Business Finance I BCO 212
Agustin Mackinlay
a.mackinlay@euruni.edu
Week 10, Fall 2015
_
Building a stock market index
Reading exercises
Introducing forward and futures markets
1
[1] Building a Stock Market Index
You have all heard about a stock market in
Business Finance I BCO 212
Agustin Mackinlay
a.mackinlay@euruni.edu
Week 10, Fall 2015
_
Introducing the Cost of Equity: the build-up approach
Stock price estimates: the Dividend Discount Model
Exercises
Building a stock market index
Reading exercises
Int
Business Finance I BCO 212
Agustin Mackinlay
a.mackinlay@euruni.edu
Week 9, Fall 2015
_
The Weighted Average Cost of Capital
An introduction to the cost of debt
Estimating the cost of equity with the build-up method
Calculating the (pre-tax) Weighted Aver
Business Finance I BCO 212
Agustin Mackinlay
a.mackinlay@euruni.edu
Week 8, Fall 2015
_
An introduction to bond pricing
Yield-to-maturity
The inverse relationship
Bond pricing exercises
An introduction to the cost of debt
1
[1] An introduction to bond pri
Business Finance I BCO 212
Agustin Mackinlay
a.mackinlay@euruni.edu
Week 7, Fall 2015
_
A review of Assignment No. 1 and Mid-Term Exam
n introduction to bond pricing
Debt finance: lots of innovation!
Characteristics of bonds
Bond issuance and the liquidit
Business Finance I BCO 212
Agustin Mackinlay
a.mackinlay@euruni.edu
Week 5, Fall 2015
_
Cash flow determination
Changes in working capital and cash flow determination
Debt financing in the real world
An introduction to bond pricing
1
[1] Cash Flow Determi
Business Finance I BCO 212
Agustin Mackinlay
a.mackinlay@euruni.edu
Week 3, Fall 2015
_
Introducing Net Present Value
NPV and the Small Construction Company
The Internal Rate of Return
Cash flow determination
The Pay Back rule
1
[1] Introducing Net Presen
Business Finance I BCO 212
Agustin Mackinlay
a.mackinlay@euruni.edu
Week 4, Fall 2015
_
The Payback rule
Additional NPV and IRR exercise
Cash flow determination
Changes in working capital and cash flow determination
Trends in debt financing
Characteristic
Business Finance I BCO 212
Agustin Mackinlay
a.mackinlay@euruni.edu
Week 1, Fall 2015
_
A (brief) and mutual presentation
Grading and exams
The Objectives of Business Finance
Valuation: compound interest, Future Value, Present Value
Properties of Present
Business Finance I BCO 212
Agustin Mackinlay
a.mackinlay@euruni.edu
Week 2, Fall 2015
_
Valuation: compound interest, Future Value, Present Value
Properties of Present Value
Annuities
Perpetuities
Loan amortization
PV of uneven streams of cash
1
Future Va
Mathematics of Finance
Week 9 April 2015
Agustin Mackinlay
a.mackinlay@euruni.edu
Growing perpetuities
Properties of Present Value
An introduction to bond pricing (European bonds)
Bond valuation with semi-annual coupons
1
[1] Growing perpetuities
A growin
Mathematics of Finance
February 2015
Week 1
Agustin Mackinlay
a.mackinlay@euruni.edu
A brief (and mutual) introduction
A word on the program
Percentages and rates of return
Simple interest: present value and future value
Interest on bank balances: exercis
Mathematics of Finance
Week 4 February 2015
Agustin Mackinlay
a.mackinlay@euruni.edu
Nominal and Effective Interest Rates
Present Value with Multiple Cash-Flows
PV and FV of Ordinary Annuities
1
[1] Nominal and effective interest rates
You need to disting
Mathematics of Finance
Week 3 February 2015
Agustin Mackinlay
a.mackinlay@euruni.edu
FV and PV with compound interest
Compound Interest: semi-annual, quarterly and monthly compounding
Nominal and effective rates
Zero-coupon bonds
1
[1] FV and PV with annu
Mathematics of Finance
Week 5 February 2015
Agustin Mackinlay
a.mackinlay@euruni.edu
PV and FV of Ordinary Annuities
Other types of annuities: annuities due, delayed annuities
Perpetuities
1
[1] Ordinary annuities
An entrepreneur needs money today to star
Mathematics of Finance
Week 8 March 2015
Agustin Mackinlay
a.mackinlay@euruni.edu
More exercises with annuities
Perpetuities
Growing perpetuities
Properties of Present Value
1
[1] Annuities: exercises
(1) You have a choice of buying a copier for $10,000 i
Mathematics of Finance
Week 10 April 22,-24, 2015
Agustin Mackinlay
a.mackinlay@euruni.edu
Bond pricing (European bonds)
The meaning of the price of a bond: the yield-to-maturity
Loans: the French system
Loans: the Italian system
1
[1] Bond Valuation Basi
LOANS - FRENCH SYSTEM
1
LOANS - FRENCH SYSTEM
Fill the amortization table for a loan of 4 million, 5 years maturity and 6% annual interest rate
The loan is to be paid with the French system .
1
Loan
Annual interest rate
Number of periods
Annual payment
Lo
NOMINAL AND EFFECTIVE RATES
1 + rf
rf
r
t
n
1
2
3
=
(1 + r/n)^(nt)
effective interest rate
annual interest rate
time in years
number of compounding periods
Given the annual nominal interest rate and the compounding frequency, calculate the annual
effectiv
2
An ordinary annuity promises to pay 5,000 during the next four years. Calculate the present value of
the annuity using: (a) the sum of the discounted cash-flows; (b) the Excel =NPV function; (c) the
Excel =PV function; (d) the 'shortcut' formula. The in
2
An ordinary annuity promises to pay 5,000 during the next four years. Calculate the present value of
the annuity using: (a) the sum of the discounted cash-flows; (b) the Excel =NPV function; (c) the
Excel =PV function; (d) the 'shortcut' formula. The in
1
FV and PV WITH ANNUAL COMPOUNDING
FV and PV WITH ANNUAL COMPOUNDING
PV = FV / ( 1 + r )^t
r
annual interest rate
t
time in years
PV = FV / ( 1 + r )^t
r
annual interest rate
t
time in years
A deposits $500 in an account that earns 2.5% compounded annual
1
If the consumer price index rises from 100 to 105 in one year and you invest at a 7%
simple interest rate, what is your real interest rate?
Interest rate
Consumer price index
Inflation rate
0
100
Answer
1
105
1
If the consumer price index rises from 100
1
Brazilian company Petrobras is borrowing money with two bonds in euros. Calculate their
price: (a) The first bond matures five years from now and a coupon of 5%. The next coupon payment
is due one year from now. The market interest rate for this bond is
1
Total apples
Bad apples
200
2
Bad apples
Percentage
10
3
Old price
% price reduction
New price
$120
25%
4
Original cost
% price increase
$400
15%
5
Original car value
% loss of value
Value after 1 year
$5,000
20%
6
Population in 2003
Rate of growth
Popu
Calculate the present value of a perpetual payment of $250 if the interest rate is 4.75% under three scenario
(1) first payment occurs one year from now; (2) first payment occurs immediately; (3) first payment is delayed
for ten years.
Payment
Interest ra
A Review of Final Exam Themes
1
A perpetuity has a present value of $75,000. The annual payment is $4,500.
What is the annual interest rate?
Payment
Present value
Interest rate
Proof
2
A growing perpetuity has a present value of $125,000. The annual payme
1
Expected cash-flow
Discount rate
Rate of growth of cash-flow
Present value ordinary
Present value ordinary
Present value delayed
Present value delayed
23.1
9.5%
2.5%
(a) The growing perpetuity
one year from now
Years Cash-flow
PV
0
1
2
3
4
5
6
7
8
9
10
FV and PV WITH ANNUAL COMPOUNDING
PV = FV / ( 1 + r )^t
r
t
1
annual interest rate
time in years
A deposits $500 in an account that earns 2.5% compounded annually and keeps the money for
three years. In another account, B deposits $500 at 5.1% compounded