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For Examination of Fundamentals of Corporate Finance

1) Find the interest rate implied by the following combinations of present and future values:

Present Value Years Future Value

$400 11 $684

$183 4 $249

$300 7 $300

2) What is the present value of the following cash-flow stream if the interest rate is 5 percent?

3) Find the effective annual interest rate for each case:

4) Find the APR (the stated interest rate) for each case:

5) If the appropriate discount rate for the following cash flows is 12 percent compounded quarterly, what is the present value of the cash flows?

6) You’ve been offered investments that will double your money in 10 years. What rate of return are you being offered? Check your answer using the Rule of 72.

7) Solve for the unknown number of years in each of the following:

8) Assume the total cost of a college education will be $200,000 when your child enters college in 18 years. You presently have $15,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child’s college education?

9) You’re trying to save to buy a new $120,000 Ferrari. You have $40,000 today that can be invested at your bank. The bank pays 4 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

10) A bank is offering 12 percent compounded quarterly. If you put $100 in an account, how much will you have at the end of one year? What’s the EAR? How much will you have at the end of two years?

11) Now that you know how to convert a quoted rate to an EAR, consider going the other way.

As a lender, you know you want to actually earn 18 percent on a particular loan. You want to quote a rate that features monthly compounding. What rate do you quote?

12) What is an APR? What is an EAR? Are they the same thing?

13) You plan to make a series of deposits in an individual retirement account. You will deposit $1,000 today, $2,000 in two years, and $2,000 in five years. If you withdraw $1,500 in three years and $1,000 in seven years, assuming no withdrawal penalties, how much will you have after eight years if the interest rate is 7 percent? What is the present value of these cash flows?

14) You are looking into an investment that will pay you $12,000 per year for the next 10 years. If you require a 15 percent return, what is the most you would pay for this investment?

15) Suppose you borrow $10,000. You are going to repay the loan by making equal annual payments for five years. The interest rate on the loan is 14 percent per year. Prepare an amortization schedule for the loan. How much interest will you pay over the life of the loan?

16) If you deposit $1,000 at the end of each of the next 20 years into an account paying 8.5 percent interest, how much money will you have in the account in 20 years? How much will you have if you make deposits for 40 years?

17) What is Bond? What is Corporate Bond? What is government Bond?

18) What is Coupon? What is Coupon Rate? What is Current Yield? What is Yield to Maturity (YTM)? What is Face Value (FV)?

19) What is Common Stock? What is Preferred Stock? What is dividend?

20) A Microgates Industries bond has a 10 percent coupon rate and a $1,000 face value. Interest is paid semiannually, and the bond has 20 years to maturity. If investors require a 12 percent yield, what is the bond’s value? What is the effective annual yield on the bond?

21) A Macrohard Corp. bond carries an 8 percent coupon, paid semiannually. The par value is $1,000, and the bond matures in six years. If the bond currently sells for $911.37, what is its yield to maturity? What is the effective annual yield?

22) A bond has a 7% coupon and pays interest semi-annually. What is the amount of each interest payment if the face value of a bond is $1,000?

23) A bond has a 9% coupon rate, matures in 12 years and pays interest semi-annually. The face value is $1,000.

What is the current price of this bond if the market rate of return is 8.3%?

24) A bond is currently selling at a price of $977.03. The face value is $1,000 and the coupon rate is 8%. Interest is paid semi-annually.

How many years is it until this bond matures if the market rate of return is 8.4%?

25) A 6% bond pays interest annually and matures in 14 years. The face value is $1,000 and the current market price is $896.30.

What is the yield to maturity?

26) A 6% bond pays interest annually and matures in 14 years. The face value is $1,000 and the current market price is $896.30.

What is the yield to maturity?

27) You are considering purchasing a 10-year, zero coupon bond with a face value of $1,000.

How much are you willing to pay for this bond if you want to earn a 12% rate of return? Assume annual compounding.

28) Winslow, Inc. issues 20-year zero coupon bonds at a price of $224.73. The face value is $1,000.

What is the amount of the implicit interest for the first year of this bond’s life?

29) The closing price of a bond is quoted in the newspaper as 101.366.

What is the market price if the face value is $1,000?

30) Microhard has issued a bond with the following characteristics:

Principal: $1,000

Time to maturity: 20 years

Coupon rate: 12 percent, compounded semiannually

Semiannual payments

Calculate the price of this bond if the stated annual interest rate, compounded semiannually, is:

a) 5 percent

b) 15 percent

c) 2 percent

31) What different between bonds and Stocks?

32) A 6% bond pays interest annually and matures in 14 years. The face value is $1,000 and the current market price is $896.30.

What is the yield to maturity?

33) Bits ‘n Pieces pays a constant annual dividend of $.50 a share. The market price of the stock is $5.41 today.

What is the rate of return on this stock?

34) JLE, Inc. just paid their annual dividend of $1.10 a share. JLE’s policy is to increase the dividend by 2% annually.

How much are you willing to pay today for a share of this stock if you require an 11% rate of return?

35) Alex’s Ventures, Inc. stock has a 13% rate of return and a current market price of $16.18. The company pays annual dividends. The last dividend paid was $1.40 per share.

What is the growth rate of this stock?

36) Suppose the following bond quote for IOU Corporation appears on the financial page of today’s newspaper. If this bond has a face value of $1,000, what closing price appeared in yesterday’s newspaper?

37) The Brigapenski Co. has just paid a cash dividend of $2 per share. Investors require a 16 percent return from investments such as this. If the dividend is expected to grow at a steady 8 percent per year, what is the current value of the stock? What will the stock be worth in five years?

38) What is the payback period, NPV, IRR, and PI for the following set of cash flows? The cost of capital is 12%.

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39) .

XYZ Company is considering the purchase of a new machine that would increase the speed of manufacturing and save money. The net cost of this machine is $70, 000. The annual cash flows have the following projections.

Year Cash Flow

1. $21,000

2. 29,000

3. 36,000

4. 16,000

5. 9,000

a) If the cost of capital is 14 percent, what is the net present value (NPV)?

b) What is the internal rate of return ( IRR)

c) Should the project be accepted? Why?

40) .Compute the internal rate of return (IRR) for the cash flows of the following two projects.

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41) .

Determine the net present value for a project that costs $104,000 and would yield after-tax cash flows of $16,000 the first year, $18,000 the second year, $21,000 the third year, $23,000 the fourth year, $27,000 the fifth year, and $33,000 the sixth year. Your firm's cost of capital is 12.00%.

42) .

Determine the internal rate of return for a project that costs $78,000 and would yield after-tax cash flows of $12,000 the first year, $14,000 the second year, $17,000 the third year, $19,000 the fourth year, $23,000 the fifth year, and $29,000 the sixth year.

43) .

Suppose you are offered $5,000 today but you must make the following payments.

|Year |Cash Flows ($) |

|0 |5,000 |

|1 |-2,500 |

|2 |-2,000 |

|3 |-1,000 |

|4 |-1,000 |

a) What is the IRR of this offer?

b) If the approximate discount rate is 10 percent, should you accept this offer?

c) If the approximate discount rate is 20 percent, should you accept this offer?

d) What is the NPV of the offer if the approximate discount rate is 10 percent? 20 percent?

e) Are the decision under the NPV rule in part (d) consistent with those of the IRR rule?

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