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