B294 - Unit 3
Mathematical concepts and statistical tools
Variance
Covariance and correlation
Average
Mean
Add data together
Divide by data set number
Weighted
Data x weights
Divide by weights
Range
Standard deviation
Variance
Square data set
Difficult to relate to data set
Square root of variance
Same units as data set
Covariance
Coefficient correlation
Relationship between two variables
Negative
Positive
move in same direction
Move in opposite directions
0
-1
+1
No correlation
Perfect negative correlation
Perfect positive correlation
As one increases, other decreases
As one increases the other decreases
Session 1
Time value of money
Cost of capital
Three factors
Inflation
Opportunity cost
Risk
Future
Cash flows
Benefits
May not happen
Greater for greater return
Greater for loss
Smaller for smaller reward
Smaller loss
Increase in cost over time
Can money be spent elsewhere?
Interest
Simple
Compound
% per year
% applies to new balance
Future value formula
Future value (FV) = Present value(1 + annual interest rate) squared by number of years
Discounted cash flows
Reverse of compounding
PV = FV / (1+r) squared by number of years
Session 2
The cost of capital
Debt and equity
Have costs
Investor
Company
Between investment options
Different projects
Overall financing
Allows project completion
Opportunity cost
Expected return in light of
Inflation
Risk
Greater than
Reflect those taken
Risk return trade-off
Risk free rate of return
Safe investments
Gilts
Savings account
Unlikely government won't pay
The cost of equity
E(Rh) = Rf + Rp
E(Rh) = expected rate of return on share h
Rf = risk free rate
Rp = Risk premium
Compensates opportunity cost
Excess return for higher risk investments
Reducing risk
Portfolio diversification
Markovitz (1952)
Risk reduced via spread of assets
Different companies in different markets
Specific risk can be eliminated
Theoretically
Capital asset pricing model (CAPM)
Simplified assumptions
Investor behaviour
Functionality of markets
Dividend valuation model (DVM)
Determine trade-off between expected return and risk
The cost of debt
Investment carries risk
Interest/capital may not be repaid
Require higher returns
In exchange for risk
Credit risk premium
Historical cost of debt
Tax-shield
Interest payments deducted from taxable profits
Dividends non-tax deductible
Capital structure
Debt / equity mix
Weight of costed capital (WACC)
Provides base discount rate for investment appraisal
Cost of investment
Combines all finance sources
Return must be higher than WACC to generate profit