The Timing Problem
IRR and PI Problem Cases: Borrowing vs. Lending
Consider the following two projects.
Evaluate with IRR and PI given a hurdle rate of 20%
For borrowing projects, the IRR rule must be reversed:
accept the project if the IRRhurdle rate
Relevant cash flows
The main principles behind which cash flows to
include in capital budgeting analysis are as follows:
1. Only include cash flows that change as a result of
the project being analyzed. Include all cash flows
that are impacted by the pro
Risk Aversion and Introduction
to Modern Portfolio Theory
Optimal Capital Allocation
We seek to optimally allocate investment
funds between safe and risky assets
T-bills to proxy the risk free asset
a stock portfolio as a risky asset
The Capital Asset Pricing Model
Capital Asset Pricing Model
Sharpe, Lintner and Mossin are researchers credited with
its development (in the mid 1960s)
CAPM is an extension of the Markowitz portfolio selection
Derived using principles o
11. Option-Pricing Models
profit that could be made if the option was
Call: IVC =
Put: IVP =
the difference between the option price and the
Call: C - IVC
Put: P - IVP
How Securities are Traded
Types of Markets
Direct search markets
Trading partners must locate each other (search costs)
Consist of thinly traded nonstandard goods with low
As trading volume increases, the services of a br
Bonds Duration and
Effective Bond Maturity
Consider the following two bonds
The stated maturity of
bond A is
bond B is
Effective Bond Maturity
4. Bonds Valuation
Face or par value
annual coupon payments ($)
Zero coupon bond
actual price paid when buying the bond
Invoice price = quoted price + accrued interest
Markets and Instruments
Markets and Instruments
Money Market Instruments
Government raises funds by issuing T-bills
Sold at a discount to f
The Recent History of
Investing and the
Short (Recent) History of Investing
The Crash of 1929 and the Great Depression
One-day panic in 1987
The technology bubble in the nineties and
The bear market of the new millennium
UNIVERSITY OF MANITOBA
I. H. ASPER SCHOOL OF BUSINESS
DEPARTMENT OF ACCOUNTING AND FINANCE
FIN 3410 - INVESTMENTS
Sections A01 and A02
Dr. Usha R. Mitto
Individual solutionanswers to this problem will vary.
In principle, potential losses are unbounded, growing directly with increases in
the price of Alcan.
If the stop-buy order can be filled at $78, the maxi
1. a. No. The increase in price did not add to the productive capacity of the
b. Yes, the value of the equity held in these assets has doubled.
c. Future homeowners as a whole are worse off, since mortgage liabil
1. (a) for sure.
(b) and (d) are firm-specific.
(c) and (e) can be either firm-specific or due to marketwide factors.
2. (a) and (c) enter into the portfolio variance and thus affect portfolio risk.
3. (a) is true by defini
1. Your holding period return for the next year on the money market fund depends
on what 30-day interest rates will be each month when it is time to roll over
maturing securities. The one-year savings de
Option Strategies and Payoffs
Market Price and Exercise
In the Money an immediate exercise of the
option would be profitable
Call: S > X
Put: S < X
Out of the Money an immediate exercise of
the option would not be profitable
8. Factor Models
Shortfalls of the Mean-variance
theory & CAPM
The estimation procedure is a formidable task.
Security analysis for n assets, involves
n expected returns,
n variances terms
n(n-1)/2 covariance terms
With roughly 4 000 TSX
NPV Profile where are the IRR's?
Calculation problems what did we find?
Assume a hurdle rate of 15%.
Evaluate using IRR.
Does not exist
No or Multiple IRR Problem What to do?
IRR cannot be used in this circums
Project Externalities Example
Suppose McDonalds is considering adding sushi to its
menu. The estimated NPV of the sushi project is $20m.
However, closer analysis reveals that some of the sushi
sales will be to customers normally purchasing Big Macs.
Net Working Capital: Example
Increased NWC requirements due to the new project:
A check on NWC changes
Note: over the entire life of a project, the cash
flows due to changes in net working capital
normally sum up to zero.
This is because the net working
Risk-Free Interest Rates
A default-free zero-coupon bond that matures on
date n provides a risk-free return over the same period.
Thus, the Law of One Price guarantees that the
risk-free interest rate equals the yield to maturity on
such a bond.
Bond Cash Flows, Prices, and Yields
States the details of the bond
Final repayment date
The time remaining until the repayment date
Promised interest payments
Does not m
CCA Calculations: Example
The cost of a new asset is $1,000.
The CCA rate is 40%.
The corporate tax rate is 20%.
The opportunity cost of capital is 10%.
The following table indicates the calculations of CCA,
UCC, and resulting CCA Tax Shield (savings
Caution: Depreciation vs. CCA
The depreciation amount used for financial
reporting and GAAP is likely not the amount used
for tax purposes.
In Canada, capital cost allowance (CCA) replaces
GAAP depreciation for tax purposes.
Thus, to be correct, deprec
Dynamic Behavior of Bond Prices
A bond is selling at a discount if the price is less than
the face value.
A bond is selling at par if the price is equal to the
A bond is selling at a premium if the price is greater
Basics of Matrix Algebra
(Capital Market Line)
Let A denote an MN matrix, such that:
Let B denote an NL matrix, such t