Principles of Microeconomics / Unit 15 MIC 1416 review, 2 to 3 minutes
The Interest Rate as a Price
The idea
One interest rate carried through a bond, a share and a machine shows why the rate is the price of capital and what a change in it does. The rate is payment for waiting, plus inflation, plus a risk premium. Every asset is a claim on future payments, and its price is the present value of those payments at a rate that fits its risk. The bond's payments are fixed by contract, so a higher market rate lowers its price and nothing else. A share's payments are the firm's expected profits, which are forecasts, so its price moves both when the rate changes and when expectations change. A machine's returns are the firm's own forecast; it buys while the present value of returns exceeds the cost, and a higher rate turns marginal projects negative. Add these up across the economy and the demand for capital slopes down in the rate. The rate clears the market for loanable funds: households supply saving, more at higher rates as the substitution effect usually dominates, and firms demand funds for positive-value projects. A rise in the demand for capital raises the rate; a fall in saving raises it too, and the higher rate cuts the quantity of capital demanded. One number prices every claim on the future.
In practice
Worked example, at five percent and then fifteen. A two-thousand-dollar two-year bond with a five percent coupon: worth two thousand at five percent and about one thousand six hundred seventy-five at fifteen. A share in a firm expected to earn four, five and six million now, in one year and in two, with one hundred thousand shares: at five percent the profits are worth four plus four point seven six plus five point four four million, fourteen point two million, one hundred forty-two dollars a share; at fifteen percent, four plus four point three five plus four point five four, twelve point eight nine million, one hundred twenty-nine dollars. The machine costing ten thousand and returning six thousand a year for two years: plus one thousand one hundred fifty-six at five percent, minus two hundred forty-six at fifteen. One rate change lowered the bond, lowered the share, and cancelled the machine.
Where people slip
Three cautions. The rate that prices a share is not the Treasury rate; it carries the risk premium, and choosing it is a judgment, which is why share prices disagree while bond prices do not. Compound interest is the same arithmetic run forward: multiply by one plus the rate to the power of the years, so small differences in rate or time compound into large ones. And the demand for capital, like the demand for labor, is derived: it shifts with expectations, technology and the demand for what capital produces, not only with the rate.
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