1,000 when it is issued and pay the purchaser $80 per year until its maturity, at which time the final interest payment will be made and the original $1,000 will be repaid. Now, assume that over time the interest rates prevailing in the economy rise to 12% and that there is now only one year left to this bond’s maturity. This makes the bond an unattractive investment, since an investor can find another bond that perhaps pays 12%. To induce the investor to buy the 8% bond, the bond seller will lower its price below its face value of $1,000.
3. Calculate the price of the bond when its interest rate is less than the market interest rate. The expected payments from the bond one year from now are $1,080, because in the bond’s last year the issuer of the bond will make the final interest payment and then also repay the original $1,000. Given that interest rates are now 12%, you know that you could invest $964 in an alternative investment and receive $1,080 a year from now; that is, $964(1 + 0.12) = $1080. Therefore, you will not pay more than $964 for the original $1,000 bond.
4. Consider that the investor will receive the $1,000 face value, plus $80 for the last year’s interest payment. The yield on the bond will be ($1080 – $964)/$964 = 12%. The yield, or total return, means interest payments, plus capital gains. Note that the interest or coupon rate of 8% did not change. When interest rates rise, bonds previously issued at lower interest rates will sell for less than face value. Conversely, when interest rates fall, bonds previously issued at higher interest rates will sell for more than face value.