Financial & Managerial Accounting Present Value & Future Value: In general, applied to bonds & stocks, capital investments

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1 Financial & Managerial Accounting Present Value & Future Value: In general, applied to bonds & stocks, capital investments Part I: Present Value and Future Value 1. You deposit $1,000 into a savings account which pays an interest rate of 5% annually. (A) How much will be in the account in one year? (B) If the interest rate increases to 10%, then how much will you have in one year? (C) If the interest rate was 5% again, then how much will you have in 10 years? (D) If the interest was 10%, then how much will you have in 20 years? 2. (A) One year from now you plan to purchase a $5,000 used car. Your bank is offering 10% interest on a one year CD (certificate of deposit). How much should you put into the CD in order to have enough to buy the car? (B) If the interest rate on the CD was 5%, then how much would you need to deposit in order to buy the car? 3. Suppose you want to retire in 30 years. You figure that you d be able to retire on $1,000,000 quite comfortably. Assuming an 8% annual interest rate on a bank account, how much would you have to place in the bank account today in order to hit your retirement goal? 4. (A) Your roommate asks you for a loan of $200. You agree to loan your roommate the money for one year. At the end of the one year, your roommate promises to pay you $240. What interest rate did you charge your roommate? (B) Suppose all you had was $180 and your roommate still promised to pay you $240 in one year. What is the interest rate now? 5. Assume interest is paid twice per year on a savings account. You deposit $1,000 into the savings account which pays an annual interest rate of 8%. How much will be in the account in two years? What if the savings account had paid interest four times per year? 6. Assume interest is paid once per year on a CD. Two years from now you plan to purchase a $5,000 used car. Your bank is offering 10% on a two year CD (certificate of deposit). How much should you put into the CD in order to have enough to buy the car? 7. Suppose you win the lottery! You are given two payment options. Option 1 is a lump sum payment of $750,000 today. Option 2 is a yearly payment of $100,000 for the next 10 years. (a) Assuming a discount rate of 10%, which option would you choose? (b) What if the discount rate had been 5%? (c) What discount rate would make you indifferent between the two options (note, you ll need to use Excel or a financial calculator to solve this part) 8. Assuming a discount rate of 4% find the total present value of the following payments. End of Year 1 $2,000 End of Year 2 $3,000 End of Year 3 $2,000

2 9. Suppose you are offered the following two options. Option 1 is that you receive $250,000 for the next four years. Option 2 is that you receive an annual payment of $50,000 forever (your grandchildren will get the payment after you die, etc.). Assuming a discount rate of 7%, which option would you choose? 10. Suppose you purchase a contract that will pay you $2,000 per year forever. You paid $40,000 for this contract. What is the interest rate you ll earn? Part II: Present Value applied to Debt and Equity I. Bonds (Debt) A. Discount Bonds 1. The Face Value of a one-year discount bond is $100. Your required rate of return for this 2. The Face Value of a one-year discount bond is $100. Your required rate of return for this bond is 20%. What would you be willing to pay for the bond? 3. The Face Value of a two-year discount bond is $100. Your required rate of return for this 4. The Face Value of a ten-year discount bond is $100. Your required rate of return for this 5. The Face Value of a one-year discount bond is $100. The bond is currently selling for $90. If held to maturity, what is the interest rate (or, yield to maturity) that you would earn on the bond? 6. The Face Value of a one-year discount bond is $100. The bond is currently selling for $95. If held to maturity, what is the interest rate (or, yield to maturity) that you would earn on the bond?

3 7. The Face Value of a two-year discount bond is $100. The bond is currently selling for $90. If held to maturity, what is the interest rate (or, yield to maturity) that you would earn on the bond? B. Coupon Bonds 8. The Face Value of a one-year coupon bond is $100 with a coupon rate of 10%. Your required rate of return for this 9. The Face Value of a one-year coupon bond is $100 with a coupon rate of 10%. Your required rate of return for this bond is 5%. What would you be willing to pay for the bond? 10. The Face Value of a two-year coupon bond is $100 with a coupon rate of 10%. Your required rate of return for this bond is 5%. What would you be willing to pay for the bond? 11. The Face Value of a two-year coupon bond is $100 with a coupon rate of 10%. The bond is currently selling at $92. If held to maturity, what is the interest rate (i.e., yield to maturity) on the bond? II. Preferred Stock (Hybrid) 12. A stock promises to pay a dividend of $10 per year. Your required rate of return is 10%. What is the most you would be willing to pay for this stock? 13. A stock promises to pay a dividend of $20 per year. Your required rate of return is 10%. What is the most you would be willing to pay for this stock? 14. A stock promises to pay a dividend of $10 per year. Your required rate of return is 5%.

4 What is the most you would be willing to pay for this stock? 15. A stock promises to pay a dividend of $10 per year. The stock is currently priced at $80. What is the required rate of return on this stock? 16. A stock promises to pay a dividend of $8 per year. The stock is currently priced at $80. What is the required rate of return on this stock? III. Common Stock (Equity) 17. A stock is expected to pay a $10 dividend next year. The dividend is not expected to grow. Your required rate of return is 20%. What is the most you would be willing to pay for this stock? 18. A stock is expected to pay a $10 dividend next year. The dividend is expected to grow by 10% each year. Your required rate of return is 20%. What is the most you would be willing to pay for this stock? 19. A stock is expected to pay a $10 dividend next year. The dividend is expected to grow by 5% each year. Your required rate of return is 20%. What is the most you would be willing to pay for this stock? 20. A stock is expected to pay a $20 dividend next year and grow at a rate of 6%. The stock is currently selling for $100. What is the rate of return on the stock? 21. A stock is expected to pay a $20 dividend next year and grow at a rate of 6%. The stock is currently selling for $80. What is the rate of return on the stock?

5 22. A stock is expected to pay a $20 dividend next year and grow at a rate of 6%. The stock is currently selling for $120. What is the rate of return on the stock? Part III: Present Value applied to Capital Investments 1. Lee s Law Service is considering purchasing a new riding lawn mower. The mower has a cost of $4,000 and should last for two years. Lee has estimated that the mower will generate net income of $3,000 in the first year and $2,000 in the second year. Lee utilizes a 5% discount rate. If Lee uses the Net Present Value method, should he purchase the mower? 2. Endrun Corporation is choosing among two alternative capital projects. The first project has a cost of $1 million and is expected to generate net income of $1.2 million in the first and only year of the life of the project. The second project costs $50 million and is expected to generate net income of $4 million each year forever. Endrun utilizes the internal rate of return method to decide on capital projects. Which project should it do?