Suppose you manage a rock group called "Mutant Larvae," currently being booked as a warm-up act for more popular bands. The group's third album suddenly goes platinum and phones begin to ring. Promoters want "Larvae" to headline upcoming concerts, but it is solidly booked for the next six months at $5,000 per appearance. Who will benefit from the group's popularity during the next six months? Promoters who contracted with your band prior to its hit album will profit by selling out their concerts even if they raise ticket prices. How long will these economic profits (which could also be considered rents) continue to be received by individual concert promoters?
Being a smart promoter yourself, you will quit booking Larvae as an opening act and will raise its fee when you negotiate future contracts so individual concert promoters will earn only normal profits. This capitalizes rents from the group's popularity. The group's fee now reflects the higher ticket prices and attendance for each performance. If you held exclusive rights to book the group, you could sell the contract for a fat profit.
Capitalization is the transformation of future income streams into current value or wealth and quickly eliminates economic profits.
Similar capitalization processes occur in farming. If international grain prices soar, farmers temporarily enjoy economic profits. But the price of farmland rises when expected profits are capitalized into higher land values. Even farmers who own their land find the opportunity cost of holding their land rises, squeezing out the economic profit derived from farming. Their higher wealth naturally would keep most of them from mourning this fate.
Investors prefer more income to less, and they want it sooner rather than later. Thus, the capitalized value of an income stream will be larger (a) the greater the expected income stream, and (b) the more quickly income is realized. Truly understanding these relationships requires knowing how to calculate present values and rates of return.
Investment generates future output and yields an income stream to the investor. The income stream per period as a percentage of the dollar outlay for a capital good is the rate of return. Determining whether an investment will be profitable requires calculating its present value, which is the value today of all expected future income.
The present value of an asset is the discounted value today of the expected income stream associated with the asset.
Suppose you were offered a guaranteed $100 payable one year from today and that your savings account earned 6 percent interest annually. What is the most you would willingly pay for this IOU? Certainly less than $100. You can calculate the amount at which you will do equally well by having your funds in either the savings account or this IOU by answering the question: How much money would I have to put in the bank at a 6 percent annual interest rate so that when the interest earned in one year is added to the original amount, the total equals $100? This problem boils down to 1.06(PV)= $100, where PV stands for present value. If you divide both sides of this equation by 1.06 and then solve for PV= $100/1.06, you have the answer. Similar questions can be answered for any interest rate, any time period, or any amount of money using the following formula:
Yt = payment expected at time t.
i = annual interest rate or discount rate.
t = time period.
n = number of periods when payments are expected.
å = an arithmetic operator meaning "sum across."
If you use a 6 percent interest rate to discount the $100 payable one year from today, the PV = $100/1.06, which equals $94.34. This amount in a savings account paying 6 percent interest would yield $94.34 ´ (.06) = $5.66; at the end of the year your principal plus interest would total to $94.34 + $5.66, which is $100. If you had to wait two years for the $100, what is the most you would pay, assuming the interest rate is 6 percent? The answer is $89, because $100/[1+ .06]2 = $89. Naturally, an IOU paying $100 next year plus $100 two years hence would be worth $94.34 + $89.00= $183.34.
State legislatures came under tremendous pressure during the 1980s to hold taxes in check. Many responded by enacting state lotteries. Federal "truth-in-lending" laws were enacted to help borrowers avoid misunderstandings about interest rates and present values. Focus 1 indicates how misleading state lotteries are because their advertising fails to reflect the importance of discounting future income streams.
The present value formula may appear formidable, but there is a shortcut in calculating present values if the annual income expected from an asset is fixed into the indefinite future at a constant Yt. Such assets, known as perpetuities, are computed with the following equation:
Present Value for Perpetuities
Thus, if a parcel of land is expected to generate annual rent of $10,000 forever, and the interest rate is 10 percent (.10), the parcel's present value is $100,000. If a government bond promises to pay $1,000 annually forever to its owner, and the interest rate is 8 percent, it is worth $12,500. Bonds of this type, called consols, are issued by the Bank of England.
Investors usually have some idea of the income stream they might expect from an investment. We can determine the rate of return (r) by solving the following formula:
Rate of Return Calculation
where P equals the price of the investment good, r equals the annual rate of return, and all other variables are as defined earlier. Since we know price (P) and expected income in each time period (Yt), the only unknown is r, the rate of return. For example, if an asset selling for $100 today will pay $110 a year from today, the rate of return is 10 percent. A $112 payment in a year yields a rate of return of 12 percent. Thus, the larger the expected income in each time period, the greater the rate of return for a given price.
How are present values and rates of return related to each other and to the capitalization process? If the present value is at least as great as the price (PV P), then the expected rate of return is at least as great as the interest rate ( r i); you will invest because the asset appears profitable. You will not invest if an asset's price exceeds your estimate of present value because the expected rate of return will be less than the market rate of interest.
Generally, we know the price (P), the going interest rate (i), and the income expected each year (Yt) when we evaluate an investment.
When this equation holds, an investment is a break-even proposition. For example, if an investor could expect $224 one year hence, and the interest rate were 12 percent, a $200 price makes an investment a break-even proposition. However, your assessment of the present value of an asset may be either higher or lower than the going price. Similarly, you may estimate the rate of return as either above or below the market interest rate.
Present value calculations solve for the current worth of an income stream by discounting expected future income with the market interest rate, both of which we know. Rate of return analysis also assumes we know how much income to expect in the future and when it will be received, but solves for an unknown implicit interest rate (r) by using the known current price to arrive at a solution.
Parallels in calculations of present values and rates of return may make it seem that maximizing one is equivalent to maximizing the other. Unfortunately, this perception can be misleading and result in misplaced investment priorities. Consider two one-time financial investments. Suppose that you have exactly $1,000 available. Your first option is a coupon for $10 guaranteed to quadruple to $40 in one day---a 300 percent return that is almost immediate. Unfortunately, buying the $10 coupon will prevent you from exercising your second risk-free option---your $1,000 will double in a day, yielding only a 100 percent return. Despite the fact that you must forgo the investment with the higher rate of return, doubling the $1,000 investment is clearly preferable to quadrupling a $10 investment over the same period.
Which of the following is more valuable as an investment? (a) A $5,000 investment in a Christmas tree lot will double your funds by generating a rate of return of 100 percent, but only for one month. (b) A $1 billion investment in a vitamin pill plant will generate a 1 percent net return per month forever. Even though the annualized return from the tree lot greatly exceeds 1,200 percent (because of compounding), the investment in the pill factory is much more valuable. The key to sound investment is, "When in doubt, maximize present values---not rates of return."
Competition for profits is vigorous. If you are astute, several other astute investors will probably assess any given investment much as you do. If present value appears to substantially exceed price, bidding wars will rapidly drive the price toward present value. Even if you do manage to pick up what you view as a bargain, you certainly would not then sell it for less than its present value to you.
Thus, the equilibrium price of any asset is its present value. Moreover, competition causes the rate of return expected from any asset, after adjusting for risk, to equal the market rate of interest. The process that discounts expected future income by the interest rate to arrive at present value and price is capitalization.
How might you use your knowledge of the capitalization process? Assume you own 1,000 shares of a wildcat oil company earning $1 per share per year. If market conditions required a 10 percent rate of return, shares of stock would sell for $10. What if the firm hit a gusher expected to triple its annual earnings? Stock shares would soar to roughly $30 after the gusher was announced. What rate of return could people expect who bought stock after this discovery? Roughly 10 percent, just as before. Similar capitalizations determine the prices of all sorts of resources and financial investments. We suggested earlier that predictable income streams are quickly capitalized.
One possible road to riches entails finding assets for which the current owners have underestimated future earning power. You can then purchase these assets relatively cheaply. When the true earning capacity of the assets becomes known, you can become rich by selling the assets for considerably more. One roadblock that makes this a difficult avenue to wealth, however, is vigorous competition from many other bright bargain hunters.
At times, attempts to discover bargains lead people who acquire insider information about financial securities to break the law. Profit is likely for anyone who acts on information about events that will affect the values of assets in predictable ways---but only if they act before that information is widely publicized.