11. Asset Markets - Solutions

11. Asset Markets - Solutions - Chapter 11 NAME Asset...

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Unformatted text preview: Chapter 11 NAME Asset Markets Introduction. The fundamental equilibrium condition for asset markets is that in equilibrium the rate of return on all assets must be the same. Thus if you know the rate of interest and the cash ﬂow generated by an asset, you can predict what its market equilibrium price will be. This condition has many interesting implications for the pricing of durable assets. Here you will explore several of these implications. Example: A drug manufacturing firm owns the patent for a new medicine. The patent will expire on January 1, 1996, at which time anyone can pro- duce the drug. Whoever owns the patent will make a profit of \$1,000,000 per year until the patent expires. For simplicity, let us suppose that prof- its for any year are all collected on December 31. The interest rate is 5%. Let us figure out what the selling price of the patent rights will be on January 1, 1993. On January 1, 1993, potential buyers realize that owning the patent will give them \$1,000,000 every year starting 1 year from now and continuing for 3 years. The present value of this cash ﬂow is \$ 1 , 000 , 000 (1 . 05) + 1 , 000 , 000 (1 . 05) 2 + 1 , 000 , 000 (1 . 05) 3 ∼ \$2 , 723 , 248 . Nobody would pay more than this amount for the patent since if you put \$2,723,248 at 5% interest, you could collect \$1,000,000 a year from the bank for 3 years, starting 1 year from now. The patent wouldn’t sell for less than \$2,723,248, since if it sold for less, one would get a higher rate of return by investing in this patent than one could get from investing in anything else. What will the price of the patent be on January 1, 1994? At that time, the patent is equivalent to a cash ﬂow of \$1,000,000 in 1 year and another \$1,000,000 in 2 years. The present value of this ﬂow, viewed from the standpoint of January 1, 1994, will be \$ 1 , 000 , 000 (1 . 05) + 1 , 000 , 000 (1 . 05) 2 ∼ \$1 , 859 , 310 . A slightly more diﬃcult problem is one where the cash ﬂow from an asset depends on how the asset is used. To find the price of such an asset, one must ask what will be the present value of the cash ﬂow that the asset yields if it is managed in such a way as to maximize its present value. Example: People will be willing to pay \$15 a bottle to drink a certain wine this year. Next year they would be willing to pay \$25, and the year after that they would be willing to pay \$26. After that, it starts to deteriorate and the amount people are willing to pay to drink it falls. The interest rate is 5%. We can determine not only what the wine will sell for but also when it will be drunk. If the wine is drunk in the first year, it would have to sell for \$15. But no rational investor is going to sell the wine for 148 ASSET MARKETS (Ch. 11) \$15 in the first year, because it will sell for \$25 one year later. This is a 66 . 66% rate of return, which is better than the rate of interest. When the interest rate is 5%, investors are willing to pay at least \$25 / 1 . 05 = \$23...
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This note was uploaded on 07/16/2010 for the course ECON 21 taught by Professor Johng.sessions during the Summer '09 term at Dartmouth.

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11. Asset Markets - Solutions - Chapter 11 NAME Asset...

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