The Time Value of Money: Present Value and Future Value

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May Stevens
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1 The Time Value of Money: Present Value and Future Value 1. [Future Value] (A) You deposit $1,000 into a savings account which pays an interest rate of 5%. How much will be in the account in one year? FV = 1000(1+.05) = = $1,050 (B) If the interest rate increases to 10%, then how much will you have in one year? FV = 1000(1+.10) = = $1, [Present Value] (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? PV = 5,000/(1.10) = $4,545 (B) If the interest rate on the CD was 5%, then how much would you need to deposit in order to buy the car? PV = 5,000/(1.05) = $4, [interest rate] (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? R = (240/200)-1 = 20% (B) Suppose all you had was $180 and your roommate still promised to pay you $240 in one year. What is the interest rate? R = (240/180) -1 = 33% 4. [Future Value] Assume interest is paid once per year on a saving account. You deposit $1,000 into a savings account which pays an interest rate of 5%. How much will be in the account in two years? FV = 1,000 (1.05)(1.05) = $1, [Present Value] 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? PV = 5,000/(1.10)2 = $4,132

2 Value of 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 bond is 10%. What would you be willing to pay for the bond? P = 100/(1.10) = $ 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? P = 100/(1.20) = $ The Face Value of a two-year discount bond is $100. Your required rate of return for this bond is 10%. What would you be willing to pay for the bond? P = 100/(1.10)^2 = $ The Face Value of a ten-year discount bond is $100. Your required rate of return for this bond is 10%. What would you be willing to pay for the bond? P = 100/(1.10)^10 = $ 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? R = (100/90)-1 = 11.11% 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? R = (100/95)-1 = 5.26% 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? R = (100/90)^(1/2)-1 = 5.41%

3 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 bond is 10%. What would you be willing to pay for the bond? P = ( )/(1.10) = $ 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? P = ( )/(1.05) = $ 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? P = (10)/(1.05) + ( )/(1.05)^2 = $ 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? Cannot do! 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? P = 10/.10 = $ 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? P = 20/.10 = $ A stock promises to pay a dividend of $10 per year. Your required rate of return is 5%. What is the most you would be willing to pay for this stock? P = 10/.05 = $200

4 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? R = 10/80 = 12.5% 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? R = 8/80 = 10% 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? P = 10 / (.20 0) = $ 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? P = 10 / (.20.10) = $ 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? P = 10 / (.20.05) = $ 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? R = (20/100) +.06 = 26% 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? R = (20/80) +.06 = 31% 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? R = (20/120) +.06 = 16.67% + 6% = 22.67%

5 Capital Investment Analysis: Not Using the Time Value of Money 1. U-Poor Coffee is considering purchasing a new coffee press costing $1 million. The coffee press is estimated to last for 4 years with no salvage value. U-Poor has estimated that the coffee press will raise annual income (after depreciation expense) by $400,000 over the 4 year period. Calculate the average rate of return from the purchase. 2. U-Poor is considering another capital investment project. This investment project is a new warehouse costing $10 million and lasting for 10 years. The estimated annual income (after depreciation expense) is $500,000 for the life of the warehouse. Calculate the average rate of return from this purchase. If U-Poor is only going to do one of these projects, then which is best? 3. Kudos (an Internet greeting card company) is considering purchasing a new server for $50,000. Kudos estimates that the server will generate annual cash revenues of $30,000 and require annual cash expenses of $10,000. Calculate the cash payback period for this investment.

6 Capital Investment Analysis: Using the Time Value of Money 4. 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? 5. 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?

Time Value of Money. Ex: How much a bond, which can be cashed out in 2 years, is worth today

Time Value of Money. Ex: How much a bond, which can be cashed out in 2 years, is worth today Time Value of Money The time value of money is the idea that money available now is worth more than the same amount in the future - this is essentially why interest exists. Present value is the current