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1 Title page Debt» What's Behind the Numbers?» Scenic Video

2 Agenda Introduction Single cash flow Future value formula Present value formula Tables Multiple cash flows Present value formula Annuities Risk and return Excel Present values Internal rates of return Take-aways

3 Introduction: present value intuition Suppose you want to buy your best friend a birthday gift six months from now that cost $100 and you plan to put just enough money in a risk-free, interest-bearing savings account today to ensure you will have exactly $100 in the bank six months from now (so you can buy the gift at that time). If you know the answer to the following questions, you can easily grasp the present value concept: 1. Should you put exactly $100 in the bank today, less than $100, or more than $100? 2. If you decide you want to buy a gift for $200 instead of $100, should you put more money in the bank today than if you plan to purchase a $100 gift? 3. If you find your friend s birthday is actually nine months from today rather than six months, should you put more (or less) money in the bank today than you originally planned to put in when you thought it was six months from today? 4. If you assume your friend s birthday is six months from today but you find out the interest rate the bank will pay on your savings account is actually higher than you originally anticipated, should you put more (or less) money in the bank than you originally anticipated with the lower interest rates?

4 Introduction: key concepts Present Values and Future Values The amount you put in the bank today is called the present value of a $100 cash flow six months from now discounted at the savings-account interest rate. The $100 you will receive six months from now is called the future value of the amount you put in the savings account today. Factors that Determine Present Values Future value: The higher the future value to be discounted, the greater the present value. Discount rate: The higher the discount rate, the lower the present value. Investment horizon: The longer the investment period, the smaller the present value. Factors that Determine Future Values Present value: The higher the present value invested today, the greater the future value. Rate of return: The higher the rate of return on the investment, the greater the future value. Investment horizon: The longer the investment period, the larger the future value.

5 Single cash flow: future value formula

6 Single cash flow: future value formula

7 Single cash flow: future value formula

8 Single cash flow: future value formula

9 Single cash flow: future value formula

10 Single cash flow: present value formula

11 Single cash flow: future value table

12 Single cash flow: present value table

13 Multiple cash flows: present value formula

14 Multiple cash flows: present value formula

15 Multiple cash flows: annuities

16 Multiple cash flows: annuities

17 Risk and Return The riskier an expected future cash flow, the higher the expected return investors will require (rate of return, r) Stated alternatively, the less investors will be willing to pay for the investment today (present value).

18 Excel: Determining present value of specified future cash flows

19 Excel: Determining internal rate of return

20 Excel: Determining internal rate of return

21

22 Take-aways What should you know? Present value is one of the most important concepts in finance: a dollar today is worth more than a dollar in the future. Intuitively and from the future value formula, we see that three factors determine the future value of a present cash flow: The bigger the present value, the bigger the future value The bigger the rate of return, the bigger the future value The longer the investment horizon, the bigger the future value Similarly, from the present value formula, we see that three factors determine the present value of a future cash flow: The bigger the future value, the bigger the present value The bigger the discount rate, the smaller the present value The longer the investment horizon, the smaller the present value Present values and future values can be determined using formulas, tables, or Excel functions The present value of a distinct series of future cash flows is the sum of their present values An annuity is a series of identical future cash flows. Annuity tables and functions simplify annuity calculations. The riskier the expected future cash flows, the higher the discount rate and the lower the present value The internal rate of return is the discount rate that discounts a specified series of future cash flows to a specified present value.

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