Chapter 3 and Chapter 4
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Chapter 3
Problems: 1,3,4,5,6,7,8,12,17,18,19,21-24,28 & 31.
1. Honda Motor Company is considering offering a $2000 rebate on its minivan, lowering the vehicle’s price from $30,000 to $28,000. The marketing group estimates that this rebate will increase sales over the next year from 40,000 to 55,000 vehicles. Suppose Honda’s profit margin with the rebate is $6000 per vehicle. If the change in sales is the only consequence of this decision, what are its costs and benefits? Is it a good idea?
Rebate
No-Rebate
Cars Sold
55000
40000
$
6000
8000
Profit Margin
330,000,000
320,000,000
Profit increases by $10,000,000 – it’s a good decision
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?
Take the stock
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?
Take the cash because the value in the future is unknown.
4. Suppose Bank One offers an interest rate of 5.5% on both savings and loans, and Bank Two offers an interest rate of 6% on both savings and loans.
a.
What arbitrage opportunity is available? Take the loan with bank one, at 5.5%, and invest with bank two at 6%.
b.
Which bank would experience a surge in the demand for loans? Which bank would receive a surge in deposits? Demand for bank one, and surge for bank two.
c.
What would you expect to happen to the interest rates the two banks are offering? Bank One would increase its rate, or bank two would decrease its rate.
6. Some companies cross-list their shares, meaning that their stock trades on more than one stock
exchange. For example, BlackBerry (BB) trades on both the TSX and NASDAQ. If its price in
Toronto is 10 Canadian dollars per share and anyone can exchange Canadian dollars (CAD) for U.S. dollars (USD) at the rate of 0.95 USD/CAD, what must BB’s price be on NASDAQ?
BB’s stock would trade for $9.50 ($10 x 0.95) USD.
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 a one-tonne supply of shrimp. The market price of shrimp is $10,000 per tonne.
a.
What is the value of a tonne of shrimp to him?
b.
Would this value change if he were not allergic to shrimp? Why or why not?
8. Brett has almond orchards, but he is sick of almonds and prefers to eat walnuts instead. The owner of the walnut orchard next door has offered to swap this year’s crop with him in an even exchange. Assume he produces 1000 tonnes of almonds and his neighbour produces 800 tonnes of walnuts. If the market price of almonds is $1.00 per tonne and the market price of walnuts is $1.10 per tonne,
a.
Should he make the exchange?
Almonds = $1000, Walnuts = $880
b.
Does it matter whether he prefers almonds or walnuts? Why or why not? NO.
9. You have $100 and a bank is offering 5% interest on deposits. If you deposit the money in the bank, how much will you have in one year? $105
12. Excel Solution
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 if you will pay the bank $58 in one year?
c.
Should you lend the money to your friend or deposit it in the bank?
a. $58.30….$55 x (1 +r)….$55 x 1.06
b. $54.72….$5/(1+6%) c. You should deposit the fund in the bank…..Instructors advice, never lend out money to friends.
17. You are purchasing a new TV at Visions Electronics and the salesperson is trying to convince
you to buy a five-year extended warranty. The cost of the warranty to you today will be $399. However, if there is no claim against the warranty, you will get a store credit for $399 to spend five years from now. Assume you won’t have any problems with your TV and you plan on buying more electronics at Visions in five years (so you would be certain to use the store credit). Also assume the interest rate is 6% per year.
a.
What is the value to you today of the promised store credit? $399/(1.06)^5
= 298.15
b.
Given your answer to part (a), what is the net cost of the extended warranty? Net cost of the warranty is $100.84…(399 – 298.15)
Texas Instrument BA II Plus N = Time or # of periods in the calculation or # of payments
I/Y = Interest rate, nominal rate, discount rate
PV = Present Value
PMT = Payment
FV = Future Value
P/Y = Payment per year
C/Y = Compounds per year
BGN or END
18. Excel Solution
Suppose the interest rate is 4%.
a.
Having $200 today is equivalent to having what amount in one year?
b.
Having $200 in one year is equivalent to having what amount today?
c.
Which would you prefer, $200 today or $200 in one year? Does your answer depend on when you need the money? Why or why not?
a.
$200 today is equal to $208 in one year.
b.
$200 in one year is equal to $192.30
c.
$200 today is preferred.
N = 1
I/Y = 4
PV = -200
PMT = 0
FV = CPT ? 208
P/Y = 1
C/Y = 1
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BGN or END
19. You are considering a savings bond that will pay $100 in 10 years. If the interest rate is 2%, what should you pay today for the bond?
You would pay = $100/(1+2%)^10 = $82.03
21. Consider the following alternatives:
i.
$100 received in 1 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.
i $100/(1.1) = 90.91
ii $200/(1.1)^5 = 124.18
iii $300/(1.1)^10 = 115.66
b.
What is your ranking if the interest rate is only 5% per year?
i $100/(1.05) =95.24
ii $200/(1.05)^5 =156.71
iii $300/(1.05)^10 = 184.17
c.
What is your ranking if the interest rate is 20% per year?
I 83.33
II 80.38
III 48.45
22. Excel Solution
Suppose you invest $1000 in an account paying 8% interest per year.
a.
What is the balance in the account after 3 years? How much of this balance corresponds to compound interest, how much corresponds to simple interest, and how much corresponds to interest on interest?
N = 3
I/Y = 8
PV = -1000
PMT = 0
FV = ? CPT = $1,
259.71…….
Compound interest is $1,259.71 – 1000 = $259.71
P/Y = 1
C/Y = 1
BGN or END
Simple interest is $1,000 x 8% x 3 years = $240
b.
What is the balance in the account after 25 years? How much of this balance corresponds to compound interest, how much corresponds to simple interest, and how much corresponds to interest on interest?
23. Calculate the future value of $2000 in
a.
5 years at an interest rate of 5% per year.
N = 5
I/Y = 5
PV = -2000
PMT = 0
FV = ? CPT $2,552.56…….$2000 x (1+5%)^5 P/Y =1
C/Y = 1
BGN or END
b.
10 years at an interest rate of 5% per year. $3,257.89
c.
5 years at an interest rate of 10% per year. $3,221.02
24. What is the present value of $10,000 received
a.
12 years from today when the interest rate is 4% per year? $6,245.97
N = 12
I/Y = 4
PV = CPT? $6,245.97
PMT = 0
FV = 10,000
P/Y =1
C/Y = 1
BGN or END
b.
20 years from today when the interest rate is 8% per year? $
2,145.48
c.
6 years from today when the interest rate is 2% per year? $8,879.71
28. Your mom is thinking of retiring. Her retirement plan will pay her either $250,000 immediately on retirement or $350,000 five years after the date of her retirement. Which alternative should she choose if the interest rate is
a.
0% per year?
b.
8% per year?
c.
20% per year?
Today
Retirement
5years later
A)
250,000
250,000
350,000
B)
250,000
367,332
350,000
C)
250,000
622,080
350,000
Alternative way to get to solution is to calculate the present value of $350,000 at retirement.
31. Your grandfather put some money into 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?
At 25, the value of the account is $3,996 x 1.08^7 = $6,848
b.
What if you left the money until your 65th birthday?
At 65, the value of the account is $3,996 x 1.08^47 = $148,779.12
c.
How much money did your grandfather originally put into the account?
$3,996/(1.08)^18 = $1,000
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Chapter 4 1,3,4,6,7,8,9,13,20,21,27,32,33,34,38,39
10/(1.1)^1 =9.09 20/(1.1)^2 = 16.53
30/(1.1)^3 = 22.54
40/(1.1)^4 = 27.32
50/(1.1)^5 = 31.05
PV = $106.53
= 2000/1.085 + 3000/1.085^2 + 3500/1.085^3 + 3975/1.085^4
= $10,000.12 Yes, we pay off the loan.
N = 1
2
3
4
I/Y = 8.5
8.5
8.5
8.5
PV = ? ?
?
?
PMT = 0
0
0
0
FV = 2,000
3000
3500
3975
P/Y =1
C/Y = 1
BGN or END
$500/1.015 + $550/1.015^2……850/1.015^8 = $5,023.75
6. You currently have a one-year-old loan outstanding on your car. You make monthly payments of $300. You have just made a payment. The loan has four years to go (i.e., it had an original term of five years). Show the timeline from your perspective. How would the timeline differ if you created it from the bank’s perspective?
See whiteboard
7. You plan to deposit $500 in a bank account now and $300 at the end of one year. If the account earns 3% interest per year, what will the balance be in the account right after you make the second deposit?
$500 x 3% = $515 + 300 = $815
8. You have just received a windfall from an investment you made in a friend’s business. She will be paying you $10,000 at the end of this year, $20,000 at the end of the following year, and $30,000 at the end of the year after that (three years from today). The interest rate is 3.5% per year.
a.
What is the present value of your windfall?
$55,390.33
b.
What is the future value of your windfall in three years (on the date of the last payment)?
$55,390.33 x 1.035^3 = $61,412.25
9. Suppose you receive $100 at the end of each year for the next three years.
a.
If the interest rate is 8%, what is the present value of these cash flows?
b.
What is the future value in three years of the present value you computed in part (a)?
c.
Suppose you deposit the cash flows in a bank account that pays 8% interest per year. What is the balance in the account at the end of each of the next three years (after your deposit is made)? How does the final bank balance compare with your answer in part (b)?
12. You want to endow a scholarship that will pay $10,000 per year forever, starting one year from now. If the school’s endowment discount rate is 7%, what amount must you donate to endow the scholarship?
$10,000/7% = $142,857.14
13. How would your answer to Problem 12 change if you endow it now, but it makes the first award to a student 10 years from today?
$142,857.14/1.07^9 = $77,704.82
20. Assume that your parents wanted to have $160,000 saved for university by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on
your birthday and earned 8% per year on their investments.
a.
How much would they have to save each year to reach their goal?
N = 18
I/Y = 8
PV = 0
PMT = ? CPT = $4272.34
FV = 160,000
P/Y = 1
C/Y = 1
BGN or END
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b.
If they think you will take five years instead of four to graduate and decide to have $200,000 saved, just in case, how much more would they have to save each year to reach their new goal? $
5,340.42
27. You started an investment account 10 years ago with $1000 and it now has grown to $5000.
a.
What annual rate of return have you earned (you have made no additional contributions to the account)?
N = 10
I/Y = ? 17.46%
PV = -1000
PMT = 0
FV = 5000
P/Y = 1
C/Y = 1
BGN or END
b.
If the investment account earns 15% per year from now on, what will the account’s value be 10 years from now?
N = 10
I/Y = 15%
PV = -5000
PMT = 0
FV = ? $20,227.79
P/Y = 1
C/Y = 1
BGN or END
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