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2. Financial Math II BMA Ch 3 Compounding PV of Cash Flow Stream Perpetuities Annuities Real v. Nominal Interest (and Discount) Rates (inflation)

3. Present Value We have replaced FV with C in PV formula. C t now designates Cash Flow in year t In Session 2, –t=1 –C = 100 –PV of $100 one year from now is $89.29 We can calculate the PV of cash flow at any time in future, using compounding

4. Compounding –Annual PV (1+r) (1+r) = FV 2 PV (1+r) 2 = FV 2 PV (1+r) t = FV t PV = FV t / (1+r) t Ex: What is the PV of $100 received two years from now, if r =.12?

5. Compounding –Discrete, but more frequently than annual FV t = PV (1 + r/m) mt PV = FV t / (1 + r/m) mt Ex: What is the value in one year of an investment of 100 at 8 percent compounded annually? quarterly? daily? Note: More frequent compounding results in higher effective annual yield

6. Present Value of Cash Flow Stream General Ex: What is the PV of the following stream of cash flows: yr 1: 100 yr 2: 150 yr 3: 165, if r=.07?

7. Present Value of Cash Flow Stream Perpetuity – Constant stream of cash flows forever Applications: 1.Valuation of non-growth stocks 2.Estimation of terminal values in investment decisions

8. Present Value of Cash Flow Stream Growing Perpetuity – Stream of cash flows that grows at a constant rate forever Application: Valuation of growth stocks

9. Present Value of Cash Flow Stream Annuity – Constant stream of cash flows for a term Don’t memorize! Applications: 1.Valuation of bonds 2.Valuation of your lottery winnings Ex: What is the value of winning a $1,000,000 lottery, if payout is in 20 annual installments?

10. Real v. Nominal Interest (and Discount) Rates Nominal rate –Rate stated on a financial instrument –Known a priori Real rate –Nominal rate adjusted for inflation –Can only be known after the fact Exact math relationship (1+nom) = (1+real)*(1+inf)1.1=1.038*1.06 Common approximation nom = real + inf.1 ≈.038 +.06 close enough