02 pre final review - university of manitoba1 stangeland © 2002 1 pre-final review for 9.220, ter m...

1

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

2


Lecture 1 Material


II. Types of Businesses

1. Sole Proprietorship

2. Partnership

3. Corporation

3


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)

Co

ntin

gen

t V

alu

e o

f th

e F

irm

's S

ecu

riti

es (

$ m

illio

ns)


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


Co

ntin

gen

t V

alu

e o

f th

e F

irm

's S

ecu

riti

es (

$ m

illio

ns)

Never Negative – Limited Liability

4


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


Co

ntin

gen

t V

alu

e o

f th

e F

irm

's

Sec

uri

ties

($

mill

ion

s)

Debt

EquityTotal 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.

5


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

6


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

7


$0

$20

$40

$60

$80

$100

$120

$0 $20 $40 $60 $80 $100 $120

Th

ou

sand

s

Thousands

Consumption Today

Co

nsu

mp

tio

n 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

Th

ou

sand

s

Thousands

Consumption Today

Co

nsu

mp

tio

n 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.

Consumption Opportunity Set

8



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

Th

ou

sand

s

Thousands

Consumption Today

Co

nsu

mp

tio

n t

+1


Slope =

Maximum @ t+1 = ?

Maximum Today = ?

9


$0

$20

$40

$60

$80

$100

$120

$0 $20 $40 $60 $80 $100 $120

Th

ou

sand

s

Thousands

Consumption Today

Co

nsu

mp

tio

n t

+1


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

Th

ou

san

ds

Thousands

Consumption Today

Co

nsu

mp

tio

n t

+1

10


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

Th

ou

sand

s

Thousands

Consumption Today

Co

nsu

mp

tio

n t

+1


Original Endowment

New Cash flows if the real investment is taken

11


$0

$20

$40

$60

$80

$100

$120

$0 $20 $40 $60 $80 $100 $120

Th

ou

sand

s

Thousands

Consumption Today

Co

nsu

mp

tio

n t

+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.

12


Lecture 3 Material


PV of a Growing Annuity

n

n

rgr

gC

gr

CPV

)1(

1)1(110 +

•−+•−

−=

nn

rgr

C

gr

CPV

)1(

1110 +

•−

−−

= +

++−

−=

n

n

r

g

gr

CPV

)1(

)1(11

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

13


Simple (non-growing) series of cash flows

� For constant

annuities and

constant

perpetuities, the

time value

formulas are

simplified by

setting g = 0.

r

CPV0 = regular perpetuity

+−=

n0 r)(1

11

r

CPV

[ ]1r)(1r

CFV 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:� PV

0of 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.

14


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!

2 4

C

310

If in doubt, draw a time line.

15


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.

16


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.

17


Step 2: continuedEffective 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(1ror )r(1)r(1 g

d

g

d

L

L

gddL

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.

18


Continuous Compounding – self study (continued)

Using the previous formula and mathematical limits …

)rln(1r

,r tor from

...direction other in theconvert To

interest of rate compoundedly continuous

thebe tosaid is r ,m As

e r1 ,m As

periodper effectivegcompoundin continuous with periodper

gcompoundin continuous with periodper periodper effective

quoted

reffective

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.

19


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).

$45

19.5

$45

1

. . .

. . .

$45

+ $1,000

20

(Maturity

Date)

$45$45

1.50.5Year 0

20


Lecture 7 Material


Definitions – Spot Rates

� The n-period current spot rate of interest denoted rnis 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.

21


Definitions – Forward Rates (continued)

� To calculate a forward rate, the following equation is useful:

1 + fn

= (1+rn)n / (1+r

n-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%

22


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?

23


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%

24



� 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] < f

2=

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%

25




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

-$15,000+$15,0001

+$10,000-$10,0000

Project B Cash Flows

Project A Cash Flows

Year

Conventional Cash Flows or Lending/Investing Type Project

Unconventional Cash Flows or

Borrowing Type Project

26


The non-existent or multiple IRR problem

� Example:

� Do the

evaluation using

IRR and a

hurdle rate of

15%

� IRRA=?

� IRRB=?

+$500,000-$500,0002

-$800,000+$800,0001

+$350,000-$312,0000

Cash flows of Project B

Cash flows of Project A

Year


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

NP

V

Project AProject B

27


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.

28


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”).

29


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!

1

0

Year

+$101,000

-$100,000

Cash flows of Project A

+$50,001

-$50,000

Cash flows of Project B

Incremental Cash flows of A instead

of B

(i.e., A-B)


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).

30


Capital Rationing – Example(All $ numbers are in thousands)

1.1451.1361.111.11.0909PI

26%25%14.84%21%20%IRR

$1.4545$2.727$2.2$2.0$4.545NPV

$0$0$37.862$0$02

$12.6$25-$10$24.2$601

-$10-$20-$20-$20-$500

Proj. EProj. DProj. CProj. BProj. AYear


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 = NPV

E+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 = NPV

E+D+C=$6,381.82

� The PI rankings produce the best set of investments to accept given the capital rationing constraint.

31


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.

32


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.

33


Which cash flows are relevant to the project analysis, which are not?

Interest Expense

(or financing

charges)

Side Effects (or

incidental effects)

Opportunity Costs

Sunk Costs

Is it Relevant to

the analysis? Why?

Type of Cash FlowExamples


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.

34


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%)

=+CCA•Tc

=+$10 •0.4

=+$4

$0CCA

$10

CCA

=-Exp(1-Tc)

=-$10(1-.4)

=-$6

-Exp

-$10

Exp

$10

Expense

=Rev(1-Tc)

=$10(1-.4)

=$6

Rev

$10

Rev

$10

Revenue

After-tax

cash flow

Before-tax cash flow

Before-tax

amount

Item

35


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

36


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

( ) ( )ncnc

k1

1

dk

TdS

k12

k1

dk

TdCPV

+⋅

+⋅⋅−

+

+

+⋅⋅= ShieldsTax 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 Amount1

+ PVincremental cash flows caused by the project2

+ PVincremental working capital cash flows caused by the project1

– PVCapital Gains Tax3

+ PVCCA Tax ShieldsFootnotes: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.

37


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

38


� 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 willrequire 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%.

39


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 β 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?

40


� (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

41


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

42


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

43


Relationship among the Three

Different Information Sets

All informationrelevant to a stock

Information setof publicly available

information

Informationset 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.

44




Self Study – fill in the blank cells

Construction of a Synthetic European Put:

initial transactions at date t

� where Stis 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

Initial net cash flow (will be an outflow):

� Buy a call option on the stock with same exercise price and same expiration date

� Invest the present value of the exercise price (E) at the risk free rate (or long the risk-free asset)

� short 1 share of stock

45


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):

E-ST

ST < E

0Net cash flow at the expiration date T:

� liquidate the long call option position (discard or exercise depending upon which is optimal)

� liquidate the long risk-free asset position (collect the proceeds from the investment)

� liquidate the short stock position (buy the stock)

ST ≥ E


Lecture 19-20 Material

46


Integration of all effects on capital structure

Costs Distress financial Expected

Equity of CostsAgency of Savings

PV

PV

1

)1()1(1

−

+

×

−−×−−+= B

T

TTVV

B

SCUL


Lecture 21 Material

47


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)

-$2$10Spot = $320

-$12-$10Spot = $300

-$12-$30Spot = $280

$38$50Spot = $360

$18$30Spot = $340

Net amount received (final payoff net of initial cost) given final spot prices below:

-$12$0Initial Cost

Long Call Option, E=$310

Long Futures Contract @ $310

Derivative Used:

48


Speculating: Futures vs. Options

Net Profit Received from Speculating in Gold

-$125-$100

-$75-$50-$25

$0$25$50$75

$100$2

00

$225

$250

$275

$300

$325

$350

$375

$400

Final Spot Price of Gold

Pro

fit

from

S

pec

ula

tin

gLong 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.

02 pre final review - university of manitoba1 stangeland © 2002 1 pre-final review for 9.220, ter m...

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