BUS286 Corporate Finance Lesson 1
yusra@kaplan.com
Groups will be formed by Lesson 2 or 3.
Corporate (Business/Organisational) Finance
Firm
Corporation
Industrial (non-financial institution)
Domestic
Corporate Finance Decisions
(1) Investment Decisions generate returns
- Capital Investments
Investment (assets)
Real Assets Financial Assets
Eg. shares, bonds etc
Property, Equipment,
Machinery, IT system etc.
- to produce more goods and services
Capital investments (long-term)
Capex – Capital Expenditures
(2) Financing Decisions – Raising of funds
- Sell financial assets
(3) Capital structure – Sources of funds (Proportion)
- 2 mains sources: Debt eg. loans, bonds or Equity eg.
ordinary shares
Differences
Debt Equity
Eg. Loans, Bonds Eg. Ordinary and preferred shares
No ownership (lender) Ownership (shareholder)
- voting rights
Maturity No maturity
Interest is obligation Dividend is not obligation
Methods/Tools
Decisions --------------------- Objective/goal of firm
Increase Value of firm ---- Increase in share price
What is goal of firm?
- Maximisation of sales/market share? X
- Maximisation of Profits? X
- Maximisation of Shareholders’ Wealth
Example: Berkshire-Hathaway – Warren Buffet
1972 - $1
2002 - $7,000
Start: 2.20 pm
Attendance Taking: 3.00 pm
Break: About 3.30 pm (20 minutes)
Financial Mathematics – Time Value of Money
Financial Calculator: Texas BA2 Plus
Time Value of Money
If I were to give you $1,000, do you want it now or one year
from now?
Investment Inflation Risk
Interest rate
Simple Interest Compound Interest
Simple Interest
- principal is constant interest is constant
Interest rate = i = 10%
Time Line
|--------------------|-----------------------|
0 1 2
$100 I1=$10 I2=$10
Bal=$110 Bal=$120
Total interest = Principal x Interest rate x no. of years
= 100 x 0.1 x 2 = $20
Compound interest
- principal is not constant interest is not constant
- interest is earned on principal and previous period interest
i = 10%
|--------------------|-----------------------|
0 1 2
$100 I1=$10 I2=$10+$1=$11
Bal=$110 Bal=$121
i=10%
|--------------------|-----------------------|--------------|
0 n=1 n=2 n=3
$100 $110 $121 FV=100(1+0.1)^3
=100(1+0.1)^1 =110(1+0.1)
=100(1+0.1)(1+0.1)
=100(1+0.1)^2
Present Value(PV) Future Value (FV)
FV=100(1+0.1)^3
FV = PV(1+ i)^n Future Value/Compounding
|--------------------------------------|
0 n
FV/Compounding
|--------------------------------------|
0 n
PV/Discounting
PV = FV/(1+i)^n Present Value/Discounting
i = (FV/PV)^1/n - 1
FV = PV(1+i)^n
(1+i)^n = FV/PV
nln(1+i) = ln(FV/PV)
n = ln(FV/PV) / ln(1+i)
For simple interest less than one year eg. 30 days and if
interest rate is annual rate
FV = PV (1 + i (30/365) )
i = 10.6%
|--------------------------------------|
0 90 days = 500,000
? PV/Discounting
PV = 500,000/(1+0.106(90/365))^1
Always use 6 decimal places at least – final answer 2
decimals
FV = PV(1+i)^n
Annual compounding – interest is computed once a year
i = annual interest rate
n = no. of years
Non-annual compounding – interest is computed more than
once a year
Semi-annual = i/2, n x 2
Quarterly = i/4, n x 4
Monthly = i/12, n x 12
Daily = i/365, n x 365
Interest rates
Annual Percentage Rate
(Quoted/Nominal) (EIR – effective interest)
If non-annual compounding,
EAR = (1 + j/m)^m - 1
j = nominal rate (annual percentage rate)
m = no. of times compounded in a year
Eg. monthly m = 12
EAR = (1 + j/m)^m - 1
54 day return = 2.43%
Annual percentage return = 2.43 x 365/54 = 16.42%
m = 365/54
EAR = (1 + 0.1624/(365/54)) ^ (365/54)
Interest Rates
Nominal (Quoted) Real
Nominal = 1.5%
Inflation rate = 1.0%
Real interest rate = 1.5 – 1.0 = 0.5%
Nominal interest rates = Real interest rate + inflation rate
(Approximation method)
Cash Flows
Single Amount Multiple Amounts
FV, PV
Unequal Equal/Annuity
FV, PV FV or FVA
PV or PVA
Unequal: Future Value
What is value at end of Year 3?
i = 10%
|---------------|-----------------|------------|
0 1 2 3
$100 $200 $300
FV = 100(1+0.1)^2 + 200(1+0.1)^1 + 300(1+0.1)^0
Unequal: Present Value
What is the value today?
PV = 100/(1+0.1)^1 + 200/(1+0.1)^2 + 300/(1+0.1)^3
[3.28] FVA = C/i [ (1+i)^n – 1 ]
[3.19] PVA = C/i [ 1 – 1/(1+i)^n ]
|------------|--------------|-------------|
0 1 2 3
100 100 100
C = 100 (annuity)
n = no. of times cash flows occur
Annuities
Ordinary Due
(End of Year) (Begin of Year)
|-----|------|---------| |----------|--------|------|
0 1 2 3 0 1 2 3
100 100 100 100 100 100
FVA(ord) = C/i [ (1+i)^n – 1 ] FVA(due)=FVA(ord) x (1+i)
PVA(ord) = C/i [ 1 – 1/(1+i)^n ] PVA(due)=PVA(ord)x(1+i)
Deferred Annuity (PVA) [3.24]
Annuity starts k years from today
PVA = PVA(ord) x 1/(1+i)^(k-1)
PVA = C/i [ 1 – 1/(1+i)^n ] x 1/(1+i)^(k-1)
PVA = C/i [ 1 – 1/(1+i)^n ] – Investment outlay
= 2770/i [ 1 – 1/(1+i)^5 ] – 10,000
Solve for i
Use IRR function
