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Chapter 13
CHAPTER 13
CAPITAL AND financial markets
ANSWERS TO EVEN-NUMBERED ONLINE Review Questions
2.If you receive $100 now, you can put it in the bank and earn interest; after one year you will have (1 + r)$100, where r is the interest rate. This amount exceeds the alternative of $100 received one year from now. That is, (1 + r) $100 > $100.
4.There is a positive (direct) relationship between the present value of a future payment and the size of that payment, and an inverse relationship between the present value of a future payment and the interest rate. The further in the future a payment will be received, the smaller is the present value of that future payment.
6.a. There is an inverse relationship between a bond’s price and its yield.
b.There is an inverse relationship between a bond’s price and the riskiness of the firm that issued it.
c.There is a positive relationship between a bond’s price and its face value.
8.The efficient markets view is that stock prices reflect all information available in the market, and therefore each stock’s price reflects the best estimate of the present value of future receipts expected by shareholders. This implies that there are no exploitable patterns in stock prices, so no one can beat the stock market on a consistent basis.
EVEN-NUMBERED PROBLEM SET
2. a.Yes, you should approve the purchase of the inventory control software, because the total present value of salary savings = $60,000/(1.07) + $60,000/(1.07)2 + $60,000/(1.07)3 + $60,000/(1.07)4 = $203,232.68, which exceeds the $200,000 purchase price.
b. The answer would change. You should not approve the purchase of the inventory control software if the annual relevant discount rate is 9%, because the total present value of salary savings would only be $194,383.19 (= $60,000/(1.09) + $60,000/(1.09)2 + $60,000/(1.09)3 + $60,000/(1.09)), which is less than the $200,000 purchase price.
c.The answer would change. You should not approve the purchase because the total present value of salary savings, $203,232.68, is less than the $220,000 purchase price.
- Compared to the answer in part (a), the answer would not change. You should approve the purchase of the software, because the total present value of salary savings = $60,000/(1.07) + $60,000/(1.07)2 + $60,000/(1.07)3 + $60,000/(1.07)4 + $60,000/(1.07)5 + $60,000/(1.07)6 = $285,992.38, which exceeds the $220,000 purchase price.
4.a.Your firm should purchase 2 computers, since the present value of each of the first two computers is greater than their purchase price of $2600.
The present value of the first computer
= $3000/(1.1)1 + $3000/(1.1)2 + $3000/(1.1)3 = $7460.55
The present value of the second computer
= $2000/(1.1)1 + $2000/(1.1)2 + $2000/(1.1)3 = $4973.70
The present value of the third computer
= $1000/(1.1)1 + $1000/(1.1)2 + $1000/(1.1)3 = $2486.85
The present value of the fourth computer
= $500/(1.1)1 + $500/(1.1)2 + $500/(1.1)3 = $1243.43
b.Your firm should purchase 3 computers, since the present value of the first three computers is greater than their purchase price of $2600.
The present value of the first computer
= $3000/(1.05)1 + $3000/(1.05)2 + $3000/(1.05)3 = $8169.79
The present value of the second computer
= $2000/(1.05)1 + $2000/(1.05)2 + $2000/(1.05)3 = $5446.50
The present value of the third computer
= $1000/(1.05)1 + $1000/(1.05)2 + $1000/(1.05)3 = $2723.25
The present value of the fourth computer
= $500/(1.05)1 + $500/(1.05)2 + $500/(1.05)3 = $1361.62
6.The total value of your gold mine is $40,000 = (5 × $400)/0.05 = $2000/0.05.
8.a. If the discount rate is 5%, this bond will sell for $100,000.
- If the discount rate is 10%, this bond will sell for $87,565.74.
10.If the discount rate is 10%, people will pay $100 per share ($100 = $10/0.10). If, in the face of uncertainty, a discount rate of 15% is applied, people will pay $66.67 per share ($66.67 = $10/0.15).
12. a If the interest rate on government bonds rises, it is likely that all interest rates will rise. If so, the discount rate used in calculating the PV of Amazon.com stock will rise, thereby decreasing that PV. At any price, the quantity of Amazon stock demanded will decrease – the demand curve will shift to the left. The result would be a drop in the price per share.
b. An expectation that the government bond rate will rise should have the same effect as in part (a) – a lower price of Amazon shares.
c. New entry into Amazon’s market can be expected to lower Amazon’s profit. As a result, the PV of Amazon’s future net revenue stream will fall, lowering the demand for Amazon shares and reducing the price per share.
d. If people believe that housing prices will soon drop, housing will be a less attractive investment for them. As a result, they will seek alternatives – including Amazon stock. The demand curve for Amazon shares will shift rightward and the price of those shares will rise.
14. a. This would decrease the attractiveness of college. The costs would be the same, but there would be fewer years of earnings and so the PV of future earnings would be smaller.
b. This would increase the attractiveness of college by increasing the size of the annual differential between earnings of college and high school graduates. The differential would be larger in every future year and so the PV of the stream of differentials would be larger as well.
c. A higher interest rate translates into a higher discount rate, making future earnings less valuable today. The PV of costs would change too, but the impact on the PV of future earnings would be larger, because that stream extends much farther into the future. Therefore permanently higher interest rates would make college less attractive.
16. In this case, the PV of costs would be $38,640 + $40,411/1.05 + $42,324/(1.05)2 + $44,390/(1.05)3 = $153,862. Because the costs are assumed to come sooner in this case, the PV of costs is larger than when they are assumed to occur at the end of each year.
MORE challengING questions
18.a.With the sequence of rising interest rates, Project A’s PV is –$50 + $18.18 + $16.38 + $14.61 = –$0.83. With a negative value, it should not be undertaken. Project B has a PC of –$33 + $18.18 + $24.57 + $29.22 = $36.97. Project B should be undertaken.
b.With the sequence of falling interest rates, Project A’s PV is –$50 + $18.18 + $16.68 + $15.43 = $0.29. Project B’s PV is –$33 + $18.18 + $25.02 + $30.86 = $41.06. Both projects should be undertaken.
- For any given current interest rate, fewer projects will be viable if the interest rate is expected to rise over time, and more projects will be viable if the interest rate is expected to fall over time.