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Time Value of Money

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1. How long will it take $10,000 to reach $50,000 if it earns 10% interest compounded semiannually?
a.) 17 years
b.) 33 years
c.) 16.5 years
d.) 8.5 years

2. You require an 8% annual return on all investments. You will receive $1,000,
$2,000, and $3,000 respectively for the next three years (end of year) on a particular investment. What is the most you be willing to pay for this investment?
a.) $5,022
b.) $2,577
c.) $6,000
d.) $4,763

3. Your partners have promised to give you $25,000 on your wedding day if you
Wait 10 years to get married. Your sister is getting married today. What amount should she receive in today's dollars to match you gift? The appropriate discount rate is rate 12%.
a.) $8,049
b.) $10,000
c.) $22,321
d.) $25,000

4. You want to start saving for retirement. If you deposit$2,000 each year at the end
Of the next 60 years and earn 11% on the investment, how much will you have when you retire?
a.) $792,000
b.) $1,048,114
c.) $9,510,132
d.) $10,556,246

5. What is the present value of a semi-annual ordinary annuity payment of $7,000
made for 12 years with a required annual return of 5%?
a.) $65,145
b.) $128,325
c.) $125,195
d.) $62,043

6. You get a 25-year loan of $150,000 with a 8% annual interest rate. What are the
annual payments?
a.) $14,052
b.) $2,052
c.) $13,965
d.) $13,427

7. Your grandmother is offered a series of $6,000 starting one year from today. The
Payments will be made at the end of each of the next 10 years. Similar risk investments are yielding 7%. What should she pay for the investment?
a.) $60,000
b.) $45,091
c.) $42,141
d.) $30,501

8. Company XYZ purchased some machinery and gave a five-year note with a
Maturity value of $20,000. The discount rate is 8% annually and the interest is discounted monthly. How much did the company borrow?
a.) $13,612
b.) $13,424
c.) $19,346
d.) $12,000

9. Your father loans you $12,000 to make it through your senior year. His
Repayment schedule requires payments of $1401.95 at the end of year the next 15 years. What interest rate is he charging you?
a.) 7.0%
b.) 7.5%
c.) 8.0%
d.) 8.5%

10. What is the future value of an annuity due if your required return is 10%, and
Payments are $1,000 for 10 years?
a.) $15,937
b.) $16,145
c.) $17,531
d.) $11,000

11. You deposit $10,000 in a bank and plan to keep it there for five years. The bank
Pay 8% annual interest compounded continuously. Calculate the future value at the end of five years.
a.) $14,693
b.) $15,000
c.) $14,918
d.) $14,500

12. Calculate the present value of $100,000 received in six months. Use an annual
discount rate of 10%. Do not adjust the discount rate to a semi-annual rate. Keep it annual and adjust to the appropriate value.
a.) $95,346
b.) $56,447
c.) $90,909
d.) $100,000
13. You get a twenty-year amortized loan of $100,000 with a 5% annual interest rate.
what are the annual payments?
a.) $8,718
b.) $37,689
c.) $4,762
d.) $8,024

14. What is the present value of $100,000 received in fifteen years with an annual
Discount rate of 5% discounted monthly?
a.) $25,000
b.) $48,102
c.) $47,310
d.) $207,893

15. A gallon of milk cost $3.59 today. How much will it cost you to buy a gallon of
milk for your grandchildren in 35 years if inflation averages 5% per year?
a.) $3.77
b.) $6.28
c.) $12.34
d.) $19.80

16. You borrow $95,000 for 12 years at an annual rate of 12%. What are the monthly
Payments required to amortize this loan?
a.) $1,248
b.) $15,336
c.) $11,400
d.) $3,936

17. As a gift from your parents, you just received $50,000 for your education for the
Next four years. You can earn an annual rate of 8% on your investments. How much can you withdraw each year (end of year) just using up the $50,000?
a.) $12,000
b.) $11,096
c.) $11,750
d.) $15,096

18. You would like to retire on $1,000,000. You plan on a 7% annual investment rate
(3.5% semi-annually) and will put away $7,500twice a year at the end of each semi-annual period. How long before you can retire? Round to the nearest figure.
a.) 51years
b.) 25 years
c.) 35 years
d.) 66 years

19. What is the present value of an annual annuity payment of $7,000 made for 12
Years with a required return of 5% with the first payment starting today?
a.) $3,898
b.) $65,145
c.) $62,043
d.) $11,200

20. What a deal! Your new car only cost $28,300 after rebates and trade. If you
Finance it for 60 months at 6% annual interest, what will be you rmonthly payments?
a.) $471.67
b.) $544.40
c.) $547.12
d.) $1,751.08

Essay. Write your answer in the space provided or on a separate sheet of paper.

21. Sum the present values of the following cashflows to be received at the end of
each of the next six years $1,500, $3,500, $$3,750, $4,250, $5,000 when the discount rate is 4%.

22. How long it will take for $2,500 to become $8,865 if it is deposited and earns 5% per year compounded annually? (Calculate to the closet year.)

23. Company XYZ purchased equipment and gave a three-year note with maturity value of $12,006. The annual discount rate for the note was 14% discounted semi-annually. Calculate how much they borrowed.

24. Calculate the resent value of each of the alternatives below, if the discount rate is 12%.
a.) $45,000 today in one lump sum.
b.) $70,000 paid to you in seven equal payments of $10,000 at the end of each of the next seven years.
c.) $80,000 paid in one lump sum 7 years from now.

25. A bank agrees to give you a loan of $12,000,000 and you have t pay $1,309,908
Per year for 26 years. What is your rate of interest? What would the payments be if this were a monthly payment loan?

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The attached excel file has the calculations.
The attached doc file has the answers and explanations.

1. How long will it take $10,000 to reach $50,000 if it earns 10% interest compounded semiannually?
a.) 17 years
b.) 33 years
c.) 16.5 years
d.) 8.5 years

2. You require an 8% annual return on all investments. You will receive $1,000,
$2,000, and $3,000 respectively for the next three years (end of year) on a particular investment. What is the most you be willing to pay for this investment?
a.) $5,022
b.) $2,577
c.) $6,000
d.) $4,763

3. Your partners have promised to give you $25,000 on your wedding day if you
Wait 10 years to get married. Your sister is getting married today. What amount should she receive in today's dollars to match you gift? The appropriate discount rate is rate 12%.
a.) $8,049
b.) $10,000
c.) $22,321
d.) $25,000

The amount should be the PV of your payment. Amount is 25,000/1.12^10 = 8,049

4. You want to start saving for retirement. If you deposit$2,000 each year at the end
Of the next 60 years and earn 11% on the investment, how much will you have when you retire?
a.) $792,000
b.) $1,048,114
c.) $9,510,132
d.) $10,556,246

5. What is the present value of a semi-annual ordinary annuity payment of $7,000
made for 12 years with a required annual return of 5%?
a.) $65,145
b.) $128,325
c.) $125,195
d.) $62,043

6. You get a 25-year loan of $150,000 with a 8% annual interest rate. What are the
annual payments?
a.) $14,052
b.) $2,052
c.) $13,965
d.) $13,427

7. Your grandmother is offered a series of $6,000 starting one year from today. The
Payments will be made at the end of each of the next 10 years. Similar risk investments are yielding 7%. What should ...

Solution Summary

The solution explains various multiple choice questions relating to time value of money

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See Also This Related BrainMass Solution

Time value of money - calculator operations

1. Find the annual interest rate. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Present Value Future Value Time Period Annual Interest Rate
$ 100 $ 122.01 4 years %

200 281.82 5 %

100 113.28 6 %

2. If you take out an $8,300 car loan that calls for 48 monthly payments starting after 1 month at an APR of 6%, what is your monthly payment? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Monthly payment $

b. What is the effective annual interest rate on the loan? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Effective annual interest rate %

3. If the interest rate this year is 8.6% and the interest rate next year will be 10.6%, what is the future value of $1 after 2 years? What is the present value of a payment of $1 to be received in 2 years? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Future value $
Present value $

4. Compute the future value of a $120 cash flow for the same combinations of rates and times: (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Future Value
a. r = 12%, t = 8 years $
b. r = 12%, t = 16 years
c. r = 6%, t = 8 years
d. r = 6%, t = 16 years

5. A factory costs $420,000. You forecast that it will produce cash inflows of $130,000 in year 1, $190,000 in year 2, and $320,000 in year 3. The discount rate is 10%.

a. Calculate the PV of cash inflows. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present value $

b. Is the factory a good investment?

No
Yes

6. Investments in the stock market have increased at an average compound rate of about 5% since 1911. It is now 2012.

a. If you invested $1,000 in the stock market in 1911, how much would that investment be worth today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Investment $

b. If your investment in 1911 has grown to $1 million, how much did you invest in 1911? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present value $

7. Sure Tea Co. has issued 4.2% annual coupon bonds that are now selling at a yield to maturity of 6% and current yield of 5.8000%. What is the remaining maturity of these bonds? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Remaining period years

8. A 6-year Circular File bond pays interest of $80 annually and sells for $986. What are its coupon rate and yield to maturity? (Do not round intermediate calculations. Round "Coupon rate" to 1 decimal place and "Yield to maturity" to 2 decimal places.)

Coupon rate %
Yield to maturity %

9. A 2-year maturity bond with face value of $1,000 makes annual coupon payments of $86 and is selling at face value. What will be the rate of return on the bond if its yield to maturity at the end of the year is (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Rate of Return
a. 6% %

b. 8.6% %

c. 10.6 %

10. A 25-year Treasury bond is issued with face value of $1,000, paying interest of $56 per year. If market yields increase shortly after the T-bond is issued, what is the bond's coupon rate? (Round your answer to 1 decimal place.)

Coupon rate %

11. A bond's credit rating provides a guide to its risk. Long-term bonds rated Aa currently offer yields to maturity of 7.9%. A-rated bonds sell at yields of 8.2%. Assume a 10-year bond with a coupon rate of 7.4% is downgraded by Moody's from Aa to A rating.

a. Calculate the initial price. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Initial price $

b. Calculate the new price. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

New price $

12. Steady As She Goes, Inc., will pay a year-end dividend of $2.90 per share. Investors expect the dividend to grow at a rate of 6% indefinitely.

a. If the stock currently sells for $29 per share, what is the expected rate of return on the stock? (Do not round intermediate calculations.)

Expected rate of return %

b. If the expected rate of return on the stock is 18.5%, what is the stock price? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Stock price $

13. Arts and Crafts, Inc., will pay a dividend of $7 per share in 1 year. It sells at $70 a share and firms in the same industry provide an expected rate of return of 14%. What must be the expected growth rate of the company's dividends? (Do not round intermediate calculations.)

Expected growth rate %

14. No-Growth Industries pays out all of its earnings as dividends. It will pay its next $6 per share dividend in a year. The discount rate is 21%.

a. What is the price-earnings ratio of the company? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

P/E ratio

b. What would the P/E ratio be if the discount rate were 20%? (Round your answer to 2 decimal places.)

P/E ratio

15. Grandiose Growth has a dividend growth rate of 20%. The discount rate is 12%. The end-of-year dividend will be $4 per share.

a. What is the present value of the dividend to be paid in year 1? Year 2? Year 3? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Present Value
Year 1 $
Year 2
Year 3

16. Waterworks has a dividend yield of 9.25%. If its dividend is expected to grow at a constant rate of 6.25%, what must be the expected rate of return on the company's stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Expected rate of return %

17. Computer Corp. reinvests 50% of its earnings in the firm. The stock sells for $70, and the next dividend will be $3.50 per share. The discount rate is 15%. What is the rate of return on the company's reinvested funds? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Rate of return %

The following are the cash flows of two projects:

Year Project A Project B
0 −$350 −$350
1 180 250
2 180 250
3 180 250
4 180
________________________________________

18. What is the payback period of each project? (Round your answers to 2 decimal places.)

Project Payback Period
A years
B years

19. The following are the cash flows of two projects:

Year Project A Project B
0 −$280 −$280
1 160 180
2 160 180
3 160 180
4 160

a. If the opportunity cost of capital is 10%, what is the profitability index for each project? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Project Profitability Index
A

B

b. Does the profitability index rank the projects correctly?

20. The following are the cash flows of two projects:

Year Project A Project B
0 −$220 −$220
1 100 120
2 100 120
3 100 120
4 100

a. Calculate the NPV for both projects if the discount rate is 10%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Project NPV
A $
B

b. Suppose that you can choose only one of these projects. Which would you choose?

Project B
Project A

The following table presents sales forecasts for Golden Gelt Giftware. The unit price is $40. The unit cost of the giftware is $20.

Year Unit Sales
1 34,000
2 42,000
3 16,000
4 10,000
Thereafter 0
________________________________________

21. It is expected that net working capital will amount to 20% of sales in the following year. For example, the store will need an initial (year-0) investment in working capital of .20 × 34,000 × $40 = $272,000. Plant and equipment necessary to establish the Giftware business will require an additional investment of $212,000. This investment will be depreciated using MACRS and a 3-year life. After 4 years, the equipment will have an economic and book value of zero. The firm's tax rate is 30%. What is the net present value of the project? The discount rate is 20%. (Do not round intermediate calculations. Round your answer to the nearest dollar amount.)

Net present value $

22. Canyon Tours showed the following components of working capital last year:

Beginning End of Year
Accounts receivable $27,400 $24,700
Inventory 13,700 15,900
Accounts payable 16,200 19,900
________________________________________

a. What was the change in net working capital during the year? (Negative amount should be indicated by a minus sign.)

Change in net working capital $

b. If sales were $37,700 and costs were $25,700, what was cash flow for the year? Ignore taxes.

Cash flow $

23. The owner of a bicycle repair shop forecasts revenues of $236,000 a year. Variable costs will be $69,000, and rental costs for the shop are $49,000 a year. Depreciation on the repair tools will be $29,000. The tax rate is 40%.

a. Calculate operating cash flow for the year by using all three methods: (a) adjusted accounting profits; (b) cash inflow/cash outflow analysis; and (c) the depreciation tax shield approach.

Method Operating Cash Flow
Adjusted accounting profits $
Cash inflow/cash outflow analysis
Depreciation tax shield approach

Quick Computing installed its previous generation of computer chip manufacturing equipment 3 years ago. Some of that older equipment will become unnecessary when the company goes into production of its new product. The obsolete equipment, which originally cost $35.5 million, has been depreciated straight-line over an assumed tax life of 5 years, but it can be sold now for $17.1 million. The firm's tax rate is 40%. What is the after-tax cash flow from the sale of the equipment? (Enter your answer in millions rounded to 2 decimal places.)

After-tax cash flow $ million

25. Ilana Industries, Inc., needs a new lathe. It can buy a new high-speed lathe for $1.3 million. The lathe will cost $38,000 per year to run, but will save the firm $138,000 in labor costs, and will be useful for 10 years. Suppose that for tax purposes, the lathe will be depreciated on a straight-line basis over its 10-year life to a salvage value of $300,000. The actual market value of the lathe at that time also will be $300,000. The discount rate is 7%, and the corporate tax rate is 35%. What is the NPV of buying the new lathe? (Negative amount should be indicated by a minus sign. Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to 2 decimal places.)

NPV $

26. A new project will generate sales of $73.4 million, costs of $41.4 million, and depreciation expense of $9.4 million in the coming year. The firm's tax rate is 40%.

a. Calculate cash flow for the year by using all three methods: (a) adjusted accounting profits; (b) cash inflow/cash outflow analysis; and (c) the depreciation tax shield approach. (Enter your answers in millions rounded to 2 decimal places.)

Method Cash Flow
Adjusted accounting profits $ million
Cash inflow/cash outflow analysis million
Depreciation tax shield approach million

b. Are the above answers equal?

27. Modern Artifacts can produce keepsakes that will be sold for $50 each. Nondepreciation fixed costs are $1,500 per year and variable costs are $30 per unit.

a. If the project requires an initial investment of $2,000 and is expected to last for 5 years and the firm pays no taxes. The initial investment will be depreciated straight-line over 5 years to a final value of zero, and the discount rate is 10%. What are the accounting and NPV break-even levels of sales? (Do not round intermediate calculations. Round your answers to the nearest whole number.)

Accounting break-even levels of sales units
NPV break-even levels of sales units

b. What will be the accounting and NPV break-even levels of sales, if the firm's tax rate is 40%? (Do not round intermediate calculations. Round your answers to the nearest whole number.)

Accounting break-even levels of sales units
NPV break-even levels of sales units

28. Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $100. The materials cost for a standard diamond is $50. The fixed costs incurred each year for factory upkeep and administrative expenses are $180,000. The machinery costs $1.3 million and is depreciated straight-line over 10 years to a salvage value of zero.

a. What is the accounting break-even level of sales in terms of number of diamonds sold?

Break-even sales

b. What is the NPV break-even level of sales assuming a tax rate of 30%, a 10-year project life, and a discount rate of 12%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Break-even sales

29. A silver mine can yield 16,000 ounces of silver at a variable cost of $34 per ounce. The fixed costs of operating the mine are $56,000 per year. In half the years, silver can be sold for $50 per ounce; in the other years, silver can be sold for only $25 per ounce. Ignore taxes.

a. What is the average cash flow you will receive from the mine if it is always kept in operation and the silver always is sold in the year it is mined?

Average cash flow $

b. Now suppose you can shut down the mine in years of low silver prices. Calculate the average cash flow from the mine.

Average cash flow $

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