Stock and Bond Valuation

Stocks and bonds are "securities"; in other words, they are tradable in markets and, as such, their values are a function of market conditions.

Bonds are long term debt instruments, the principal of which must be repaid at the end of the term. They are generally issued with fixed interest rates, called a coupon, payable semi-annually. The coupon represents the rental on the money borrowed by the corporation, usually $1000 per bond, also called its par value. The fixed interest coupon paid on the bond represents the market conditions that exist at the time the bond is issued and remain unchanged for the life of the bond. That rate is, essentially, what that company had to pay, at that time, to borrow $1000 from the market.

Over time the market changes and interest rates rise and fall. These are called "systematic changes" in the cost of money. Also changes can take place in the creditworthiness of the company which borrowed funds. This type of change is called "company specific". Since market and company conditions change there will be changes in the value of such a bond. If interest rates go lower there will be an increase in the value of all such fixed securities because while the coupon and the future par value will not change, the present value of such funds discounted by the lower rate will be higher.

Lets look at an example using an annual coupon for simplicity: the right to receive a coupon of $100 per year for the next fifteen years and the right to receive the $1000 par value at the end of that time, assuming the current appropriate rate of interest is 10% is, thus:

$100 x 7.60 (present value annuity) =$760 plus the right to receive at the end of the period a single payment of $1000 x .23939 (present value single amount)=$239.39, for a total of $1000 (more or less).

But if the interest rate in the economy changes to 9%, those same promises contained within that same bond, will have a value computed as follows:

$100 x 8.33(9%) =$833 plus $1000 x.27454(9%)=$274.54 for a total of $1107.

Thus the bond's overall value increased because interest rates went lower.

On the other hand, the elements of stock value, representing ownership in the company, are variable. That is, there are no fixed promises and dividends may or may not be paid depending on profits. Under such circumstances the value of stock is based on assumptions about the future prospects for earnings. Earnings can be utilized in two ways: They can be returned to the stockholder in the form of dividends or retained in the company for new investment, or both.

While several mathematical models are available for valuing stock, we tend to look at the most commonly used growth model, the Constant Growth Dividend Valuation model, otherwise known as the "Gordon model" after its discoverer.

The formula for this view of the value of common stock is:

P =d/k-g

The value of common stock (P) is a function of the dividend to be received by the owner (d) divided by the risk of owning such stock (k), minus the percentage of growth of those dividends (g). For example a stock paying a dividend of $2 and growing at 5% should sell for $20 if the investor needs to receive 15% on their investment to be appropriately compensated for the risk of owning it:

$2/.15-.05= $20

If the company did not pay dividends and all the money was retained for further investment by the company, the formula would be earnings per share divided by risk, minus growth.

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