Basic PV/FV Problems

1) Find the present value of $4,900 to be received 10 years from today. The discount rate is 7%.

2. Find the future value of $6,000 that will be invested at an annual rate of 7% for 15 years.
3. Susan has a 401k plan through her job and has accumulated $375,000 in her account. Her company has invested her funts in a high interest bearing account yielding 8% per year. She would like to retire with $600,000 in her account. When will she be able to retire?

4. Joe has $100,000 in an investment account. He is looking to retire in 12 years. He needs a minimum of $240,000 in order to retire. What rate of return does Joe need to make on his investment in order to be able to retire?

5. Congratualtions, you just won the lottery!!! The award was for $40,000,000. The lottery company has offered to either pay you the entire amount over 40 years at

$1,000,000 per year, or they have offered you a chunk of money today (a lump sum) instead of receiving the $1,000,000 per year for 40 years. Assuming a rate of 6%, what dollar amount does the lump sum need to be to be worth taking over the $1,000,000 per year for 40 years?

*6. Jane is contributing $5,000 each year, at the end of the year into a savings plan that is generating a 4% return. What will the account be worth in 10 years? What if Jane makes her contribution in the beginning of the year. How will that affect the value of her account in ten years?

7. A $100,000 mortage carries a 9% annual interest rate compounded monthly for a maximum of 30 years. How many monthly payments of $1,000 will it take to pay off the loan in full?

8. The future value of regular annuity of $6,000 per year for 10 years is $75,467.36. What interest rate is implied?
9. Company needs to borrow money today for a project. Your boss asked you to figure out how much the company can borrow. Your boss tells you the company can afford to pay

$45,000 each quarter for a period of twenty years with payments at the end of the quarter. Your company’s bank is willing to offer a 20 year loan with quarterly payments at an annual rate of 13.5%. What is the most that your company can borrow?

10. What is the present value of an annuity due of $2,500 per year for 10 years if the interest rate is 4% per year?

Find PV and multiply by 1.04

11. I bought a house for $600,000. I put $200,000 down and I financed the balance with a 30 year fixed mortgage at 4.5%. What is my monthly payment on this mortgage?
12. What is the present value of a preferred stock that pays an annual payment of $8,400 per year at a discount rate of 9% per year?

a)    $89,600

b)    $93,333

c)    $52,114

d)    $40,100

e)    The present value of this perpetuity is infinitely large.

• 13. You’re considering an investment in a preferred stock that offers a perpetual dividend of $2,000 per year. Its price is $25,000. What annual rate of return (discount rate) is implied in this value?

14. You are offered an investment that will pay you an annual perpetuity. The amount you must pay now to purchase the investment is $200,000. You expect to receive a return of 7% on the investment. What annual payment will you receive on this investment?

• 15. You’re considering making an investment in a project that will generate $1,000,000 per year indefinitely. To finance this project you will be using a combimation of both bonds and stocks. 60% of your financing needs will be in the form of bonds at a rate of 5%, and the remaining 40% will be issued in the form of stocks at a rate of 12%. What is the most amount of money you would consider to spend for this project (to receive a return of $1,000,000 per year, indefinitely)

UNEVEN CASH FLOWS

16. An initial investment on plant and machinery of $8,320 is expected to generate cash inflows of $3,411 , $4,070 , $5,824 and $2,065 at the end of first, second, third and fourth year respectively. At the end of the fourth year, the machinery will be sold for $900 . Calculate the present value of the investment if the discount rate is 18%. Round your answer to nearest thousand dollars.
17. You saving up to buy a car. You plan on making your first savings deposit one year from today, and then making deposits for the following 3 years. These are the amounts you plan to save at the end of each year:

Year         Projected Savings Amount

1                     $1,500

2                     $3,000

3                     $2,200

4                     $3,000

You expect to earn an annual rate of 9% per year throughout. What amount will you have available at the end, at time 4, when you will buy the car?

18. A person who is now 30 years old is planning for his retirement. He expects to save $5,000 each year for the next 35 years. Based on the current yield curve, he expects to earn an average rate of 5% per year. He will make the first deposit to his retirement savings account exactly one year from today. How much will he have in his retirement savings account in 35 years?

19. A person who is now 30 years old is planning for his retirement. He hopes to have a total of $500,000 available when he retires in 35 years. Based on the current yield curve, he expects to earn an average rate of 5% per year. He will make the first deposit to his retirement savings account exactly one year from today. How much must he save each year to reach his retirement savings goal in 35 years?

Compounded Rates

20. You just received your first credit card statement and the APR listed is 21.7%. When you look closer at the statement you see that it’s compounded daily? What’s EAR?

EAR: (1+21.7/365)^365 =

Continuous Compounding

21. You have invested $48,000 in a security that will earn a continuously compounded rate of 12% for a period of 15 years. What amount will the investment grow to by the end of the investment?

22. Your bank is offering you an investment that will return $50,000 in exactly 16 years. The discount rate is 5% per year with continuous compounding/discounting. What is the most you should pay for this investment?

23. A bank offers you a credit card with a stated APR of 8%. Upon closer inspection you see that the loan continuously compounds. What is the EAR on this continuous compounding loan?

24. Joe’s Pizza, Inc. just paid a dividend, D₀, of $1/share on its common stock. Investors expect that its dividend will grow at a constant rate of 10% per year, and they require a return of 15% on this stock. What is the value of this stock based on the discounted dividend model?
25. Mike’s Pizza just paid a dividend, D₀, of $0.50/share on its common stock. Investors expect that its dividend will decline at a constant rate of 10% per year. That is, the expected growth rate g is -10%. They require a return of 15% on this stock. What is the value of this stock based on the discounted dividend model?

26. A year ago, an investor purchased bonds in General Electric at par. The bond had a coupon of 8% at the date of issue. The bond declined over the course of the year to 94. What is the current yield on the bond?

27. A year ago, an investor purchased 100 shares of General Electric stock at a price of $20.00/share. The firm has just paid its annual dividend of $1.50. Now the share is priced at

$15.75 per share in the market. What is his holding period return on the stock?

28. Consider a $1,000 par value bond issued by AT&T with a maturity date in 20 years and a stated coupon of 8.5%. Suppose another bond of equal risk carries a rate of 7.5%. What is the intrinsic value of the bond? What should it be worth?
29. Suppose you buy a bond for $1230 with an 11.3% coupon maturing in 7 years. Suppose bond pays quarterly. What’s the bonds yield to maturity?

30. XYZ bonds have a face value of $1,000 and a 10% coupon paid semiannually; the bonds mature in 5 years. What is the current yield if the yield to maturity is 5%?
31. You made a purchase of Emerson Electric stock one year ago today. The purchase price was 32.73. Over the course of the year you have collected $1.32 in cash dividends, and the stock has appreciated to 37.75. What is your holding period rate of return?
32. A zero coupon bond will mature in 8 years and pay its face value of $1,000. Its current market value is $590. What is its implicit yield to maturity based on annual compounding?

33. A zero coupon bond will mature in 7 years and pay its face value of $1,000. Its current market value is $700. What is its implicit yield to maturity based on semi-annual compounding?

34. Joe is looking to buy a used car for $10,000. He is going to borrow the money at a rate of 12%, to be paid back in 5 equal and annual installments. How much is each one of Joe’s payments?

35. XYZ Inc. has some bonds outstanding, currently with 10 years remaining to maturity. The coupon rate is 8%, and the interest is paid semi-annually. The face value of the

bonds is $100. What is the present value of the interest coupon stream if the yield to maturity is 10%?

36. XYZ Inc. has some bonds outstanding, currently with 20 years remaining to maturity. The coupon rate is 6%, and the interest is paid semi-annually. The face value of the bonds is $1,000. What is the present value of the principal payment of par value at maturity stream if the yield to maturity is 12%?]
37. One year ago you purchased a zero coupon bond and paid $725 for it. It now has 6 years remaining to maturity, and its yield to maturity is 8%. Its face value is $1,000. Find the change in dollar value of the bond in this period.

38. Joe bought 100 shares of XYZ stock for $50. XYZ pays a dividend of $3 per year. One year later XYZ’s stock price has dropped to $41. What is XYZ’s current dividend yield?