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

Chapter Sixteen: Valuing the Future - Concepts in Capital & Finance 408 cash flows based on the higher rate of 6% become more valuable, and will increase the value of each year’s payment and associated present value of the bond to $1,043. Should the purchaser of the bond decide to sell it, he or she would incur a capital gain , since the sales price would exceed the purchase price (the face value of $1,000). If the interest rate were to rise to 8% the day after the issue, each year’s cash flow would be worth less, since other purchasers of bonds could buy a bond with an 8% yield, and the present value would fall below par (the face value) to only $920. If the purchaser decided to sell the bond, he or she would suffer a capital loss. Capital gains are usually charged a lower tax rate than ordinary income in part because the gain is not indexed to inflation. As the earlier example illustrates, a bond is also subject to risk in that if interest rates change, the bond’s price will change. So if an investor loans money to a firm at a low interest rate and interest rates rise, the investor may suffer a capital loss. What determines the size of the capital loss? The two factors are the interest rate change and the amount of time the investment is held. It is probably intuitive to most readers that if the interest rate increase is larger, the capital loss would be larger. As an exercise, use a calculator to find the present value of the same series of cash flows in Figure 16.4 with an interest rate of 20%. You should find the present value to be $580.82, a much larger percentage loss (~42%) than when the interest rate rose only to 8% (an 8% capital loss). So there is a capital risk if the bond is not held to maturity. But if the bond is held to maturity, there is low risk to the payment itself; if the firm does not go bankrupt it is contractually obligated to pay $60 each year. This is contrasted with a common stock, whose dividend payment can be changed by the board of directors at any time. The other potential contributor to loss for a bond is the length of term. If instead of a five-year bond as in Figure 16.5 , we had a 20-year bond, what would happen when the interest rate rose to 8% the day after it was issued? We need to carry the cash flows out for T=20, but this is otherwise identical to what we have in Figure 16.5 . At this point, it is easier to do on a financial calculator (or you can use any number of websites to perform the calculation) and you will arrive at a present value for this bond of $803.63, a significantly larger capital loss than for the same interest rate change applied to a five- year bond. This outcome suggests that longer-term bonds are significantly more risky (higher variability in yield) than short-term bonds. EFFICIENT MARKET HYPOTHESIS Every asset market that is publicly traded (bonds, stocks, etc.) benefits from the knowledge of potentially millions of investors. Each investor, seeking only personal private gain, contributes knowledge that drives the efficient allocation of capital in a market economy. This is yet another application of Adam Smith’s “invisible hand” which guides individuals to produce a socially useful outcome through the exercise of enlightened self-interest. Those that have the best knowledge to contribute to market prices tend to have higher profits; those that err more in making financial “votes” for the allocation of capital suffer losses. Capital gain: An investment incurs a capital gain if the sales price of the investment exceeds the purchase price.