Chapter 3 Time Value of Money: An Introduction
Problem 4
Suppo Bank One offers a risk-free interest rate of 5.5% on both savings and loans, and Bank Enn offers a risk-free interest rate of 6% on both savings and loans.
a. What arbitrage opportunity is available?
b. Which bank would experience a surge in the demand for loans? Which bank would receive a surge in deposits?
c. What would you expect to happen to the interest rates the two banks are offering?
a. Take a loan from Bank One at 5.5% and save the money in Bank Enn at 6%.
b. Bank One would experience a surge in the demand for loans, while Bank Enn would receive a surge in deposits.
c. Bank One would increa the interest rate, and/or Bank Enn would decrea its rate.
Problem 7
Bubba is a shrimp farmer. In an ironic twist, Bubba is allergic to shellfish, so he cannot eat any shrimp. Each day he has one-ton supply of shrimp. The market price of shrimp is $10,000 per ton.
精力充沛a. What is the value of a ton of shrimp to him?hue
b. Would this value change if he were not allergic to shrimp? Why or why not?
a. The value of one ton of shrimp to Bubba is $10,000 becau that is the market price.
b. No. As long as he can buy or ll shrimp at $10,000 per ton, his personal preference or u for shrimp is irrelevant to the value of the shrimp.
Problem 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?
b. How much money could you borrow today is you pay the bank $58 in one year?
c. Should you loan the money to your friend or deposit it in the bank?
a. If you deposit the money in the bank today you will have:
b. If you lend the money to your friend for one year and borrow against the promid $58 repayment, then you could borrow:
c. From a financial perspective, you should deposit the money in the bank, as it will result in more money for you at the end of the year.
Problem 16
Calculate the future value of $2000 in
a. Five years at an interest rate of 5% per year.
b. Ten years at an interest rate of 5% per year.
c. Five years at an interest rate of 10% per year.
d. Why is the amount of interest earned in part (a) less than half the amount of interest earned in part (b)?
a. Timeline:
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2000 | FV= ? |
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b. Timeline:
c. Timeline:
d. Becau in the last 5 years you get interest on the interest earned in the first 5 years as well as interest on the original $2,000.
Problem 22
Your grandfather put some money in an account for you on the day you were born. You are now 18 years old and are allowed to withdraw the money for the first time. The account currently has $3996 in it and pays an 8% interest rate.
a. How much money would be in the account if you left the money there until your 25th birthday?
b. What if you left the money until your 65th birthday?
c. How much money did your grandfather originally put in the account?
a. Timeline:
18 | 19 | 20 | 21 | | | | 25 |
汉语发音词典0 | 1 | 2 | 3 | | | 7 |
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3,996 areacode | FV=? |
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b. Timeline:
18 | 19 | 20 | 21 | | | | 65 |
0 | 1 | 2 | 3 | | | 47 |
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3,996 | FV ? |
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c. Timeline:
Chapter 4 Time Value of Money: Valuing Cash Flow Streams
Problem 1
You have just taken out a five-year loan from a bank to buy an engagement ring. The ring costs $5000. You plan to put down $1000 and borrow $4000. You will need to make annual payments of $1000 at the end of each year. Show the timeline of the loan from your perspective. How would the timeline differ if you created it from the bank’s perspective?
0 | 1 | 2 | 3 | 4 | 5 |
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4000 | –1000 | –1000 | –1000 | –1000 | –1000 |
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From the bank’s perspective, the timeline is the same except all the signs are reverd.
Problem 9
The British government has a consol bond outstanding paying £100 per year forever. Assume the current interest rate is 4% per year.
a. What is the value of the bond immediately after a payment is made?
b. What is the value of the bond immediately before a payment is made?
Timeline:
a. The value of the bond is equal to the prent value of the cash flows. By the perpetuity formula:
b. The value of the bond is equal to the prent value of the cash flows. The cash flows are the perpetuity plus the payment that will be received immediately.
Problem 30
You are saving for retirement. To live comfortably, you decide you will need to save $2 million by the time you are 65. Today is your 30th birthday, and you decide, starting today and continuing on every birthday up to and including your 65th birthday, that you will put the same amount into a savings account. If the interest rate is 5%, how much must you t aside each year to make sure that you will have $2 million in the account on your 65th birthday?
