Lecture 3: Discounted Cash Flow Model

1. Lecture 3: Discounted Cash Flow Model Lecturer: Shaling Li Acc&Fin Dept, PBS University of Portsmouth 22 October, 2009

2. Re-cap from last week Real world: UK London exchange Theoretical world: Rationality Frictionless market Liquidity Government role + Models, results S.LI, ACCFIN, PBS

3. Structure of this lecture • Nutshell of the Discounted Cash Flow (DCF)model • Key definitions • Modelling • Applications S.LI, ACCFIN, PBS

4. Why use models? • They are easy to understand representations of something we cannot normally see. • Advantages: • Simplification of complex problems • Scientific understanding of performance and fundamental Limits • Simulations of systems • Disadvantages: • Depends on the reliability of assumptions • Cannot explain everything, has limitations S.LI, ACCFIN, PBS

5. Nutshell of this model Input Output S.LI, ACCFIN, PBS

6. Key definitions • Time value of money • The value of money earns a given amount of interest over a given amount of time • Example: £100 of today's money invested for one year and earning 5% interest will be worth £105 after one year. • Today’s £100 is more valuable than tomorrow’s £100 • Interest rate (i) • A measure of time value of money • Example: 5% S.LI, ACCFIN, PBS

7. Key definitions • Present value (PV) • Present value is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors. • Example: what is the present value of £100 one year later with interest rate 5%? (Answer: £95.24) • Future value (FV) • Future value measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate. • Example: what is the future value of £100 in one year time with interest rate 5%? (Answer: £105) S.LI, ACCFIN, PBS

8. A very basic example PV FV S.LI, ACCFIN, PBS

9. Discounted Cash Flow Model • More complexity added • Single-period case to the multiple-period case • Single cash flow to multiple of cash flows S.LI, ACCFIN, PBS

10. Complexity added-1 • The single-period case to the multiple-period case • Example: £100 of today's money invested for one year and earning 5% interest will be worth £105 after one year. • Example: £100 of today's money invested for three years and earning 5% interest will be worth ??? after three years. • Simple interest method: £100 + 3*100*5% = £115 • Compounding interest method: £100*(1+5%)3=£115.76 S.LI, ACCFIN, PBS

11. PV with compounding interest 0 1 2 3 4 5 FV PV S.LI, ACCFIN, PBS

12. Complexity added-2 • Future values (FV) of multiple of cash flows • Example: Invest £100 of today's money invested for first year, £150 in the beginning of the second year and £300 in the beginning of the third year, earning 5% interest. What would be the future value in the beginning of third year. • Future value = £100*(1+5%)3 +150*(1+5%)2+300*(1+5%) = £596.14 • 0 1 2 3 100 150 300 S.LI, ACCFIN, PBS

13. Complexity added-2 • Present values (PV)of multiple of cash flows • Example: Receive £100 in the end of the first year, £150 in the end of the second year and £300 in the end of the third year, earning 5% interest. What would be the present value of today. • Present value = £100/(1+5%)+150/(1+5%)2+300/(1+5) 3= £490.44 • 0 1 2 3 300 150 100 S.LI, ACCFIN, PBS

14. The full DCF model 0 1 2 3 4 5 FV PV S.LI, ACCFIN, PBS

15. PV with multiple cash flows • If there is a perpetual cash flow (in theory), how to calculate the present value? • C: constant cash flow in an unlimited years in the future • i: discount rate S.LI, ACCFIN, PBS

16. Important issues • Draw the timeline and cash flows • Be careful with money flow point (in the beginning or end of year t) • Be familiar with the simple model and the complex one S.LI, ACCFIN, PBS

17. Applications-Bond investment • Bond – should you buy the bond or not • Here is the deal: pay £977 to purchase the bond with face value £1000 with 10% fixed interest rate on the paper, matured in six years. • Calculate present value of all the future cash flows S.LI, ACCFIN, PBS

18. Applications-Bond investment • The present value of the bond will depend on the actual interest rate / discount rate (not the fixed interest rate on the bond) • If actual interest rate is 8%, PV=£1092, buy • If actual interest rate is 10%, PV=£1000, buy • If actual interest rate is 12%, PV=£917, not buy S.LI, ACCFIN, PBS

19. Application-Stock investment • Invest in a stock and receive dividend annually (suppose perpetual cash flow) • Example, the price for one share of company ABC is 250p per share and the dividend payout is 15p per share. The discount rate is 5% • Present value of the perpetual annual dividend income is 15/0.05=300p • Current price is 250p • Conclusion: Buy S.LI, ACCFIN, PBS

20. How to calculate it with Excel S.LI, ACCFIN, PBS

21. Important issues • Bond investment • How to know the interest rate/discount rate? • Stock investment • How to know the future cash flow? • How to know the discount factor? • There are the gaps between theory and real world. S.LI, ACCFIN, PBS

22. Summary • Why use model to describe the real world? • Key definitions to understand DCF model • Basic model • Complexity added to the model • Application: Bond and Stock investment S.LI, ACCFIN, PBS