T here are a number of factors that affect a stock’s price and its value to

T here are a number of factors that affect a stock’s price and its value to

investors. The financial manager regularly has to figure out whether a particular investment is good or bad. A good investment will enhance shareholder wealth. A bad one won’t. To decide whether an investment is good or bad, the manager must determine whether the benefits from the investment—often expected in future periods—will outweigh its costs.

To make the best investment decisions, the financial manager must also consider the way the investment is financed. If the firm takes on more debt, is this harmful to shareholders? If the firm issues more shares of equity, how does this affect the value of equity? Furthermore, recog- nizing that the value of equity is the difference between the value of the firm’s assets and its debt obligations, we must be aware of how debt securities are valued as well.

Valuation compares the benefits of a future investment decision with its cost. Another way of evaluating an investment is to answer the ques- tion: Given its cost and its expected future benefits, what return will a particular investment provide? In this chapter we focus on the principles of valuation and how to calculate the return on investments. In the next chapter we focus on the valuation of stocks and bonds.

PRINCIPLES OF ASSET VALUATION Suppose you are offered the following investment opportunity by a

company: Lend the company $90 today, and you will be paid $100 one

THE FUNDAMENTALS OF VALUATION

year from today by the company. Whether or not this is a good invest- ment depends on:

■ what you could have done with your $90 instead of investing it with the company, and ■ how certain you are that the company will pay the $100 in one year.

If your other opportunities with the same amount of uncertainty pro- vide a return of 10%, is this loan a good investment? There are two ways to evaluate this.

First, you can figure out what you could have wound up with after one year, investing your $90 at 10%:

Value at the end of one year = $90 + 10% of $90 = $90 1 ( + 0.10 ) = $99

Since the $100 promised is more than $99, you are better off with the investment offered by the company.

Another way of looking at this is to figure out what the $100 prom- ised in the future is worth today. To calculate its present value, we must discount the $100 at some rate. The rate we’ll use is the opportunity cost of funds, which in this case is 10%:

Value today of $100 in one year = ----------------------------- = $90.91

( 1 1 + 0.10 ) This means that you consider $90.91 today to be worth the same as

$100 in one year. In other words, if you invested $90.91 today in an investment that yields 10%, you end up with $100 in one year. Since today’s value of the receipt of $100 in the future is $90.91 and it only costs $90 to get into this deal, the investment is attractive: it costs less than what you have determined it is worth.

Since there are two ways to look at this—through its future value or through its present value—which way should you go? While both approaches get you to the same decision, the approach in terms of the present value of the investment is usually easier.

Let’s look at another example. Suppose you have an opportunity to buy an asset expected to give you $500 in one year and $600 in two years. If your other investment opportunities with the same amount of risk give you a return of 5% a year, how much are you willing to pay today to get these two future receipts?

Principles of Asset Valuation and Investment Returns

We can figure this out by discounting the $500 in year 1 at 5% and $600 in year 2 at 5%:

$600 Present value of an investment =

This investment is worth $1,020.41 today, so you will be willing to pay $1,020.41 or less for this investment:

■ if you pay more than $1,020.41, you get a return of less than 5%; ■ if you pay less than $1,020.41 you get a return of more than 5%; and,

■ if you pay $1,020.41 you get a return of 5%. Suppose you are evaluating an investment that promises $10 every

year forever. The value of this investment is the present value of the stream of $10 to be received each year to infinity where each $10 is dis- counted at the appropriate number of years at some annual rate i:

Present value of an investment = ------------------ $10 + ------------------ $10 + ------------------ $10 + + ------------------- $10 …

1 + i 1 ) ( 1 + i ( 2 ) ( 1 + i 3 i ) ∞ ( 1 + ) which we can write in shorthand notation using summation notation as:

1 Present value of an investment =

∑ -----------------

----------------- = $10

t = 1 ( 1 + i ) Or, since the last term is equal to 1/ i, we can rewrite the present value of

this perpetual stream as:

Present value of investment = $10 (1/ i) = $10/i

If the discount rate to translate this future stream into a present value is 10%, the value of the investment is $100:

Present value of investment = $10 (1/0.10) = $10/0.10 = $100 The 10% is the discount rate, also referred to as the capitalization rate,

for the future cash flows comprising this stream. Let’s look at this

THE FUNDAMENTALS OF VALUATION

investment from another angle: If you consider the investment to be worth $100 today, you are capitalizing—translating future flows into a present value—the future cash flows at 10% per year.

As you see from these examples, the value of an investment depends on:

1. the amount and timing of the future cash flows, and

2. the discount rate used to translate these future cash flows into a value today.

This discount rate represents how much an investor is willing to pay today for the right to receive a future cash flow. Or, to put it another way, the discount rate is the rate of return the investor requires on an investment, given the price he or she is willing to pay for its expected future cash flow.

We can generalize this relationship a bit more. Let CF t represent the cash flow from the investment in period t, so that CF 1 is the cash flow at the end of period 1, CF 2 is the cash flow at the end of period 2, and so on, until the last cash flow at the end of period N, CF N . If the invest- ment produces cash flows for N periods and the discount rate is i, the value of the investment—the present value—is:

Present value of an investment

= ------------------ + ------------------ 3 ------------------ CF + 2 + … + -------------------- N

CF 1 CF CF

1 2 3 ( N 1 + i ) ( 1 + i ) ( 1 + i ) ( 1 + i ) which we can write more compactly as:

CF Present value of an investment =

----------------- ∑ t

1 ( 1 + i ) In the special case where the cash flows are all equal, we can sim-

plify this by letting CF represent each cash flow and use CF in place of CF 1 , CF 2 , and so on. The valuation relation becomes:

CF 1 Present value of an investment =

----------------- = CF ∑ -----------------

( t 1 + i ) t = 1 ( 1 + i ) which we can write in terms of the annuity factor,

Principles of Asset Valuation and Investment Returns

Present value of an investment = CF Present value annuity factor ( )

If the cash flow stream is level and is promised each period forever, N is infinite. As the number of future periods approaches infinity, the present value annuity factor approaches 1/ i. Therefore, the present value of a perpetual stream of cash flows is equal to: