# note_ch27 - Chapter 27 Finance This chapter teaches the...

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Chapter 27 – Finance This chapter teaches the basics of finance. Much of this has to deal with evaluating different types of investments and understanding the risks of investments and the return to bearing those risks. For example, why are stocks – claims to a corporation’s profits – on average so much more profitable to hold than government bonds? Is now a good time to buy stocks? Or is it a good time to sell stocks? To address these questions, let’s first understand the concept of present value. Present value allows us to determine how much payments that occur in the future are worth today. For example, you are watching late night t.v., and you see one of those commercials in which someone has won the publisher’s clearinghouse sweepstakes. Meaning they have won a million dollars. Then, in the fine print at the bottom of the commercial, it says “\$25,000 paid per year over the next 40 years”.

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But we know that \$25,000 paid 40 years from now is worth less than \$25,000 paid today – because money available today can earn interest and thus grows to a higher amount in the future. Present value allows us to value payments that occur in the future. To do this, first note that we will call the interest rate we use in the calculations as “r”, and for simplicity this is constant over time. Thus, if \$100 is invested today, it will be worth (1+r)*\$100 a year from now, (1+r) 2 *\$100 two years from now, (1+r) 3 *\$100 three years from now, and so forth. Now, let’s use that same logic to construct present value. Since \$100 today is worth \$100*(1+r) a year from now, it follows that the present value – today’s value – of \$100 one year from now is: \$100/(1+r). This is because if \$100/(1+r) is invested today, it will be worth \$100 in one year: (1+r)*{\$100/(1+r)} = \$100 By the same logic, the present value of \$100 paid two years from now is \$100/(1+r) 2 , and so forth.
The fact that interest rates are positive means that payments in the future are always worth less than their face value – that is, they are discounted. The rate of discounting is higher as the interest rate, r, becomes higher. Thus, to figure out the present value of \$25,000 paid each year over the next 40 years, we would calculate it as \$25000/(1+r) + \$25000/(1+r) 2 + ….\$25000/(1+r) 40 . If the interest rate is 10%, note that the final payment of \$25,000 40 years from now is only worth about \$550 valued today! This is another way of saying that at high interest rates, principal grows quickly. For example, legend has it that the island of Manhattan was sold for \$24 about 300 years ago. At an interest rate of 8 percent, \$24 over 300 years would have grown to over 250 billion dollars. An important choice in this formula is the interest rate. The interest rate that we use in present value

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formulas will be composed of two pieces – one component is called the real interest rate and the second piece is called the expected inflation component. Thus, we have: r = infl + real rate The expected inflation component of the interest rate compensates the investor for inflation that reduces the purchasing power of dollars. That is, if
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• Spring '07
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