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Unformatted text preview: Last Last time we discussed… Time Time value of money
• Would you prefer $1000 today, or one year from today? • Time value of $$: one dollar today is worth more than one dollar tomorrow • Suppose a one‐year CD pays an annual interest rate of 2%. If you invested $1000 in this CD, how much would you have in one year? • ^^ this is referred to as the Future Value (FV) of $1000 invested for one year at an annual rate of 2%. Simple Simple vs. compound interest
• Let’s say you put $1000 in a savings account that pays 3% per year. • If you pulled out the $20 interest earned each year (and left it in your mattress), how much would you have in 5 years? In 50 years? • If you left in the accumulated interest to reinvest, how much would you have in 5 years? In 50 years? Simple Simple vs. compound interest Principal $1000 Rate 3% Period Period Simple Compound 0 1000 1000 1 1030 1030 2 1060.00 1060.90 3 1090.00 1092.73 … … … 10 1,300.00 1,343.92 20 20 1,600.00 1,806.11 50 2,500.00 4,383.91 100 4,000.00 19,218.63 Simple Simple vs. compound interest
• If you pull out the interest earned each period, then you only earn interest on the original amount
– Simple interest: interest earned only on the original principal amount invested – FV = Principal × (1 + r ×T) • When you leave $$ and accumulated interest in an investment for a long time, the interest compounds, earning you interest on interest
– Compound interest: interest earned on both the initial principal and the interest reinvested from prior periods – FV = Principal × (1 + r)T Another Another example
• You accept a starting position for $40,000. Your firm has promised you a 5% raise each year. What will be your salary 30 years from now? • Now let’s consider the flip side: Suppose two years from now, your car will need $1000 worth of maintenance repairs. Your bank offers you a 5% rate of return on deposits annually. How much should you put away right now?
– Notice how instead of compounding cash flows into the future, we are discounting them back to the present Present Present value
• Present value (PV) is the current value of future cash flows discounted at the appropriate discount rate
– The discount rate is also referred to as the opportunity cost of capital or the required rate of return.. PV 1 r FV
T or PV FV 1 r T • An investment will pay $5000 in five years. What is the present value if the relevant discount rate is 10%? Re: Re: the relevant discount rate
• Your friend says he will pay you $1000 one year from today. Your friend is unreliable and often does not keep his promises. The I‐Bond (a government bond) currently offers a 3.36% rate of return. You want to know what is the present value of your friend’s $1000 promise. Is 3.36% the appropriate discount rate? Consumption Consumption smoothing
• You currently have no money, but your trustworthy aunt promises to give you $1050 next year. Your bank has offered you a personal loan at a rate of 10%. – What is the maximum amount you can spend right now? – What if you want to spend the same amount this year as you do next year (i.e., you want to smooth consumption). • How much should you borrow from the bank? • How much will you spend in each year? Discount Discount rate (r)
• An investment pays off $1100 next year. You must put in $1000 now. What is the return on this investment (i.e., what is the discount rate)? • What if you have an investment that pays off $998.25 in three years, and you must put in $750 now. What is the annual rate of return on this investment? • Recall: PV 1 r FV
T FV • Thus, discount rate = r PV 1/ T 1 Number Number of periods (T)
• You have $1000 to invest. How long will it take to save up $1,331 if your investment pays a rate of 10% annually? • Thus, # of periods = T ln FV V ln 1 r PV Next Next class
• Discounted cash flow valuation (chapter 6) ...
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This note was uploaded on 01/31/2011 for the course MGMT 310 taught by Professor Matthewjamesbarcaskey during the Spring '08 term at Purdue University-West Lafayette.
- Spring '08