No Free Lunch: Economics for a Fallen World: Third Edition, Revised

Chapter Sixteen: Valuing the Future - Concepts in Capital & Finance 407 paid (the workers, the suppliers, the banks who loaned the company money, etc.). To compensate for this higher level of risk (variability in returns), stockholders historically receive a higher return than bondholders on average. So what if you don’t like that risk? You can loan money directly to a company if you purchase one of its bonds, which is basically an I.O.U. from the company to you . 1 A bond is a promise from a firm to pay back the principle plus a stated interest payment. The interest payment is commonly called a coupon, from older days when a bond actually had a coupon on the bottom which could be clipped off and mailed in to the firm. The firm would then mail a check back to the “coupon clipper” for the interest payment. There are many different types of bonds, with differing maturities and risks, but basically the value of every bond is calculated the same way as any other asset: a bond’s value (or price) will be equal to the discounted value of its future cash flows. A typical bond will pay the coupon once or twice per year (the interest or coupon payment) and then will pay a final interest payment and the principle in the last period. We can use our existing equation 4 to calculate the bond’s present value, with the understanding that the last cash flow will be the sum of the last coupon payment and the principle. So let’s use an example of a five-year bond with a face value of $1,000, with a coupon rate of 6% (which would yield an annual cash flow of $60 - $1,000 multiplied by 6%), as seen in Figure 16.5 . Each of the bond’s payments must be discounted back to the present value and summed to find the overall value (or price) that the bond will sell for. If the bond is issued with a 6% coupon rate and the interest rate stays at 6%, the present value will equal the face value of $1,000. If the interest rate drops the day after the bond’s issue to 5%, each of the Figure 16.5, Present Value of five year bond with a $1000 face value and annual coupons. If a firm sells a bond at a 6% coupon and a face value of $1000, the present value can be calculated as in the table above. If the interest rate stays at the initial 6% coupon rate, the present value of the bond will equal its face value. Should the interest rate fall the day after the issue to 5%, the bond’s price will rise to reflect the desirability of owning a bond that yields a higher interest rate. Conversely, if the interest rate rises, the price must fall, as purchasers would rather buy a bond paying the market interest rate of 8% rather than this bond’s lower interest rate of 6%. CF/(1+i ) CF/(1+i ) 2 CF/(1+i ) 3 CF/(1+i ) 4 CF/(1+i ) 5 Present Value if i = 6% $56.60 $53.40 $50.38 $47.53 $792.09 $1000 $1043 Cash Flow @ 1=6% $60 $60 $60 $60 $1060 if i=5% $57.14 $54.42 $51.38 $49.36 $830.54 $920 if i=8% $55.55 $51.44 $47.63 $44.10 $721.42