# Assets, Price and Interest Rate Structure.

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Asset, Price and Interest rate structure.

An asset is any item of economic value owned by an individual or corporation, especially that which could be converted to cash. Examples are: cash, securities, account receivable, inventory among others.

An asset produces a flow of income. This flow might be a series of fixed payments (in case of bonds) or a share of a company's profits (in the case of stock). According to the classical theory, the price of an asset equals the present value of the income that people expect to receive:

Asset price = present value of expected asset income.

In many cases, nobody knows exactly how much income an asset will produce. For example, nobody is certain of a company's future profits, which determine the income from stock. Given this uncertainty, the classical theory says that asset price depend on people's expectations, or best guesses, of asset income.

The rational for the classical theory is simple. People purchase asset because it yields a stream of income. The present value tells us how much this income is worth, so people are willing to pay that much for the asset.

Suppose an asset's price were below the present value of income. Say the present value is N100 and the asset price is N80. This situation wouldn't last long. At a price of N80, the asset is a great deal: buyers pay less than the worth of the assets. Lots of savers will purchase the asset, and high demand will push up the price. This continues until the price rises to N100.

Conversely, if an asset price exceeds the present value of income, then sellers receive more than the asset is worth. In this situation, the asset's owners will rush to sell, pushing down the price.

The classical theory applies to many types of assets. For example, it says that the price of an apartment building equals the present value of net rental income from the building. Let's look more closely at the theory's implication for two classes of assets, bonds and stocks.

Bond price: The income from a bond includes the periodic coupon payment and the face value received at maturity. Let's say a bond has a maturity of T years, a face value of F, and an annual coupon payment of C. assuming no chance of default, bondholders expect to receive all the promised payments. The payments are C in years 1 through T-1 and C+F in years T. the bond price is the present value of these payments.

Bond price = C + C +...+ (C + F)------------------------------1

(1+i) (1+i)2 (1+i)T

For example, suppose a bond's maturity is 3 years, so T=3. Annual coupon payments are N5 and the face value is N100. Assume the interest rate is 4 percent. In this case, equation (1) tell us

Bond price = N5 + N5 + N105

1.04 (1.04)2 (1.04)3

N102.78

Stock prices: According to the classical theory, there are two ways to determine stock prices. The first is based on the fact that stockholders own firms, so firms' earnings belong to them. If a company issues 1 million shares of stock, then each share entitles the holder to one-millionth of the company's earning. The price of a share is the present value of these earnings. If expected earnings per share are E1 in the next year, E2 in the year after that, and so on, the

Stock price = E1 +E2 + E3 +....................

(1+i) (1+i)2 (1+i)3

Alternatively, we can look at the income that flows directly to stockholders. Firms periodically make payments to stockholders called dividends. A company with 1 million shares might announce a dividend of N2 per share, paying a total of N2million. A stock's price is the present value of expected dividends. If expected dividends per share are D1 in the next year, D2 in the year after that, and so on, then

Stock price = D1 + D2 + D3 +..........

(1+i) (1+i)2 (1+i)3

WHAT IS EXPECTATIONS?

An asset price depends on the present value of expected asset income. What determines what people expect? The classical theory assumes that people's expectations are the best possible forecasts of asset income based on all public information. This assumption is called rational expectations

The price of the company's stock depends on its expected earnings. Rational expectations of earnings are based on all public information about the company. For example if a company announces a new product, expected earnings rise to reflect the product's likely impact. If the economy enters a recession, expected earnings adjust based on how the firm will be affected. Expected earnings also account for the costs of producing the firm's product, the number of competitors the firms' faces, and all other relevant factors.

VALUING INCOME STREAMS

A financial asset yields stream of income in the future. The owner of a bond receives a payment when the bond matures and may receive coupon payments before then. The owner of a firm's stock receives part of the firm's future earnings. To find the value of an asset, we must determine the value of these income streams.

In doing this the key principle is that payments have different values depending on when they are received. A naira today is worth more than a naira in the future. The reason is that you can take today's naira, put it in the bank, and receive interest. This transforms N1 today into more than one naira in the future.

Future Value

To compare payments at different times, economists begin with the concept of future value. The future value of a naira is how many naira it can produce in some future year. To understand this concept, suppose that banks pay an interest rate of 4 percent. If you deposit a naira today, it grows to N1.04 in a year. Thus the future value of a naira today is N10.4 in 1 year.

If you keep your money in the bank for a second year, it grows by another 4 percent. When N1.04 grows by 4 percent, it becomes N (10.4)(1.04), of N (10.4)2. so a naira today is worth N (10.4)2 in 2 years. If you can keep the money in the bank for a third year, it grows by 4 percent again, becoming N (10.4)3.

With a 4 percent interest rate, a naira left in the bank for n years, where n is any number, grows

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