Valuation of securities

Value

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

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

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)

Bonds

A bond is a tradable 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.

Calculation of value of Bond

There are two types of cash flows that are provided by a bond investment:

• 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 Rs.1,000) at maturity

The following timeline illustrates a typical bond’s cash flows:

• 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

Bond Terminology

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.

• 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

Stock

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.

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:
  • Dividend payments
  • The future selling price
• Again, finding the present values of these cash flows and adding them together will give us the value

• 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.
• 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:
• Assume:
  • 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