AIX Finance Lecture Student Notes

AIX Finance Lecture Student Notes - I FIRST PRINCIPLES OF...

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I. FIRST PRINCIPLES OF VALUATION Always remember: A dollar (euro) in the hand today is worth more than a dollar (euro) promised some time in the future, i.e., money has time value! If you have it today, you can invest it or use it. It is rather difficult to invest or use a promise of some future funds. A. Future Value and Compounding Investing for single period FV = P(1+r), where P = principal invested, and r = the interest rate on the investment. What is the FV of $500 invested for one year at 10%; FV = $500(1.10) = $550. Investing for more than one period FV = P(1+r) t, where t = the number of periods in the future What is the FV of $500 invested for 2 years at 10%; FV = $500(1.10) 2 = $500(1.21) = $605 Note: there are two elements in the $105 interest; o There is the interest on the principal; $50 each year (total $100), and o There is the interest on the first year’s interest; $50 x .10 = $5 This is the result of compounding. For example, the same $500 left on deposit for 5 years, at simple and compound interest would be, after 5 years: Simple interest: $750 Compound interest: $805 How does one calculate the factor (1+r) t ? You can do it manually, using your calculator, your computer or the Future Value Tables (found, along with Present Value and Annuity Tables, in most basic financial management textbooks). The Financial Tables o For any interest rate and time period, the table will give the value of $1 for that number of periods in the future. 1
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B. Present Value and Discounting What is Present Value? It is the current value of a future cash flow(s), discounted at an appropriate discount factor (or interest rate). This follows the same principle as compounding. Alternatively:What will we need today, invested at that same rate, to give us an amount equal to the future cash flow? Recall that FV = P(V)(1+r) t ; let’s do some simple algebra, then PV = FV/(1+r) t , where r is the discount rate for t periods of time in the future Let’s look at a single period example: An antique auto dealer can buy a “mint condition” 1928 Bugatti auto for $60,000. He is certain that he can resell the car in one year for $70,000. He also has the opportunity to make a well-collateralized loan to an acquaintance for one year at 12% (assume essentially no risk). What should he do? Before solving this problem, let’s introduce the concept of “Opportunity Cost .” Opportunity cost is simply the best alternative financial opportunity that exists, at the same risk level as the one under consideration. In the auto example, it is the 12% certain, that he can earn on the loan. Therefore, the appropriate discount rate is 12%. PV = $70,000/(1+0.12) = $62,500 vs. the $60,000 that he must pay for the car today. If he made the loan, then his PV (at 12%, of course) is $60,000. (If he makes the loan to his acquaintance, he will receive in one year $67,200 – his $60,000 plus the 12% interest, or $7200. $67,200/1.12) = $60,000.) Present value of multiple periods Suppose that your favorite uncle promises you $100,000 for your 30 th birthday, which is 8 years from now. He also says that if you are in a hurry, he will give you $50,000 tomorrow, which is your 22 nd birthday.
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