Chapter 3 Time Value of Money: An Introduction
3. Suppose your employer offers you a choice between a $5000 bonus and 100 shares of the company’s stock. Whichever one you choose will be awarded today. The stock is currently trading at $63 per share.
a. Suppose that if you receive the stock bonus, you are free to trade it. Which form of the bonus should you choose? What is its value?
Answer：（1）I will prefer to choose 100 shares of the company’s stock which is currently trading at $63 per share. （2）Its value is : 100*63 = $ 6300.
b. Suppose that if you receive the stock bonus, you are required to hold it for at least one year. What can you say about the value of the stock bonus now? What will your decision depend on?
Answer：（1）I think that the value of the stock bonus now is 5000 and the cash flow now is 0. （2）my decision depend on the time value of money and the interest rates.
8. Brett has almond orchards, but he is sick of almonds and prefers to eat walnuts instead. The owner of the walnut orchard next d oor has offered to swap this year’s crop with him. Assume he produces 1000 tons of almonds and his neighbor produces 800 tons of walnuts. If the market price of almonds is $100 per ton and the market price of walnuts is $110 per ton:
a. Should he make the exchange?
Answer：total price of almonds is: 1000*100 = $ 100000 ；
total price of walnuts is: 800* 110 = $ 88000
Because $ 100000 more than $ 88000, I think he should not make the exchange.
b. Does it matter whether he prefers almonds or walnuts? Why or why not? Answer：no 无关I think it does matter whether he prefers almonds or walnuts, because he is sick of almonds and prefers to eat walnuts instead, which means almonds is nothing or not valuable for him, even though at present the real price of almonds is more walnuts.
11. A friend asks to borrow $55 from you and in return will pay you $58 in one year. If your bank is offering a 6% interest rate on deposits and loans:
a. How much would you have in one year if you deposited the $55 instead? Answer: if I deposited $55, in one year, I will have get: 55*(1+6%) = $ 58.3.
b. How much money could you borrow today if you pay the bank $58 in one year? Answer: I will borrow: 58 / (1+6%) = $ 54,72
c. Should you loan the money to your friend or deposit it in the bank?
Answer: Because $58.3 is more than $ 58, I prefer to deposit my money in bank.
17. Consider the following alternatives:
i. $100 received in one year
ii. $200 received in 5 years
iii. $300 received in 10 years
a.Rank the alternatives from most valuable to least valuable if the interest rate is 10% per year.
Answer: the value of (i) now is: 100 / (1+10%) = $ 90.91
the value of (ii) now is: 200 / (1+10%)5 = $ 124.18
the value of (iii) now is: 300 / (1+10%)10 = $ 115.66
So the rank of alternatives from most valuable to least valuable is:
(ii) > (iii) > (i)
b. What is your ranking if the interest rate is only 5% per year?
Answer: the value of (i) now is: 100 / (1+5%) = $ 95.24
the value of (ii) now is: 200 / (1+5%)5 = $ 156.71
the value of (iii) now is: 300 / (1+5%)10 = $ 184.17
So the rank of alternatives from most valuable to least valuable is:
(iii) > (ii) > (i)
c. What is your ranking if the interest rate is 20% per year?
Answer: the value of (i) now is: 100 / (1+20%) = $ 83.33
the value of (ii) now is: 200 / (1+20%)5 = $ 80.38
the value of (iii) now is: 300 / (1+20%)10 = $ 48.45
So the rank of alternatives from most valuable to least valuable is:
(i) > (ii) > (iii)。