In general, the value of an asset is the price that a willing and able buyer pays to a willing and able seller
Note that if either the buyer or seller is not both willing and able, then an offer does not establish the value of the asset
Several Kinds of “Value”
There are several types of value, of which we are concerned with three:
Book Value - The asset’s historical cost less its accumulated depreciation
Market Value - The price of an asset as determined in a competitive marketplace
Intrinsic Value - The present value of the expected future cash flows discounted at the decision maker’s required rate of return
Determinants of Intrinsic Value
There are two primary determinants of the intrinsic value of an asset to an individual:
The size and timing of the expected future cash flows
The individual’s required rate of return (this is determined by a number of other factors such as risk/return preferences, returns on competing investments, expected inflation, etc.)
Note that the intrinsic value of an asset can be, and often is, different for each individual (that’s what makes markets work)
A bond is a tradeable instrument that represents a debt owed to the owner by the issuer. Most commonly, bonds pay interest periodically (usually semiannually) and then return the principal at maturity.
Most corporate, and some government, bonds are callable. That means that at the company’s option, it may force the bondholders to sell them back to the company. Ordinarily, there are restrictions on the timing of the call and the amount that must be paid.
Calculating the Value of a Bond
There are two types of cash flows that are provided by a bond investments:
Periodic interest payments (usually every six months, but any frequency is possible)
Repayment of the face value (also called the principal amount, which is usually $1,000) at maturity
The following timeline illustrates a typical bond’s cash flows:
0 1 2 3 4 5 100 100 100 100 100 1,000
Calculating the Value of a Bond (cont.)
We can use the principle of value additivity to find the value of this stream of cash flows
Note that the interest payments are an annuity, and that the face value is a lump sum
Therefore, the value of the bond is simply the present value of the annuity-type cash flow and the lump sum:
There are several terms with which you must be familiar to solve bond valuation problems:
Coupon Rate - This is the stated rate of interest on the bond. It is fixed for the life of the bond. Also, this rate time the face value determines the annual interest payment amount.
Face Value - This is the principal amount (nominally, the amount that was borrowed). This is the amount that will be repaid at maturity
Maturity Date - This is the date after which the bond no longer exists. It is also the date on which the loan is repaid and the last interest payment is made.
Bond Valuation: An Example
Assume that you are interested in purchasing a bond with 5 years to maturity and a 10% coupon rate. If your required return is 12%, what is the highest price that you would be willing to pay?
0 1 2 3 4 5 100 100 100 100 100 1,000
Some Notes About Bond Valuation
The value of a bond depends on several factors such as time to maturity, coupon rate, and required return
We can note several facts about the relationship between bond prices and these variables ( ceteris paribus ):
Higher required returns lead to lower bond prices, and vice-versa
Higher coupon rates lead to higher bond prices, and vice versa
Longer terms to maturity lead to lower bond prices, and vice-versa
A share of common stock represents an ownership position in the firm. Typically, the owners are entitled to vote on important matters regarding the firm, to vote on the membership of the board of directors, and (often) to receive dividends.
In the event of liquidation of the firm, the common shareholders will receive a pro-rata share of the assets remaining after the creditors and preferred stockholders have been paid off.
Common Stock Valuation
Just like with bonds, the first step in valuing common stocks is to determine the cash flows
For a stock, there are two:
The future selling price
Again, finding the present values of these cash flows and adding them together will give us the value
Common Stock Valuation: An Example
Assume that you are considering the purchase of a stock which will pay dividends of $2 next year, and $2.16 the following year. After receiving the second dividend, you plan on selling the stock for $33.33. What is the intrinsic value of this stock if your required return is 15%?
2.00 2.16 33.33 ?
Some Notes About Common Stock
In valuing the common stock, we have made two assumptions:
We know the dividends that will be paid in the future
We know how much you will be able to sell the stock for in the future
Both of these assumptions are unrealistic, especially knowledge of the future selling price
Furthermore, suppose that you intend on holding on to the stock for twenty years, the calculations would be very tedious!
Common Stock: Some Assumptions
We cannot value common stock without making some simplifying assumptions
If we make the following assumptions, we can derive a simple model for common stock valuation:
Your holding period is infinite (i.e., you will never sell the stock)
The dividends will grow at a constant rate forever
Note that the second assumption allows us to predict every future dividend, as long as we know the most recent dividend
The Dividend Discount Model (DDM)
With these assumptions, we can derive a model which is known as the Dividend Discount Model, or the Gordon Model
This model gives us the present value of an infinite stream of dividends that are growing at a constant rate:
The DDM: An Example
Recall our previous example in which the dividends were growing at 8% per year, and your required return was 15%
The value of the stock must be:
Note that this is exactly the same value that we got earlier
The DDM Extended
There is no reason that we can’t use the DDM at any point in time
For example, we might want to calculate the price that a stock should sell for in two years
To do this, we can simply generalize the DDM:
The DDM Example (cont.)
In the earlier example, how did we know that the stock would be selling for $33.33 in two years?
Note that the period 3 dividend must be 8% larger than the period 2 dividend, so:
Po = EPS1 (1-b)
Where EPS1 = EPS at the end of year 1
b= Retention ratio
r= Rate of return on re-investments, i.e., ROI
Ke= Required rate of return of the equity invetsors
P = D + r/Ke (E-D)
Where P = Market Price of the share
D = Dividend Per Share
r = Rate of Return on investment by the firm
ke = Equity capitalisation rate of investors
D = Dividend Per Share
E = Earnings Per Share
Earnings Multiplier Approach
Price Earnings Ratio (P/E ratio)
Value = EPS * P/E Ratio
Accounting Profits is used for EPS calculation
Other Valuation Models
Price to Book Value Ratio
Price to Sales Ratio
Preferred stock represents an ownership claim on the firm that is superior to common stock in the event of liquidation. Typically, preferred stock pays a fixed dividend periodically and the preferred stockholders are usually not entitled to vote as are the common shareholders.
Preferred Stock Valuation
Preferred stock is very much like common stock, except that the dividends are constant (i.e., the growth rate is 0%)
Therefore, we can use the DDM with a 0% growth rate to find the value:
Preferred Stock: An Example
Suppose that you are interested in purchasing shares of a preferred stock which pays a $5 dividend every year. If your required return is 7%, what is the intrinsic value of this stock?