1. Time value of Money u By the end of this class you should … u Understand basic time value of money concepts –Be able to apply concepts to: »Determine the present value of a future cash flow »Determine the present value of an annuity »infer effective interest rates

2. Time Value of Money - Examples u Would you rather have $100 today or $100 in one year? u Would you rather have $100 today or $120 in one year? u What’s the deal?

3. Time value of Money- Examples u How much do I need to save for my retirement? u I win the lottery and want to spend it all, but still pay for my kids’ education. How much do I spend? u I win the texas lottery ($1,000,000). Can I exchange the winning ticket for a $1,000,000 home? –What’s the deal?

4. Time Value of Money u Is this just a make-work program for accountants? u Where, if anywhere, are present values used in accounting? (specially Financial Accounting)

5. Vocabulary u PV:Present Value u FV:Future Value u Pmt:Payment u n:Number of “periods” u r:Discount rate, Borrowing rate

6. Basics of Present Values: single payments, compound interest u FV = PV (1+ r) - for one period u FV = PV(1+r)(1+r) –for two periods u FV = PV(1+r) n –for n periods u PV = FV(1+r) -n u Note: the discount rate, r, must be on the same basis as the periods, n. For example, if the periods are years, the rate must be annual. If the periods are quarters, the rate must be in effective quarterly rate.

7. More Vocabulary u Stated Rate = Coupon Rate = Nominal Rate u Effective Rate = rate that considers compounding u APR = Annual Percentage Rate = Annualized Effective rate u Real Rate = Nominal rate - inflation u Principal = Face Value = Par Value u Coupon Payment = Interest Payment

8. Basics of Present Value: Streams of Payments u Example: An insurance contract (annuity) will pay you $100,000 per year for the next 20 years. How much will the contract cost? u PV annuity = Payment ( PV annuity factor, r = ?, n = ?) u This factor is simply the sum of the series of single payment factors u Annuity in Arrears: first payment at time 1 ( also known as an Ordinary annuity) u Annuity Due: first payment at time 0 –use calculator

9. Maya --- ROI u September 1, 1997 you buy 100 shares o Maya, Inc., at $50/share. You want to earn 12% compounded annually u What is the minimum price that would achieve this by August 31, 1997? u What is the minimum price that would achieve this by August 31, 1998? u What is the minimum price that would achieve this by August 31, 1999 ? u On August 31, 1999 you sell the shares for $6,000. What annual compound rate of return did you earn?

10. Maya --- ROI u You want to earn a 12% rate of return compounded annually. How much would you pay for: u 1) 100 shares of Maya that you expect to sell for $5,500 in one year? u 2) 100 shares of Maya that you expect to sell for $5,500 in two years? u 3) 100 shares of Maya that you expect to sell for $5,500 in five years and which pay dividends of $5.00 per share at the end of each year ?

11. Rite-Aid -- Lease or Buy? u Buy a computer for $15,000 or u Lease it for $305 per month for 36 months ( first and last payment due up front), $8,500 purchase option at the end of the three years u Need computer for six years, so you would exercise the option u Hydron’s annual cost of capital is 8.5% compounded monthly u What qualitative factors need to be considered before making a final decision?

12. Take-Home Point u Time value of money is an important concept and is used ( in conjunction with the principle of objectivity) in many places in the F/S u You should understand the vocabulary of “present values” u You should be able to compute present and future values of single payments and streams of payments u You should understand the decision rules investors and managers use when they apply time of money techniques

13. Next time u Understanding basic valuation methods and their relationships to the F/S –Apply the methods to Maple Leaf Gardens.