Lecturer: Shaling Li Acc&Fin Dept, PBS University of Portsmouth 22 October, 2009

Re-cap from last week S.LI, ACCFIN, PBS2 Theoretical world: Rationality Frictionless market Liquidity Government role + Models, results Real world: UK London exchange

Structure of this lecture Nutshell of the Discounted Cash Flow (DCF)model Key definitions Modelling Applications S.LI, ACCFIN, PBS3

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, PBS4

Nutshell of this model S.LI, ACCFIN, PBS5 Input Output

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, PBS6

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, PBS7

A very basic example S.LI, ACCFIN, PBS8 FV PV

Discounted Cash Flow Model More complexity added 1. Single-period case to the multiple-period case 2. Single cash flow to multiple of cash flows S.LI, ACCFIN, PBS9

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*5% = £115 ) Compounding interest method: £100*(1+5%) 3 =£ S.LI, ACCFIN, PBS10

PV with compounding interest S.LI, ACCFIN, PBS11 FV PV

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%) *(1+5%) *(1+5%) = £ S.LI, ACCFIN, PBS

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%) /(1+5) 3 = £ S.LI, ACCFIN, PBS

The full DCF model S.LI, ACCFIN, PBS14 FV PV

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, PBS15

Important issues 1. Draw the timeline and cash flows 2. Be careful with money flow point (in the beginning or end of year t) 3. Be familiar with the simple model and the complex one S.LI, ACCFIN, PBS16

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, PBS17

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, PBS18

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, PBS19

How to calculate it with Excel S.LI, ACCFIN, PBS20

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, PBS21

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, PBS22