In this chapter, we used general present value formulas from the previous chapter to price bonds and stock.
Pure discount bonds and perpetuities can be viewed as the polar cases of bonds. The value of a pure discount bond (also called a zero coupon bond, or simply a zero) is:
Level payment bonds can be viewed as an intermediate case. The coupon payments form an annuity, and the principal repayment is a lump sum. The value of this type of bond is simply the sum of the values of its two parts.
The yield to maturity on a bond is the single rate that discounts the payments on the bond to its purchase price.
A stock can be valued by discounting its dividends. We mentioned three types of situations:
The case of zero growth of dividends.
The case of constant growth of dividends.
The case of differential growth.
An estimate of the growth rate of a stock is needed for the formulas for situations 4(b) or 4(c). A useful estimate of the growth rate is
g = Retention ratio x Return on retained earnings
It is worthwhile to view a share of stock as the sum of its worth if the company behaves like a cash cow (the company does no investing) and the value per share of its growth opportunities. We write the value of a share as:
We showed that, in theory, share price must be the same whether the dividend growth model or the formula here is used.
From accounting, we know that earnings are divided into two parts: dividends and retained earnings. Most firms continually retain earnings to create future dividends. One should not discount earnings to obtain price per share because part of earnings must be reinvested. Only dividends reach the stockholders, and only they should be discounted to obtain share price.
We suggested that a firm's price-earnings ratio is a function of three factors:
The per-share amount of the firm's valuable growth opportunities.
