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Principle 7: Time and the Value of Money Are Closely Related
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A basic idea underlying finance theory is that a dollar today is worth more than a dollar tomorrow. We invest today s dollars to purchase the greater cash flows of tomorrow. In fact, any financial or investment decision involves spending money today and receiving cash payments in the future. To assess whether an investment is a diamond or a dog, you must be able to compare the value of money that you invest today with the value of the money that you expect to receive in the future. To make this comparison effectively, you must understand the simple math that underlies the time value of money compounding and discounting. When we value a company, we first estimate the future profits that we expect the company to earn. The projection of profits involves multiplying earnings by a series of inputs that estimate growth over a period of time a process that s known as compounding. Once we estimate future profits, we use another math concept to bring those future dollars back to today s values a process known as discounting.
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Compounding and Future Value
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A key to the pricing of any investment is to understand the concepts of discounting and compounding. Compounding is the process of going from today s value, or present value (PV ), to some expected but unknown future value (FV ). Compounding also means to multiply by a number greater than 1.0, over a number of time periods. You ll soon see what we mean by this statement. Future value is the amount of money that an investment will grow to at some future date by earning interest at a certain rate. Let s look at an example to see how compounding and future value works.
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The 10 Principles of Finance and How to Use Them
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TABLE 2-5 GHI Steady Growth Company Compounding and Future Value Schedule
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Beginning Stock Value $10.00 $10.80 $11.66 $12.60 $13.60 Growth in Value $0.80 $0.86 $0.93 $1.01 $1.09 $4.69 Ending Stock Value $10.80 $11.66 $12.60 $13.60 $14.69
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Year 1 2 3 4 5 Total Growth in Value
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Suppose that Jane buys stock for $10 per share in GHI Steady Growth Company (which pays no dividend), and the shares increase in value (exactly and miraculously) at the rate of 8 percent per year. If Jane holds the stock for five years, what is the ending value of a share Table 2-5 shows how the stock price of GHI will grow over time, compounding by 8 percent per year over the five-year period. The future value of the GHI compounded at a rate of 8 percent is $14.69. In this example, when we compound we multiply the beginning stock value of $10 by 1.08 over five periods: $10 * (1.08) * (1.08) * (1.08) * (1.08) * (1.08) $14.69
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When we compound, if r is the compounding rate (also called a growth rate, interest rate or yield ), n is the number of years, PV is the present value of a single payment investment, then the future value (FV ) of the investment is: FV PV (1.0 r)^n
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In math terms, this says that when you compound the number PV at a rate r for n periods, the future value is equal to the present value times (1.0 plus the compounding rate), raised to the nth power. Jane s GHI Steady Growth Stock example looks like this: $14.69 $10 * (1.0 .08)^5
STREETSMART GUIDE TO VALUING A STOCK
Discounting and Present Value
The math underlying discounting and the calculation of present value is the exact flip side to compounding and future value. Discounting is the process of going from an expected future value to a present value. Discounting also means to multiply by a number less than 1.0, over a number of time periods. Present value is what an investment is worth today, if an expected future value is discounted at a certain rate and for a period of time. Let s look at an example to see how discounting and present value works. Today s your birthday, and Uncle Larry promises you a present $100 to be given to you at some time in the next five years. What is the present value of Uncle Larry s $100 promise This is a tough one. Uncle Larry is usually reliable, but he s a tad overweight and is not in great health. There s a slight chance that he may die before he pays off, so risk is involved. You re also not sure exactly when that $100 is going to flow to you. With the uncertainty of both risk and timing, this sounds like a problem for a present value table. In Table 2-6 we lay out the possibilities, with the number of years, n, ranging from 0 to 5, and the discounting rates ranging from 6 percent to 8 percent to 10 percent. The numbers listed in Table 2-6 are known as discount factors. These factors give the present value of a dollar that you expect to receive at some time, n, in the future, discounted at a rate, r. As you can see in Table 2-6, as n increases and the payment is expected further into the future, the present value factor decreases meaning that the
TABLE 2-6
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