SEATTLE UNIVERSITY
PROF. KEN SHAH FINC 340 Spring 2007
HOME WORK # 1
Due: January 24 beginning of class
INSTRUCTIONS:
I. Write your group number and all the member names.
II. Where I ask for time lines, make sure the cash flows have appropriate + or - signs.
III. Maximum score possible: 40
IV. Type of print clearly – Fill in the answer sheet and attach on top of your work pages. You must show all your work to get credit. Sloppy handwriting/presentation will not be graded.
Group # / Names (Last, First)1.
2.
3.
Answers:
1. FV: Amount: $100
r = 7% per period / r = 15% per periodi. / # of periods = 30
ii. / # of periods = 75
2. PV: Amount: $100,000
r = 5% per period / r = 20% per periodi. / # of periods = 5
ii. / # of periods = 100
3. Stock Returns
Stock / $ Return / % Return / % Cap. Gain / % Div. Yld.i. / Red Hook Brewery
ii. / IBM
4. & 5. Annuities
CompoundingPeriod / Number of Years / APR
% / PV / FV
i. / Quarter / 8 / 12
ii. / Semi-Annual / 10 / 13.25
6. & 7. APR/EAR
CompoundingPeriod / APR / EAR / # of Periods
I/yr = 13.5%
i. / Quarter
ii. / Month
8. PV of $3000
i. / 1st PMTEnd of 6 yrs
ii. / 1st PMT
End of 12 yrs
9.
i. / Value at End of 7 yearsii. / PV at t=0
10. Retirement Payment = ______
11. Mortgage Loan
i) cheapest optionii) monthly pmt
iii)Interest of 100th
Principal of 100th
iv) Balloon after 15 years
v) Bimonthly pmts
# of years
11. Cheaper Option: ______
Reason: ______
1. Using your calculator, find the future value (FV) in each of the following cases. Although you will use a calculator, indicate in every case the formula used and write down the inputs to the formula.
Amount: $100
r = 7% per period / r = 15% per periodi. / # of periods = 30
ii. / # of periods = 75
2. Using your calculator, find the present value (PV) in each of the following cases. As, above, in every case, indicate the formula and the inputs to the formula.
Amount: $100,000
r = 5% per period / r = 20% per periodi. / # of periods = 5
ii. / # of periods = 100
3. Calculate the following in each of the following cases (show your work):
a) Dollar return
b) Percentage return
c) Percentage capital gain
d) Percentage dividend yield
Stock / Purchase Price / Sale Price / Dividendsi. / Red Hook Brewery / $30 / $23 / $3.00
ii. / IBM / 90 / 97 / 1.20
4. Calculate the present values for the following ordinary annuities. Although you will use the calculator, write down the formula and show the inputs to the formula and draw the time line and show the cash flows on the time line in each case:
CompoundingPeriod / Number of Years / Annual Int. Rate (APR) / Payments
i. / Quarter / 8 / 12% / $5,600
ii. / Semi-Annual / 10 / 13.25% / $5,000
5. Calculate the future values for each of the two cases above in problem 4. Although you will use the calculator, write down the formula and show the inputs to the formula in each case.
6. Calculate the APR and EAR for each of the following:
CompoundingPeriod / Number of Years / PV or FV / Payments
i. / Quarter / 8 / FV=$212,000 / $5,600
ii. / Month / 6 / PV=$20,000 / $350
7. Calculate the number of periods (i.e. quarters, months) it would take to obtain the present value or future value in the above problem if the interest rate was 13.5% in each of the two cases.
8. Calculate the present value (at t = 0) of a $3000 annual perpetuity when the first payment begins at the end of (i) 6 years (ii) 12 years. Interest rate is 6.25% per year. Draw the time line and show the cash flows on the time line in each case.
9. You plan to invest $2,000 3 years from now (at t = 3) in an account paying 8% per year. (i) How many dollars will you have at the end of 7 years from now if the interest is compounded quarterly? (ii) What is the present value now (at t = 0) of the amount you found in part (i) at the same rate but compounded continuously? Draw the time line and show the cash flows on the time line in each case.
10. Retirement: It’s never too late to plan for retirement! You will retire in 40 years from today. You estimate that after retiring, you will live for a further 15 years, and that you will need $150,000 a year to live comfortably in retirement. How much must you contribute monthly to your retirement plan over the next 40 years if your money earns an interest of 12% per year throughout the rest of your life? Draw the time line and show the cash flows.
11. Mortgage: I recently bought a $245,000 home in Wallingford for which I borrowed $214,600 from a mortgage banker and put the remaining as down payment. I was told that I would incur ‘closing costs’ at the time of purchase, that is out-of-pocket expenses, of $5,000 in order to buy the house (the closing costs are fees charged for things such as using escrow officer, charge for wire transfer of funds, title transfer, insurance etc.). The mortgage banker quoted me the following annual rates for a 30-year fixed-rate mortgage loan with monthly payments (it turns out that if I pay a higher interest rate, I can avoid paying the points and/or the closing costs):
A. 7.25% + 2 points and I pay the closing costs
B. 7.50% + 1 point and I pay the closing costs
C. 7.80% + 0 points and I do not pay closing costs
i. Which one of the above options is the cheapest option for me? Show your analysis and reasoning carefully. (Hint: What is the EAR for each of the three options? Note that no matter which option I choose, the monthly payments, are based on the amount of $214,600.)
For the following questions, assume that I chose option C:
ii. What is the monthly payment?
iii. What is the amount of i) interest and ii) principal for my 100th payment?
iv. What is my ‘balloon’ payment if I want to pay off the loan after 20 years?
v. Assume that the monthly dollar payment you found in question (ii) are made in two bi-monthly installments: the monthly payment is divided in half, and half is paid on the 1st of the month and half on the 15th of the month. How many years would it take to pay off the entire amount I borrowed if the payments are bi-monthly instead of monthly?
12. Car Buy or Lease: Last month, the local area Saab dealers offered the following lease or buy options on the Saab 900S Turbo Convertible model which sells for a cash price of $32,000:
Buy: You can buy the car. Under the terms of purchase, you will pay $4,000 down and finance the rest through the dealer by paying $710 a month for 4 years (48 months).
Lease: You can lease the car. Under the terms of the lease, you will pay $4,000 down, and $399 payments per month for 4 years. At the end of four years, you must make an additional payment of $19,500 to the dealer and keep the car.
Which of these two options is the cheapest: buy or lease? Explain carefully showing all the calculations and drawing the time lines showing cash flows for the two options.
[Optional Question (no points - just try to figure it out! J): This one is a slightly tricky question. Suppose now you have the option to return the car under and just walk away at the end of the 4-year lease. You also know (for sure) that the market value of the car at the end of 4 years is $22,000. That is, you can just as easily buy or sell a similar car (same condition, mileage etc.) for $22,000. How would this option change your decision to buy or lease? Explain with calculations.]
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