02_PreFinal.ppt

Stangeland © 2002 1
Pre-final review
For 9.220, Term 1, 2002/03
02_PreFinal.ppt

Introduction
 Today’s Goal
 Highlight important topics to review
 Work through more difficult concepts
 Answer questions raised by students
 No new material
 No extra exam hints

Lecture 1 Material

II. Types of Businesses
1. Sole Proprietorship
2. Partnership
3. Corporation

Value of Debt at time of Repayment
(repayment due = $10 million)
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35 40 45
Value of the Firm's Assets at the time the debt
is due ($ millions)
Contingent
Value
of
the
Firm's
Securities
($
millions)

Value of Equity at time of Debt Repayment
(repayment due = $10 million)
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35 40 45
is due ($ millions)
Contingent
Value
of
the
Firm's
Securities
($
millions)
Never Negative – Limited Liability

Total Value of the Firm
= Debt + Equity
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35 40 45
is due ($ millions)
Contingent
Value
of
the
Firm's
Securities
($
millions)
Debt
Equity
Total Firm Value

IV. The Principal-Agent (PA) Problem
 Corporations are owned by shareholders
but are run by management
 There is a separation of ownership and control
 Shareholders are said to be the principals
 Managers are the agents of shareholders
 and are are supposed to act on behalf of the
shareholders
 The PA problem is that managers may not
always act in the best way on behalf of
shareholders.

V. Self study – will be examined
 Financial Institutions
 Financial Markets
 Money vs. Capital Markets
 Primary vs. Secondary Markets
 Listing
 Foreign Exchange
 Trends in Finance

Lecture 2 Material

Arbitrage Defined
 Arbitrage – the ability to earn a risk-free
profit from a zero net investment.
 Principal of No Arbitrage – through
competition in markets, prices adjust so
that arbitrage possibilities do not persist.

III. Two-period model
Consider a simple model where an
individual lives for 2 periods, has an
income endowment, and has
preferences about when to consume.
 Endowment (or given income) is
$40,000 now and $60,000 next year

$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Thousands
Thousands
Consumption Today
Consumption
t+1
Two-period model: no market
Without the ability to
borrow or lend using
financial markets, the
individual is restricted to
just consuming his/her
endowment as it is earned:
i.e., consume $40,000 now and consume
$60,000 in one year.
Income
Endowment

$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Thousands
Thousands
Consumption Today
Consumption
t+1
Intertemporal Consumption
Opportunity Set
Assume a market for borrowing
or lending exists and the interest
rate is 10%. This opens up a large
set of consumption patterns
across the two periods.

Opportunity Set
1. What is the slope of the consumption
opportunity set?
2. What is the maximum possible consumption
today and how is this achieved?
3. What is the maximum possible consumption in
t+1 and how is this achieved?

$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Thousands
Thousands
Consumption Today
Consumption
t+1
Opportunity Set
Slope =
Maximum @ t+1 = ?
Maximum Today = ?

$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Thousands
Thousands
Consumption Today
Consumption
t+1
Opportunity Set
A person’s preferences will
impact where on the
consumption opportunity set
they will choose to be.
Patient
Hungry

An increase in interest rates
A rise in interest rates will make saving
more attractive …
…and borrowing less attractive.
The equilibrium interest rate in the
economy exactly equates the demands of
borrowers and savers. As demands change,
the interest rate adjusts to equate the supply
and demand for funds across time.
$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Thousands
Thousands
Consumption Today
Consumption
t+1

Real Investment Opportunities –
Example 1
Consider an investment opportunity that costs
$35,000 this year and provides a certain
cash flow of $36,000 next year.
Is this a good opportunity?
Time 0 1
Cashflows -$35,000 +$36,000

$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Thousands
Thousands
Consumption Today
Consumption
t+1
Example 1
Original
Endowment
New Cash flows if the
real investment is taken

$0
$20
$40
$60
$80
$100
$120
$0 $20 $40 $60 $80 $100 $120
Thousands
Thousands
Consumption Today
Consumption
t+1
Example 1
Consumption Opportunity Set by
borrowing or lending against the
original endowment
Consumption Opportunity Set after real investment is taken
Should the individual take the real investment opportunity?
No! It leads to dominated consumption opportunities.

VI. The Separation Theorem
 The separation theorem in financial markets says that
all investors will want to accept or reject the same
investment projects by using the NPV rule, regardless
of their personal preferences.
 Separation between consumption preferences and
real investment decisions
 Logistically, separating investment decision making
from the shareholders is a basic requirement for the
efficient operation of the modern corporation.
 Managers don’t need to worry about individual
investor consumption preferences – just be
concerned about maximizing their wealth.

Lecture 3 Material

PV of a Growing Annuity
n
n
r
g
r
g
C
g
r
C
PV
)
1
(
1
)
1
(
1
1
0








n
n
r
g
r
C
g
r
C
PV
)
1
(
1
1
1
0





 










 n
n
r
g
g
r
C
PV
)
1
(
)
1
(
1
1
0
PV of the
whole
growing
perpetuity
Subtract off the PV
of the latter part of
the growing
perpetuity
PV0 is the PV one
period before the
first cash flow

Simple (non-growing) series of
cash flows
 For constant
annuities and
constant
perpetuities, the
time value
formulas are
simplified by
setting g = 0.
r
C
PV0  regular perpetuity








 n
0
r)
(1
1
1
r
C
PV
 
1
r)
(1
r
C
FV n
n 


regular
annuity
We can use the PMT button
on the financial calculator for
the annuity cash flows, C

IV. Some final warnings
 Even though the time value calculations
look easy  there are many potential
pitfalls you may experience
 Be careful of the following:
 PV0 of annuities or perpetuities that do not begin
in period 1; remember the PV formulas given
always discount to exactly one period before the
first cash flow.
 If the cash flows begin at period t, then you
must divide the PV from our formula by (1+r)t-1
to get PV0.
 Note: this works even if t is a fraction.

Be careful of annuity payments
 Count the number of payments in an annuity. If
the first payment is in period 1 and the last is in
period 2, there are obviously 2 payments. How
many payments are there if the 1st payment is
in period 12 and the last payment is in period 21
(answer is 10 – use your fingers). How about if
the 1st payment is now (period 0) and the last
payment is in period 15 (answer is 16
payments).
 If the first cash flow is at period t and the last
cash flow is at period T, then there are T-t+1
cash flows in the annuity.

Be careful of wording
 A cash flow occurs at the
end of the third period.
 A cash flow occurs at
time period three.
 A cash flow occurs at the
beginning of the fourth
period.
 Each of the above
statements refers to the
same point in time!
0 1 2 3 4
C
If in doubt, draw a time line.

Lecture 4&5 Material

Annuities and perpetuities
 The annuity and perpetuity formulae require the rate
used to be an effective rate and, in particular, the
effective rate must be quoted over the same time
period as the time between cash flows. In effect:
 If cash flows are yearly, use an effective rate per
year
 If cash flows are monthly, use an effective rate per
month
 If cash flows are every 14 days, use an effective rate
per 14 days
 If cash flows are daily, use an effective rate per day
 If cash flows are every 5 years, use an effective rate
per 5 years.
 Etc.

Step 1: finding the implied effective rate
 In words, step 1 can be described as follows:
 Take both the quoted rate and its quotation
period and divide by the compounding
frequency to get the implied effective rate
and the implied effective rate’s quotation
period.
 The quoted rate of 60% per year with monthly
compounding is compounded 12 times per the
quotation period of one year. Thus the implied
effective rate is 60% ÷ 12 = 5% and this implied
effective rate is over a period of one year ÷ 12 = one
month.

Step 2: Converting to the desired
effective rate
 Example: if you are doing loan
calculations with quarterly payments,
then the annuity formula requires an
effective rate per quarter.
 Once we have done step 1, if our
implied effective rate is not our
desired effective rate, then we need
to convert to our desired effective
rate.

Step 2: continued
Effective to effective conversion
 In the previous example, 5% per month is equivalent to
15.7625% per 3 months (or quarter year). This result is due to
the fact that (1+.05)3=1.157625
 As a formula this can be represented as
 where rg is the given effective rate, rd is the desired effective
rate.
 Lg is the quotation period of the given rate and Ld is the
quotation period of the desired rate, thus Ld/Lg is the length of
the desired quotation period in terms of the given quotation
period.
1
)
r
(1
r
or
)
r
(1
)
r
(1 g
d
g
d
L
L
g
d
d
L
L
g 






Step 3: finding the final quoted rate
 In words, step 3 can be described as follows:
 Take both the implied effective rate and its
quotation period and multiply by the
compounding frequency of the desired final
quoted rate. This results in the desired final
quoted rate and its quotation period.
 In our example, the desired quoted rate is a rate
per year compounded quarterly. Therefore the
compounding frequency is 4. We multiply
15.7625% per quarter by 4 to get 63.05% per
year compounded quarterly.

Continuous Compounding – self
study (continued)
Using the previous formula and mathematical limits …
)
r
ln(1
r
,
r
to
r
from
...
direction
other
in the
convert
To
interest
of
rate
compounded
ly
continuous
the
be
to
said
is
r
,
m
As
e
r
1
,
m
As
period
per
effective
g
compoundin
continuous
with
period
per
g
compoundin
continuous
with
period
per
period
per
effective
quoted
r
effective
quoted









Mortgage continued
 How much will be left at the end of the 5-year contract?
 After 5 years of payments (60 payments) there are 300
payments remaining in the amortization. The principal
remaining outstanding is just the present value of the
remaining payments.
 How much interest and principal reduction result from
the 300th payment?
 When the 299th payment is made, there are 61 payments
remaining. The PV of the remaining 61 payments is the
principal outstanding at the beginning of the 300th period
and this can be used to calculate the interest charge which
can then be used to calculate the principal reduction.

Lecture 6 Material

Bond valuation and yields
 A level coupon bond pays constant semiannual coupons
over the bond’s life plus a face value payment when the
bond matures.
 The bond below has a 20 year maturity, $1,000 face
value and a coupon rate of 9% (9% of face value is
paid as coupons per year).
Year 0 0.5 1 1.5 . . . 19.5
20
(Maturity
Date)
$45 $45 $45 . . . $45 $45
+ $1,000

Lecture 7 Material

Definitions – Spot Rates
 The n-period current spot rate of interest denoted rn
is the current interest rate (fixed today) for a loan
(where the cash is borrowed now) to be repaid in n
periods. Note: all spot rates are expressed in the
form of an effective interest rate per year. In the
example above, r1, r2, r3, r4, and r5, in the previous
slide, are all current spot rates of interest.
 Spot rates are only determined from the prices of
zero-coupon bonds and are thus applicable for
discounting cash flows that occur in a single time
period. This differs from the more broad concept of
yield to maturity that is, in effect, an average rate
used to discount all the cash flows of a level coupon
bond.

Definitions – Forward Rates
(continued)
 To calculate a forward rate, the
following equation is useful:
1 + fn = (1+rn)n / (1+rn-1)n-1
 where fn is the one period forward rate
for a loan repaid in period n
 (i.e., borrowed in period n-1 and repaid in period n)
 Calculate f2 given r1=8% and r2=9%
 Calculate f3 given r3=9.5%

Forward Rates – Self Study
 The t-period forward rate for a loan
repaid in period n is denoted n-tfn
 E.g., 2f5 is the 3-period forward rate for a loan
repaid in period 5 (and borrowed in period 2)
 The following formula is useful for
calculating t-period forward rates:
1+n-tfn = [(1+rn)n / (1+rn-t)n-t]1/t
 Given the data presented before, determine 1f3
and 2f5
 Results: 1f3=10.2577945%; 2f5=10.4622321%

Definitions – Future Spot Rates
 Current spot rates are observable today and can be
contracted today.
 A future spot rate will be the rate for a loan obtained
in the future and repaid in a later period. Unlike
forward rates, future spot rates will not be fixed (or
contracted) until the future time period when the loan
begins (forward rates can be locked in today).
 Thus we do not currently know what will happen to
future spot rates of interest. However, if we
understand the theories of the term structure, we can
make informed predictions or expectations about
future spot rates.
 We denote our current expectation of the future spot
rate as follows: E[n-trn] is the expected future spot
rate of interest for a loan repaid in period n and
borrowed in period n-t.

Term Structure Theories:
Pure-Expectations Hypothesis
 The Pure-Expectations Hypothesis states
that expected future spot rates of interest
are equal to the forward rates that can be
calculated today (from observed spot
rates).
 In other words, the forward rates are
unbiased predictors for making
expectations of future spot rates.
 What do our previous forward rate
calculations tell us if we believe in the Pure-
Expectations Hypothesis?

Liquidity-Preference Hypothesis
 Empirical evidence seems to suggest that
investors have relatively short time
horizons for bond investments. Thus, since
they are risk averse, they will require a
premium to invest in longer term bonds.
 The Liquidity-Preference Hypothesis states
that longer term loans have a liquidity
premium built into their interest rates and
thus calculated forward rates will
incorporate the liquidity premium and will
overstate the expected future one-period
spot rates.

 Reconsider investors’ expectations for inflation and
future spot rates. Suppose over the next year,
investors require 4% for a one year loan and expect
to require 6% for a one year loan (starting one year
from now).
 Under the Liquidity-Preference Hypothesis, the current
2-year spot rate will be defined as follows:
 (1+r2)2=(1+r1)(1+E[1r2]) + LP2
 where LP2 = liquidity premium: assumed to be
0.25% for a 2 year loan
 (1+r2)2 = (1.04)x(1.06) + 0.0025 so r2=5.11422%

 Restated, if we don’t know E[1r2], but
we can observe r1=4% and
r2=5.11422%,
 then, under the Liquidity-Preference
Hypothesis, we would have E[1r2] < f2 =
6.24038%.
 From this example, f2 overstates E[1r2] by
0.24038%
 If we know LP2 or the amount f2 overstates
E[1r2], then we can better estimate E[1r2].

Projecting Future Bond Prices
 Consider a three-year bond with annual coupons (paid
annually) of $100 and a face value of $1,000 paid at
maturity. Spot rates are observed as follows: r1=9%,
r2=10%, r3=11%
 What is the current price of the bond?
 What is its yield to maturity (as an effective annual
rate)?
 What is the expected price of the bond in 2 years?
 under the Pure-Expectations Hypothesis
 under the Liquidity-Preference Hypothesis
 assume f3 overstates E[2r3] by 0.5%

IRR Problem Cases: Borrowing vs. Lending
 Consider the
following two
projects.
 Evaluate with IRR
given a hurdle rate
of 20%
 For borrowing
projects, the IRR
rule must be
reversed: accept the
project if the
IRR≤hurdle rate
Year
Project A
Cash
Flows
Project B
Cash
Flows
0 -$10,000 +$10,000
1 +$15,000 -$15,000
Conventional Cash Flows or
Lending/Investing Type Project
Unconventional
Cash Flows or
Borrowing Type
Project

The non-existent or multiple IRR problem
 Example:
 Do the
evaluation using
IRR and a
hurdle rate of
15%
 IRRA=?
 IRRB=?
Year
Cash flows
of Project A
Cash flows
of Project B
0 -$312,000 +$350,000
1 +$800,000 -$800,000
2 -$500,000 +$500,000

NPV Profile – where are the IRR's?
-$60,000
-$40,000
-$20,000
$0
$20,000
$40,000
$60,000
$80,000
0% 20% 40% 60% 80% 100%
Discount Rate
NPV
Project A
Project B

No or Multiple IRR Problem – What to do?
 IRR cannot be used in this circumstance,
the only solution is to revert to another
method of analysis. NPV can handle these
problems.
 How to recognize when this IRR problem
can occur
 When changes in the signs of cash flows happen
more than once the problem may occur
(depending on the relative sizes of the individual
cash flows).
 Examples: +-+ ; -+- ; -+++-; +---+

Special situations for DCF analysis
 When projects are independent and the firm has few
constraints on capital, then we check to ensure that
projects at least meet a minimum criteria – if they do,
they are accepted.
 NPV≥0; IRR≥hurdle rate; PI≥1
 If the firm has capital rationing, then its funds are
limited and not all independent projects may be
accepted. In this case, we seek to choose those projects
that best use the firm’s available funds. PI is especially
useful here.
 Sometimes a firm will have plenty of funds to invest, but
it must choose between projects that are mutually
exclusive. This means that the acceptance of one
project precludes the acceptance of any others. In this
case, we seek to choose the one highest ranked of the
acceptable projects.

Incremental Cash Flows: Solving
the Problem with IRR and PI
 As you can see, individual IRR's and PIs are not good
for comparing between two mutually exclusive
projects.
 However, we know IRR and PI are good for evaluating
whether one project is acceptable.
 Therefore, consider “one project” that involves
switching from the smaller project to the larger
project. If IRR or PI indicate that this is worthwhile,
then we will know which of the two projects is better.
 Incremental cash flow analysis looks at how the cash
flows change by taking a particular project instead of
another project.

Using IRR and PI correctly when projects are
mutually exclusive and are of differing scales
 IRR and PI analysis of incremental cash
flows tells us which of two projects are
better.
 Beware, before accepting the better
project, you should always check to see
that the better project is good on its own
(i.e., is it better than “do nothing”).

Incremental Analysis – Self Study
 For self-study,
consider the
following two
investments and
do the
incremental IRR
and PI analysis.
The opportunity
cost of capital is
10%. Should
either project be
accepted? No,
prove it to
yourself!
Year
Cash flows
of Project A
Cash
flows of
Project B
Incremental
Cash flows
of A instead
of B
(i.e., A-B)
0 -$100,000 -$50,000
1 +$101,000 +$50,001

Capital Rationing
 Recall: If the firm has capital rationing, then its
funds are limited and not all independent projects
may be accepted. In this case, we seek to choose
those projects that best use the firm’s available funds.
PI is especially useful here.
 Note: capital rationing is a different problem than
mutually exclusive investments because if the capital
constraint is removed, then all projects can be
accepted together.
 Analyze the projects on the next page with NPV, IRR,
and PI assuming the opportunity cost of capital is
10% and the firm is constrained to only invest
$50,000 now (and no constraint is expected in future
years).

Capital Rationing – Example
(All $ numbers are in thousands)
Year Proj. A Proj. B Proj. C Proj. D Proj. E
0 -$50 -$20 -$20 -$20 -$10
1 $60 $24.2 -$10 $25 $12.6
2 $0 $0 $37.862 $0 $0
NPV $4.545 $2.0 $2.2 $2.727 $1.4545
IRR 20% 21% 14.84% 25% 26%
PI 1.0909 1.1 1.11 1.136 1.145

Capital Rationing Example:
Comparison of Rankings
 NPV rankings (best to worst)
 A, D, C, B, E
 A uses up the available capital
 Overall NPV = $4,545.45
 IRR rankings (best to worst)
 E, D, B, A, C
 E, D, B use up the available capital
 Overall NPV = NPVE+D+B=$6,181.82
 PI rankings (best to worst)
 E, D, C, B, A
 E, D, C use up the available capital
 Overall NPV = NPVE+D+C=$6,381.82
 The PI rankings produce the best set of investments
to accept given the capital rationing constraint.

Capital Rationing Conclusions
 PI is best for initial ranking of
independent projects under capital
rationing.
 Comparing NPV’s of feasible
combinations of projects would also
work.
 IRR may be useful if the capital
rationing constraint extends over
multiple periods (see project C).

Other methods to analyze
investment projects – self study
 Payback – the simplest capital budgeting
method of analysis
 Know this method thoroughly.
 Discounted Payback
 Not Required.
 Average Accounting Return (AAR)
 You will not be asked to calculate it, but you
should know what it is and why it is the most
flawed of the methods we have examined.

Lecture 10 Material

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 project. This is often called an
incremental analysis – looking at how
cash flows change between not doing
the project vs. doing the project.

Which cash flows are relevant to
the project analysis, which are not?
Examples Type of Cash Flow Is it Relevant to
the analysis? Why?
Sunk Costs
Opportunity Costs
Side Effects (or
incidental effects)
Interest Expense
(or financing
charges)

Conclusions on real and nominal
cash flows
 It is possible to express any cash flow
as either a real amount or a nominal
amount.
 Since the real and nominal amounts
are equivalent, the PV’s must be
equivalent, so remember the rule:
 Discount real cash flows with real rates.
 Discount nominal cash flows with
nominal rates.

Use of real cash flows
 If a project’s cash flows are expected
to grow with inflation, then it may be
more convenient to express the cash
flows as real amounts rather than
trying to predict inflation and the
nominal cash flows.

Tax consequences and after tax cash
flows (assume a tax rate, Tc, of 40%)
Item Before-tax
amount
Before-tax
cash flow
After-tax
cash flow
Revenue Rev
$10
Rev
$10
=Rev(1-Tc)
=$10(1-.4)
=$6
Expense Exp
$10
-Exp
-$10
=-Exp(1-Tc)
=-$10(1-.4)
=-$6
CCA CCA
$10
$0 =+CCATc
=+$10 0.4
=+$4

Yearly cash flows after tax
 Normally we project yearly cash flows for a
project and convert them into after-tax
amounts.
 CCA deductions are due to an asset
purchase for a project. CCA is calculated as
a % of the Undepreciated Capital Cost
(UCC). Since a % amount is deducted each
year, the UCC will never reach zero so CCA
deductions can actually continue even after
the project has ended (and thus shelter
future income from taxes). All CCA-caused
tax savings should be recognized as cash
inflows for the project that caused them.

Lecture 11 Material

PV CCA Tax Shields
 C = cost of asset
 D = CCA rate
 Tc = Corporate tax rate
 k = Discount rate for CCA tax shields
 Sn = Salvage value of asset sold in period n with lost CCA
deductions beginning in period n+1
   n
c
n
c
k
1
1
d
k
T
d
S
k
1
2
k
1
d
k
T
d
C
PV


















Shields
Tax
CCA

Summary of Capital Budgeting
Items and Tax Effects
 The following formula may help summarize the project’s
NPV calculation.
NPV = -initial asset cost1
+ PVSalvage Value or Expected Asset Sale Amount
1
+ PVincremental cash flows caused by the project
2
+ PVincremental working capital cash flows caused by the project
1
– PVCapital Gains Tax
3
+ PVCCA Tax Shields
Footnotes:
1. These items usually have the same before-tax amounts and
after-tax amounts. I.e., there is no tax effect. For asset
purchases/sales the tax effect is done through CCA effects.
2. These items usually have the after-tax cash flow equal to the
before tax cash flow multiplied by (1-Tc).
3. Capital gains tax is only triggered when the asset is sold for an
amount greater than its initial cost.

Qualitative checks (continued)
 Remember, a positive NPV indicates wealth is being
created. This is equivalent to the economic concept of
“positive economic profit”.
 When does positive economic profit occur?
 When there is not perfect competition; i.e., when
there is a competitive advantage.
 Sources of competitive advantage include:
 Being the first to enter a market or create a product
 Low cost production
 Economies of scale and scope
 Preferred access to raw materials
 Patents (create a barrier to entry, or preserve a low-
cost production process).
 Product differentiation
 Superior marketing or distribution, etc.

Midterm 2 Question

 1. Fritz, of Fritz Plumbing, has been given the opportunity to
carry Moen fixtures for the next 10 years. He needs your
advice and has supplied the following information for your
analysis of the “Moen Project”:
 Current Office Lease Costs$30,000 per yearCurrent Insurance
Costs$8,000 per yearCurrent Wages of Employees$200,000
per yearCurrent Required Inventory$60,000 Current revenue
$500,000 per year
 No working capital changes are expected due to the project.
 Revenues are expected to rise to $800,000 per year over the
life of the project and will fall back to their original levels
following the project. One more employee will be required for
the life of the project and the salary will be $30,000 per year.
 In addition, Fritz will need to upgrade his fleet of trucks to
accommodate the new Moen fixtures. If the Moen project is
accepted he will sell his current trucks now for $100,000 and
purchase new trucks now for $500,000; the new trucks would
then be sold for $50,000 in 10 years. If the Moen project is
not accepted, he will sell his current trucks in 10 years for
scrap value of $5,000. If the project is accepted Fritz will take
out a bank loan to partially finance the truck and the bank will
require annual interest charges of $1,000 per year for the next
5 years.

 (a)Specify all relevant incremental after-tax
cash flows (and their timing) that would
occur if the Moen project is accepted.
Assume a corporate tax rate of 40%.
(Ignore CCA tax shields at this point.) Do
not do any discounting at this point.
 (b)What is the present value of the
incremental CCA tax shields if the Moen
project is accepted? Assume a CCA rate of
30% and the appropriate discount rate is
equal to the risk free rate of 4%.

Note: from Lecture 15 material
 (c) Assume that the incremental cash
flows in (a) are of the same risk level as the
other assets of Fritz Plumbing. Currently, Fritz
Plumbing is financed as follows: 40% debt,
60% equity. The debt has a market price of
$1,462 per bond and pays semiannual coupons
of $60 each. The debt matures in 8 years and
has a par value of $1,000 per bond. The stock of
Fritz Plumbing has a  of 1.5. The expected
return on the market is 12%, Rf is 4% and TC is
40%. What discount rate should be used for the
NPV analysis of the incremental cash flows
specified in (a).

 (d) Assume your answer to (c) is 12%,
your answer to (b) is $150,000, and you
determined the following after tax cash
flows in (a) to be as follows:
 Time of cash flowAfter-tax amountYear
0 (now)-$500,000Each of Years 1-
10$250,000Year 10$50,000 What is the
NPV of the project? What is your advice to
Fritz?

 (e) Suppose that the risk of the Moen project was
much higher than the risk of the firm.
 (i) Without doing any calculations, explain how
your analysis, NPV, and advice would likely change
assuming the above risk difference was due to high
unsystematic risk?
 (2 points)
 (ii) Without doing any calculations, explain how
your analysis, NPV, and advice would likely change
assuming the above risk difference was due to high
systematic risk?

Lecture 12-14 Material

Examples
 What would be your portfolio beta, βp, if you had
weights in the first four stocks of 0.2, 0.15, 0.25, and
0.4 respectively.
 What would be E[Rp]? Calculate it two ways.
 Suppose σM=0.3 and this portfolio had ρpM=0.4, what
is the value of σp?
 Is this the best portfolio for obtaining this expected
return?
 What would be the total risk of a portfolio composed
of f and M that gives you the same β as the above
portfolio?
 How high an expected return could you achieve while
exposing yourself to the same amount of total risk as
the above portfolio composed of the four stocks. What
is the best way to achieve it?

Lecture 15

Conclusions on factors that affect β
 The three factors that affect an equity
β are as follows
 Cyclicality of Revenues
 Operating Leverage
 Financial Leverage
 Note: the financial leverage does not affect
asset β, it only affects equity β.
Only these two
affect asset β

Lecture 16 Material

Relationship among the Three
Different Information Sets
All information
relevant to a stock
Information set
of publicly available
information
Information
set of
past prices

Conclusions on Informational Efficiency
 Market is generally regarded as being
weak-form informationally efficient.
 Market is generally regarded as being
semi-strong-form informationally
efficient.
 Market is generally regarded as NOT
being strong-form informationally
efficient.

Self Study – fill in the blank cells
Construction of a Synthetic European Put:
initial transactions at date t
 where St is the stock price at time t
 Cet is the price at time t of the European call option
Initial Transactions: fill in the empty cells
 short 1 share of stock
 Invest the present value of the exercise
price (E) at the risk free rate (or long
the risk-free asset)
 Buy a call option on the stock with
same exercise price and same
expiration date
Initial net cash flow (will be an outflow):

Self Study – fill in the blank cells
Synthetic European Put:
transactions on the expiration date (T)
Final cash flows given the different relevant states of nature
(which depend on whether ST is less than or greater than E):
ST < E ST ≥ E
 liquidate the short stock position
(buy the stock)
 liquidate the long risk-free asset
position (collect the proceeds from
the investment)
 liquidate the long call option position
(discard or exercise depending upon
which is optimal)
Net cash flow at the expiration date T: E-ST 0

Lecture 19-20 Material

Integration of all effects on capital
structure
Costs
Distress
financial
Expected
Equity
of
Costs
Agency
of
Savings
PV
PV
1
)
1
(
)
1
(
1















 B
T
T
T
V
V
B
S
C
U
L

Lecture 21 Material

Speculating Example
 Zhou has been doing research on the price of gold and
thinks it is currently undervalued. If Zhou wants to
speculate that the price will rise, what can he do?
 Give a strategy using futures contracts.
 Zhou can take a long position in gold futures; if the
price rises as he expects, he will have money given
to him through the marking to market process, he
can then offset after he has made his expected
profits.
 Give a strategy using options.
 Zhou can go long in gold call options. If gold prices
rise, he can either sell his call option or exercise it.

Compare Speculating Strategies
(assuming contracts on one troy ounce
of gold)
Derivative Used: Long Futures
Contract @ $310
Long Call Option,
E=$310
Initial Cost $0 -$12
Net amount received (final payoff net of initial cost) given
final spot prices below:
Spot = $280 -$30 -$12
Spot = $300 -$10 -$12
Spot = $320 $10 -$2
Spot = $340 $30 $18
Spot = $360 $50 $38

Speculating: Futures vs. Options
Net Profit Received from Speculating in
Gold
-$125
-$100
-$75
-$50
-$25
$0
$25
$50
$75
$100
$200
$225
$250
$275
$300
$325
$350
$375
$400
Final Spot Price of Gold
Profit
from
Speculating
Long Futures
Contract Profit
Long Call
Option Profit

Should hedging or speculating be
done?
 Speculating: If the market is informationally efficient,
then the NPV from speculating should be 0.
 Hedging: Remember, expected return is related to
risk. If risk is hedged away, then expected return will
drop.
 Investors won’t pay extra for a hedged firm just
because some risk is eliminated (investors can easily
diversify risk on their own).
 However, if the corporate hedging reduces costs that
investors cannot reduce through personal
diversification, then hedging may add value for the
shareholders. E.g., if the expected costs of financial
distress are reduced due to hedging, there should be
more corporate value left for shareholders.

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