CGA-CANADA
ADVANCED CORPORATE FINANCE [FN2] EXAMINATION
December 2010
Marks
Time: 4 Hours
Notes:
1.
2.
3.
12
Questions 1 and 2 are multiple choice. For these questions, select the best answer for each of the unrelated items. Answer each of these
items in your examination booklet by giving the number of your choice. For example, if the best answer for item (a) is (1), write (a)(1) in
your examination booklet. If more than one answer is given for an item, that item will not be marked. Incorrect answers will be marked as
zero. Marks will not be awarded for explanations.
Except for multiple-choice questions, answers should include all supporting calculations where appropriate.
If you provide alternative answers to Questions 3, 4, 5, or 6, only the first answer will be marked. If you wish to change your answer, you
must cross out the answer you do not wish to submit for marking.
Question 1
Note:
2 marks each
a.
Which of the following is consistent with the weak form of market efficiency?
1) For the past 5 years, Jean has bought penny stocks in December and then sold all of them in
January of the following year, consistently earning at least 100% return.
2) ABC Inc. has adopted an accounting policy to recognize revenues faster. After releasing
surprisingly positive financial results purely due to this change, its share price rose sharply.
3) A recent study concluded that money managers employing an active trading strategy consistently
performed better than those using the buy-and-hold strategy.
4) The strategy of buying high beta stocks before an expected bull market yields no better results
than the market portfolio.
b. Which of the following best describes an example of unethical behaviour?
1) Big banks raised the interest rates on their mortgage loans when their own financing costs were
expected to increase.
2) A brokerage house e-mailed the public a free newsletter containing a few bits of investment
advice to attract subscriptions to its expensive premium service.
3) The executives of a bankrupt company were awarded large severance packages while the laid-off
employees received the minimum employment insurance.
4) The banking industry blamed the marked-to-market accounting rule for the massive asset
write-downs.
c.
Which of the following best describes beta?
1)
2)
3)
4)
Beta is a sensitivity analysis of a project.
Beta is the best measure of the risk of a well-diversified portfolio.
Beta is the portion of risk that can be reduced through diversification.
Beta is used to estimate the required return on all projects when a firm is in multiple lines of
business.
Continued...
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©CGA-Canada, 2010
Page 1 of 7
d. Which of the following is the best hedging strategy for a bank with a negative gap when interest rates
are expected to increase?
1)
2)
3)
4)
e.
Which of the following financing strategies will benefit the most from an expected decline in interest
rates?
1)
2)
3)
4)
f.
Aggressive strategy
Conservative strategy
Extremely conservative strategy
Maturity-matching strategy
Which of the following enables a firm to predict when and how much cash will be required?
1)
2)
3)
4)
18
Buy BA futures contracts
Buy calls on BA futures contracts
Increase rate-sensitive assets
Increase rate-sensitive liabilities
Cash budget
Pro forma balance sheet
Pro forma cash flow statement
Pro forma income statement
Question 2
Note:
3 marks each
a.
What is the payback period of a project that costs $75,000 and generates $10,000 in the first year,
$25,000 in the second year, $30,000 in the third year, and $15,000 per year for the following 5 years?
1)
2)
3)
4)
2.667 years
3 years
3.667 years
4 years
b. What is the effective annual interest rate for a discount interest term loan at a stated interest rate of 7%
compounded annually and with a compensating balance of 10%?
1)
2)
3)
4)
c.
7.53%
7.78%
8.43%
9.22%
DEF Corp. has 12 million voting shares outstanding and has to elect 8 directors. A minority group of
shareholders wants to elect 3 particular directors. DEF uses cumulative voting in its elections to the
board of directors. How many votes are required per director (at the minimum) for the minority group
to ensure it will elect 3 directors?
1)
2)
3)
4)
4 million
4.5 million
7.2 million
10.667 million
Continued...
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©CGA-Canada, 2010
Page 2 of 7
d. FLY Corp. common shares are trading at $17 on the market. Currently, the continuously compounded
risk-free rate is 2% per year and the annual standard deviation of the continuously compounded rate of
return on FLY shares is 15%. According to the Black-Scholes option-pricing model, what is the
premium for a call option on FLY common shares with an exercise price of $20 and a 120-day expiry
date?
1)
2)
3)
4)
e.
A life insurance company has a stock portfolio with a current market value of $50 million and a price
change standard deviation of 20% per year. Assuming that the price change follows a normal
distribution, what is the 95% value at risk during the next year?
1)
2)
3)
4)
f.
$10.00 million
$16.45 million
$20.00 million
$22.50 million
In 2010, GO Corp. generated 85% of its annual revenues of $200 million on credit. Its gross margin
was 30%. The average balances at December 31, 2010 were $15 million of accounts receivable,
$18 million of inventory, and $20 million of accounts payable and accrued liabilities. What was GO’s
cash conversion period in 2010?
1)
2)
3)
4)
EFN2D10
$0.0230
$0.0384
$0.2300
$3.0000
27 days
32 days
79 days
131 days
©CGA-Canada, 2010
Page 3 of 7
20
Question 3
Five Star Corp. (FSC), a manufacturer of electronic products, has set up a new division to manage its
green energy (environmentally friendly) investments. FSC is evaluating an investment in a factory that
manufactures wind turbines. Information on the division’s project, the firm itself, and the green energy
industry is as follows:
Project
Initial investment
Salvage value
Annual revenue
Annual operating costs
CCA rate
Useful life
$7 billion
Nil
$5 billion
80% of revenue
30%
20 years
Company
Tax rate
40%
Debt-to-equity ratio
50% to 50%
Levered beta
1.2
Bank loan annual interest rate (interest only at end of every year until maturity)
10%
Common shares issuing cost (deductible over 5 years)
1% of the amount to be raised
WACC
9.7%
Green energy industry and financial market
Industry debt-to-equity ratio
Industry levered beta
Industry tax rate
Yield on Treasury bill (T-bill)
Expected rate of return on S&P/TSX stock market index
35% to 65%
1.6
35%
5%
12%
FSC has decided to finance the project at the same debt-to-equity ratio as the firm. FSC may also apply for
the maximum amount ($1 billion) of the provincial government low-interest 6% loan (also interest only)
and year-end operating cost subsidies of $1 million per year from the federal government for the first 5
years. You are asked to help evaluate this project, and specifically to answer the following questions.
Required
2
a.
5
b. Indicate and calculate the discount rate(s) you would use in your evaluation. Briefly explain how to
estimate the beta for a new business division/company.
5
c.
4
d. Calculate the adjusted present value of the project and determine whether this project is financially
feasible with a debt-to-equity ratio of 50% to 50%, but without financial support from the
governments.
4
e.
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Briefly explain which of the 3 methods [adjusted present value (APV), weighted average cost of
capital (WACC), or equity residual (ERM)] you would use to evaluate this project.
Calculate the base-case net present value (NPV) excluding financial support from the governments
and determine whether this project is financially feasible if only shareholders’ equity (retained
earnings) is used to finance the project.
Calculate the adjusted NPV if FSC uses the maximum low-interest loan from the provincial
government and the 5-year operating cost subsidies from the federal government. Indicate whether the
project should be accepted.
©CGA-Canada, 2010
Page 4 of 7
15
Question 4
Diamonds For You Inc. (DFY), a British Columbia-based diamond producer, has survived the recent
economic recession. The company attributed its survival to the fact that it paid off all its debt before the
recession. Now with the Canadian economy improving and interest rates expected to rise soon, DFY plans
to re-introduce debt into its capital structure to reduce its cost of capital. DFY’s CFO, Donna, believes that
the optimal debt-to-total assets ratio should be about 30%. She has decided to recommend that the board of
directors accept the 5% perpetual loan offered by its bank to buy back some common shares. DFY’s shares
are currently undervalued by the market because of the company’s poor financial performance over the
past several years and a cut in its cash dividends 3 years ago.
DFY has 5 million common shares outstanding at a market capitalization value of $100 million. Its
earnings before interest and taxes (EBIT) are expected to be $25 million forever and it pays out all the
earnings available to shareholders as dividends. The corporate tax rate for DFY is 40%. Donna has asked
for your help in formulating her recommendation to the board.
Required
3
10
a.
Calculate DFY’s current price per share, cost of equity, and weighted average cost of capital
(WACC).
b. Calculate the amount of loan that DFY should take on to increase its debt-to-total assets ratio to 30%.
Calculate the value of the firm (assets), value of equity, cost of equity, WACC, price per share, and
the number of common shares outstanding after the share repurchase. Illustrate that DFY will reduce
its WACC after the share repurchase.
2
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c.
State the two purposes of DFY’s share repurchase.
©CGA-Canada, 2010
Page 5 of 7
10
Question 5
Call Me Inc. (CMI), a telecommunications service provider, offers wireless communications products and
services to residential and small business customers. CMI has identified an acquisition target, Good Buy
Corp. (GBC), which is an electronics retailer with stores across Canada. The financial staff identified
several previous mergers in the electronics retailing industry in the past 5 years and prepared Exhibit 5-1
to assist in estimating an offer price for GBC shares.
EXHIBIT 5-1
Key Ratios from Previous Mergers
Merger case
Premium paid
Times earnings paid
Times cash flow paid
Times book value paid
Times replacement cost paid
C1
25%
12.0
15.0
2.5
2.0
C2
15%
5.0
13.0
1.5
1.55
C3
30%
10.0
5.5
3.5
1.85
C4
40%
6.0
10.0
5.5
1.5
C5
55%
18.0
28.0
4.5
1.75
EXHIBIT 5-2
Excerpts from GBC’s Financial Statements
Income statement
Revenue
Gross profit
Operating income
Net income
Earnings available to common shareholders
Balance sheet
Preferred shares
Common shares
Contributed surplus
Retained earnings
Number of shares outstanding
$ 100M
$ 70M
$ 35M
$ 25M
$ 20M
$
$
$
$
25M
20M
30M
50M
10M
Cash flow statement
Operating cash flow
Cash flow from investing activities
Cash flow from financing activities
$ 50M
$ (25M)
$ (15M)
Market data
Market capitalization
Total replacement cost
$ 170M
$ 150M
Required
2
a.
8
b. Calculate a minimum and a maximum share price for each ratio. Determine a range of share prices
that may be paid by CMI for GBC, which excludes all prices that would be considered extreme based
on previous mergers.
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Indicate what type of merger this would be. Name one reason why CMI management would want to
acquire GBC.
©CGA-Canada, 2010
Page 6 of 7
25
Question 6
GMI is a Quebec-based operator of a chain of drugstores across Canada. The drugstores sell prescription
and non-prescription drugs and general merchandise. GMI’s CFO has asked you to study two issues and
make recommendations. The first is a bond refinancing. The bond in question is GMI’s only outstanding
callable bond. It was issued 6 years ago and has 14 years remaining to maturity. At the time of issuance,
the general interest rate was higher. GMI had to pay a 12% coupon rate to raise the $100 million needed
for its planned expansion. Since then, interest rates have declined significantly and should remain low in
the short term. However, recent positive economic data suggest that the Canadian economy has recovered
from the recession and will grow. As a result, interest rates are expected to rise significantly. The GMI
board needs to decide whether to refinance this bond now or not at all. GMI’s investment banker suggests
that GMI is able to float $100 million, 14-year bonds at an annual rate of 8%. The following summarizes
some relevant information:
GMI
Bond
Old Issue
Planned Issue
Face value
Remaining or planned maturity
Likely overlap period
Coupon rate
Call premium or flotation costs
$100M
14 years
1 month
12%, paid semi-annually
15% of the total face value
$100M
14 years
1 month
8%, paid semi-annually
2.5% of the total face value
GMI has an income tax rate of 40% and the Treasury bill rate is 2%.
The second issue is GMI’s working capital financing. GMI has been using short-term funds to finance its
regular operations. The rationale is that, because of the short-term nature of its assets, the drugstore
business should be financed with short-term funds — the maturity-matching principle. GMI also wanted to
take advantage of lower short-term interest rates during the past few years. However, as the general level
of interest rates is likely to increase, GMI’s short-term financing strategy needs evaluation. The most
pressing issue is that a $40 million short-term loan is coming up for renewal next month.
Required
9
a.
Determine whether GMI should refinance the old long-term bond issue now.
2
b. Identify the two possible negative consequences of using short-term funds to finance regular
operations.
7
c.
7
d. Assume that GMI would like to continue using a 1-year loan. Indicate how GMI could use (buy or
sell) a 3-month Canadian bankers’ acceptance (BA) futures contract (BAX) trading on the Montreal
Exchange with a $1 million face value. In particular, indicate how many futures contracts it should
buy or sell. The correlation between changes in the rate on GMI’s loan and on the bankers’ acceptance
is 0.92. The current 1-year rate is 4.5%. The price of the 3-month BA futures contract is 95.5 and is
expected to drop to 93 in one month. Each basis point variation in BAX prices represents a gain or
loss of $25. Explain how the hedging strategy works under the two opposite scenarios: an increase in
interest rates and a reduction in interest rates. Show all supporting calculations.
Identify and explain the hedging strategies available to minimize the unfavourable outcomes of the
interest-rate risk. Be specific about the appropriate position (buy or sell) in each hedging strategy.
END OF EXAMINATION
100
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©CGA-Canada, 2010
Page 7 of 7
ADVANCED CORPORATE FINANCE [FN2]
EXAMINATION
FN2
Before starting to write the examination, make sure that it is complete and that there are no
printing defects. This examination consists of 7 pages and 21 pages of attachments. There are
6 questions for a total of 100 marks.
READ THE QUESTIONS CAREFULLY AND ANSWER WHAT IS ASKED.
To assist you in answering the examination questions, CGA-Canada includes the following glossary of terms.
Glossary of Assessment Terms
Adapted from David Palmer, Study Guide: Developing Effective Study Methods (Vancouver: CGA-Canada, 1996).
Copyright David Palmer.
Calculate
Compare
Contrast
Criticize
Define
Describe
Design
Determine
Diagram
Discuss
Evaluate
Mathematically determine the
amount or number, showing
formulas used and steps taken. (Also
Compute).
Examine qualities or characteristics
that resemble each other. Emphasize
similarities, although differences
may be mentioned.
Compare by observing differences.
Stress the dissimilarities of qualities
or characteristics. (Also Distinguish
between)
Express your own judgment
concerning the topic or viewpoint in
question. Discuss both pros and
cons.
Clearly state the meaning of the
word or term. Relate the meaning
specifically to the way it is used in
the subject area under discussion.
Perhaps also show how the item
defined differs from items in other
classes.
Provide detail on the relevant
characteristics, qualities, or events.
Create an outcome (e.g., a plan or
program) that incorporates the
relevant issues and information.
Calculate or formulate a response
that considers the relevant
qualitative and quantitative factors.
Give a drawing, chart, plan or
graphic answer. Usually you should
label a diagram. In some cases, add
a brief explanation or description.
(Also Draw)
This calls for the most complete and
detailed answer. Examine and
analyze carefully and present both
pros and cons. To discuss briefly
requires you to state in a few
sentences the critical factors.
This requires making an informed
judgment. Your judgment must be
shown to be based on knowledge and
information about the subject. (Just
stating your own ideas is not
sufficient.) Cite authorities. Cite
advantages and limitations.
Explain
In explanatory answers you must
clarify the cause(s), or reasons(s).
State the “how” and “why” of the
subject. Give reasons for differences
of opinions or of results. To explain
briefly requires you to state the
reasons simply, in a few words.
Identify
Distinguish and specify the important
issues, factors, or items, usually based
on an evaluation or analysis of a
scenario.
Illustrate
Make clear by giving an example,
e.g., a figure, diagram or concrete
example.
Interpret
Translate, give examples of, solve, or
comment on a subject, usually
making a judgment on it.
Justify
Prove or give reasons for decisions or
conclusions.
List
Present an itemized series or
tabulation. Be concise. Point form is
often acceptable.
Outline
This is an organized description. Give
a general overview, stating main and
supporting ideas. Use headings and
sub-headings, usually in point form.
Omit minor details.
Prove
Establish that something is true by
citing evidence or giving clear logical
reasons.
Recommend Propose an appropriate solution or
course of action based on an
evaluation or analysis of a scenario.
Relate
Show how things are connected with
each other or how one causes another,
correlates with another, or is like
another.
Review
Examine a subject critically,
analyzing and commenting on the
important statements to be made
about it.
State
Clearly provide a position based on
an evaluation, e.g., Agree/Disagree,
Correct/Incorrect, Yes/No. (Also
Indicate)
Summarize Give the main points or facts in
condensed form, like the summary of
a chapter, omitting details and
illustrations.
Trace
In narrative form, describe progress,
development, or historical events
from some point of origin.
Advanced Corporate Finance [FN2]
PV 
Present value of a future value (FV)
amount
FV
(1  i)
n
n = number of periods
i = rate per period
FV  PV(1 i) n

1
1
(1 i) n
PV  PMT
i



Future value of a present value (PV)
amount






Present value of an ordinary annuity
PMT = periodic payment
 1 i n  1
  
FV  PMT
i




PV  C 0 
Future value of an ordinary annuity
PMT = periodic payment
Present value of an asset discounted at
the lending and borrowing rate
CF1
C
 C0  1
1 r
1 r
C0 = current cash flow
CF1 = C1 = cash flow expected next
period
r = market lending/borrowing rate
PV 
Present value of an asset discounted at
the cost of capital
CF1
C
 1
1 k 1 k
k = cost of capital
NPV 
Net present value of a single future
cash flow
CF1
C
 C0  1  C0
1 k
1 k
C0 = cost of acquiring the asset
Internal rate of return for a current
cash outflow followed by a single cash
inflow
C1
CF1
 C 0 or
 C0
1  IRR
1  IRR
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 1 of 21
CCAi = C  d  (1 – d/2)(1 – d)i–2
CCA for year i
C = capital cost
d = capital cost allowance rate of the
class
i = year 2, 3, 4, …
UCCi = C  (1 – d/2)(1 – d)i–1
UCC at beginning of year i
n
CFi
Sn

i
(1 k) n
i1 (1 k)
Present value of future incremental
cash flows without tax shield formula
method
PV  
CFi = expected cash flows at the end
of period i
k = discount rate
Sn = salvage value at the end of n
periods
n
PV  
i1
Sn
Fi

 PVTS
i
(1 k) (1 k) n
Present value of future incremental
cash flows separating out the present
value of tax shields
Fi = cash flow during period i,
excluding the tax shield
PVTS = present value of the tax shield
 C  d  T  2  k 
PVTS  


 2(d  k)   1  k 
Present value of perpetual tax shields
(half-year rule)
C = capital cost
d = capital cost allowance rate of the
class
T = tax rate
 S
d  T 
PVTSL n   n n 

(1 k) d  k 
Present value of lost perpetual tax
shields with a continuing CCA pool
UCC n d  T 
PVTSL n  


(1 k) n d  k 
Present value of lost perpetual tax
shields when terminating the asset
class (excluding a recapture or
terminal loss)
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 2 of 21
n
Fi
i 1
(1  k)
PV  

i
(1  k)
n
 C  d  T   2  k   Sn



n
 2(d  k)   1  k   (1  k)
n
Fi
i 1
(1  k) i
PV  
 UCC n

n
 (1  k)

Fi
i 1
(1  k)
 Sn

n
 (1  k)
 d  T 


  d  k 
C  d  T  2  k 



n
(1  k)
 2(d  k)   1  k 
Sn
  d  T   UCC n  S n  T 



(1  k) n
  d  k  

n
NPV  
Present value of future incremental cash
flows using the tax shield formula
method with a continuing (open) CCA
pool
Sn
i

C  d  T 


(1  k)
 2(d  k) 
Sn
n
2  k 
1  k 


n
Fi
i 1 (1 
k) i

 C d  T   2  k 



n
(1  k)
 2(d  k)   1  k 
Sn
 UCC n   d  T   (UCC n  S n )T 

  C0

n 
(1  k) n

 (1  k)   d  k  
PV NPV + C 0

C0
C0
ARR 
Net present value with the present value
of tax shields for a continuing CCA pool
 d  T 

  C0
  d  k 
NPV  
PI 
Present value of future incremental cash
flows using the tax shield formula
method when terminating the asset class
(closed pool)
Net present value with the present value
of tax shields when terminating the asset
class (closed pool)
Profitability index
ACF
Ia
Average rate of return on book value
ACF = average annual incremental aftertax cash flows (net income) from
operations over the life of the project
Ia = average book value of the investment
in the project
   x P(x)
Expected value (mean) of random
variable x
all x
 2   (x  ) 2 P(x)
Population variance of random variable x
all x
 E(x 2 )   2 where E(x 2 )   x 2 P(x)
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 3 of 21


 xy    x   x  y   y P x, y 
 xy 
Population covariance of two random
variables x and y
 xy
Coefficient of correlation (population)
xy
R1  R 2  ... R n
n
R=
 2R 
 2R
all x all y
Mean of historical returns
R 1  R  2  R 2  R  2
n
n
 ... 
R n  R  2  1 n R
n
n
2
2


R  R  2 
R1  R
R 2  R


 ...  n
n -1
n -1
n -1
t 1
1
R

Variance of returns where each outcome
has an equal probability (population)
2

1 n
 R1  R
n - 1 t 1
RP = w1R1 + w2R2 + ... + wnRn

2
Variance of returns where each outcome
has an equal probability (sample)
Return of a portfolio based on the
weighted average of the asset returns
n
R p   wi R i
n = number of securities in the portfolio
wi = weight of return i, calculated as the
ratio of the amount invested in the
security i divided by the total investment
Ri = return on security i
i 1
n
Expected return of a portfolio using
probabilities of states of the economy
ER P    Pi R Pi
i 1
i = 1, 2, … , n
n = number of possible outcomes
Pi = probability of outcome i
RPi = portfolio return associated with
outcome i
 p   Pi R Pi  E R P 
2
n
Variance of a portfolio (population)
2
i 1
n
Expected return on a portfolio using a
weighted average of expected returns
ER P    w i E R i 
i 1
wi = weight of investment i in the
portfolio
n = number of investments in the portfolio
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 4 of 21
 P = w1212 + w2222 + 2w1w21212
Variance of a two-asset portfolio
2
1 = standard deviation of investment 1
2 = standard deviation of investment 2
12 = correlation coefficient of
investments 1 and 2
n
Variance of an n-asset portfolio
n
 P 2 =   ij w i w j i  j
ij = correlation coefficient between
securities i and j
i =1 j=1
E(RPi) = wiRf + (1 – wi)E(RM)
Expected return on a portfolio containing
a risk-free asset and the market portfolio
E(RM) = expected return on the market
portfolio
wi = portion invested in the risk-free asset
Pi = (1 – wi) M
Standard deviation of a portfolio
containing a risk-free asset and the market
portfolio
wi = portion invested in the risk-free asset
M = standard deviation of the market
portfolio
 Pi
[E(RM) – Rf]
M
E(RPi) = Rf +
i 
CovR i ,R M 
M
2

Capital market line
 iM   i   M
M
Beta of an asset
2
Cov(Ri,RM) = covariance between return
on security i and market return RM
Ri,t = ai + iRM,t + ei,t
Total security return regression estimation
of beta
ai = constant term
i = beta of security i
ei,t = error term
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 5 of 21
Security premium regression estimation of
beta (characteristic line)
Ri,t – Rf,t = ai +i (RM,t – Rf,t) + ei,t
Ri,t – Rf,t = excess return over risk-free
rate (Rf)
ai = constant term
i = beta of security i
ei,t = error term
E(Ri) = Rf + i[E(RM) – Rf]
Capital asset pricing model
Rf = risk-free rate
E(RM) = expected return on the market
portfolio
i = beta of security i
p = w11 + w22 + ... + wnn
Weighted average of a portfolio beta
wi = weight of security i in the portfolio
1 = beta of security i
i = 1, 2, 3, … , n
L = U + (1 – T)(D/E)U
Beta for a levered firm
U = unlevered beta
T = tax rate
D = market value of debt
E = market value of equity
CVi 
CVi 
i
Coefficient of variation
E(R i )
i = standard deviation of project i values
E(Ri) = expected return on project i
i
Coefficient of variation for a capital
investment
E(NPVi )
i = standard deviation of project i NPV
values
E(NPVi) = expected (mean) NPV of
project i
EAR =
amount of annual interest
outstanding balance
EFN2D10 [FN2.1011]
Effective annual rate/return for annual
interest payments
CGA-Canada, 2010
Attachment 6 of 21
 k
m
EAR  1 nom  1.0
 m 
Effective annual rate for interest payments
more frequent than an annual basis
knom = nominal or stated rate
m = number of compounding periods per
year
EAR =
Effective annual rate for a loan with a
compensating balance (annual interest
payments)
k nom
1.0  CB
CB = compensating balance as a
percentage of the total loan amount
Face value =
funds needed
1.0  CB
Face value needed to obtain the desired
funds for a loan
m

k nom 


m
EAR = 1 +
  1.0
 1.0  CB 


EAR 
interest
k nom
or EAR 
face value  interest
1.0  k nom

k nom

m
EAR  1
k
 1.0  nom

m
Face value 
EAR =
Effective annual rate for a loan with a
compensating balance and interest
payments more frequent than an annual
basis
m

 1.0


Effective annual rate for a discounted loan
and interest payments more frequent than
an annual basis
funds needed
k
1 nom
m
Face value needed to obtain the desired
funds for a discounted loan
k nom
1.0  k nom  CB
Face value 
Effective annual rate for loans with
compensating balances, terms of one or
more years, and annual interest payments
funds needed
1.0  k nom  CB
EFN2D10 [FN2.1011]
Effective annual rate (non-discounted
equivalent rate) for a discounted loan with
annual interest payments
Face value needed to obtain the desired
funds for a discounted loan with a
compensating balance (annual interest
payments)
CGA-Canada, 2010
Attachment 7 of 21
Call premium = Cy  Nr / N
Value of a call premium where the
premium declines in proportion to the
number of years remaining to maturity
Cy = annual coupon
Nr = number of years remaining to
maturity
N = number of years of original maturity
d  S 
N = 
+1
D + 1

Number of shares required to elect a
desired number of directors
d = number of directors the minority
shareholders seek to elect
S = total number of shares outstanding
D = total number of directors to be elected
R on =
Pon  E
N +1
Theoretical value of a right during the
rights-on period
Pon = market price of the underlying share
during the rights-on period
E = exercise price
N = number of rights required to purchase
one new share
R ex =
Pex  E
N
Theoretical value of a right during the exrights period
Pex = market price of the underlying share
during the ex-rights period
Financial risk = L – U
Financial risk
L = total risk to shareholders of the
levered firm as measured by the standard
deviation of returns (or profits)
U = total risk to shareholders of the
unlevered firm as measured by the
standard deviation of returns (or profits)
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 8 of 21
V=
EBIT EBIT
=
kL
kU
Value of a firm in the absence of
corporate taxes
V = VL = VU
EBIT = perpetual earnings before
interest and taxes
kL = risk-adjusted discount rate for the
levered firm
kU = risk-adjusted discount rate for the
unlevered firm
k L = kU
D 
k E = k U + k U  k B  
E 
Cost of equity for a levered firm in the
absence of corporate taxes
kU = cost of equity of the unlevered firm
kB = before-tax cost of debt
D = market value of the firm’s debt
E = market value of the firm’s equity
V = D + E = D + EL
 D 
k L = k B 
+
 E + D 

Market value of the levered firm

D  E 
k U  k U  k B   
E E + D 


PV (interest tax savings) = TCD
Weighted average cost of capital for a
levered firm in the absence of corporate
taxes
Present value of interest tax savings for a
perpetual loan
TC = corporate tax rate
D = amount of debt
VU =
EBIT(1  TC )
Value of an unlevered firm in the
presence of corporate taxes
kU
Value of a levered firm in the presence
of corporate taxes
VL = V U + TC D
VU = unlevered firm’s value
TC = corporate tax rate
D = amount of debt
D 
k E  k U  k U  k B   1 TC 
E 
Cost of equity for a levered firm in the
presence of corporate taxes
kU = cost of equity to the unlevered firm
kB = before-tax cost of debt
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 9 of 21
D 
E 
WACC = k L =  k B 1 TC  +  k E
V 
V 
EL 
Weighted average cost of capital
V = value of the firm (debt + equity)
(EBIT  I)(1  TC )
kE
Estimated value of levered equity with
corporate taxes from cash earnings aftertax
EL = value of levered equity
I = total interest payment
kE = cost of levered equity
1 – TD = (1 – TC)(1 – TS)
Tax parity between tax rate on interest
income, corporate tax rate, and personal
tax rate on income from shares
TD = tax rate on interest income
TC = corporate tax rate
TS = personal tax rate on income from
shares
VU 
EBIT(1  TC )(1  TS )
kU
Value of an unlevered firm in the
presence of personal and corporate taxes
TC = corporate tax rate
TS = personal tax rate on income from
shares
kU = cost of equity of the unlevered firm
CFL = EBIT (1 – TC)(1 – TS) – I (1 – TC)(1 – TS) + I (1 – TD)
Cash flows from a levered firm
I = annual payments to debtholders
TC = corporate tax rate
TS = personal tax rate on income from
shares
TD = personal tax rate on income from
debt
 1 T 1 T 
C
S
VL = VU + 1
D

1 TD  

Value of a levered firm in the presence
of personal and corporate taxes
VU = value of the unlevered firm
D = market value of debt
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 10 of 21
VL = VU + TCD – PV(BC)
Value of a levered firm in the presence
of bankruptcy costs
VU = value of the unlevered firm
TC = corporate tax rate
D = market value of debt
PV(BC) = present value of the expected
bankruptcy-related costs
EBIT
DOL = EBIT
Sales
Sales
DOL 
Degree of operating leverage as a
function of sales level
 = change in the variable
contribution margin
(P  V)Q

EBIT
(P  V)Q  FC
Degree of operating leverage as a
function of a contribution margin
P = price per unit
V = variable cost per unit
Q = amount of sales in units
FC = fixed costs excluding financing
charges
DOL 
EPS 
PQ  VQ
sales  variable costs

PQ  VQ  FC sales  variable costs  FC
EBIT - I1  TC   PD
Degree of operating leverage as a
function of variable costs
General formula for finding EPS from
EBIT
S
I = interest payments
TC = corporate tax rate
PD = preferred dividends
S = number of common shares
outstanding





EBIT*  I1 1 TC  PD1 EBIT*  I 2 1 TC  PD 2





S1
S2
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Leverage indifference EBIT level
EBIT* = level of EBIT at which
earnings per share for each alternative is
equal
I = interest payments under each
alternative
TC = corporate tax rate
PD = preferred dividends under each
alternative
S = number of common shares
outstanding under each alternative
Attachment 11 of 21
VN = VC + TCDN
Firm value after a new debt issue
VC = current (original) market value of
the firm
TC = corporate tax rate
DN = amount of required additional
(new) debt
APV = base-case NPV + PV of financing cash flows
= NPVB + ITS – FCNS + TSFC + ITCS – IBC + OFRE
Adjusted present value
NPVB = base-case NPV
ITS = PV of interest tax shield
FCNS = PV of flotation costs of new
securities
TSFC = PV of tax shield on flotation
cost amortization
ITCS = PV of financing-related
investment tax credits and subsidies
IBC = PV of incremental bankruptcy
costs
OFRE = PV of other financing-related
effects
ITS 
T  IP1
1 kD
TSFC 
T  IPi
… 
T  FCA1
1 kD

T  IPi 1
1  k D  i 1  k D  i 1
 …
T  FCA i

 …
T  FCA i 1
1  k D  i 1  k D  i1
T  IPn
1  k D n
 …
T  FCA n
1  k D  n
For equal period amortization of flotation costs at time zero,
TSFC 
n
 (1  k
t 1
T(FC/n)
D)
t
 T(FC/n)  PVIFA (k D , n )
PV(BC) = probability of financial distress  (1 – T)  BC
Present value of interest tax shields
IPi = interest payment in period i, where
i = 1, …, n
T = corporate tax rate
kD = after-tax required rate of return on
the firm’s debt
n = number of interest payment periods
Present value of the tax shields on
flotation costs
FCAi = flotation cost amortization in
period i, where i = 1, …, n
T = corporate tax rate
kD = after-tax required rate of return on
debt
n = number of amortization periods for
the flotation costs (lesser of 5 years or
the maturity of the securities)
FC = total flotation costs
Present value of the after-tax bankruptcy
costs
BC = bankruptcy costs
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 12 of 21
IBC = PV(BC)D – PV(BC)E
Incremental present value of bankruptcy
costs
PV(BC)D = PV of bankruptcy costs
under debt financing
PV(BC)E = PV of bankruptcy costs
under equity financing
RNVi  CCA i  IPi   (1  T)  CCA i   DPi

i 1
1  k E  i
n
NPVER
 C0  D
+ PV of salvage price
+ PV of investment tax credits & subsidies
 PV of flotation costs
PV(OC) 
(1  T)OC i (1  T) OC i 1
(1  T) OC n


i 1
1 r
(1  r)
(1  r) n
Net present value of a project (equity
residual method)
RNVi = revenues – costs during period i
CCAi = capital cost allowance in period i
IPi = interest payment in period i
DPi = debt principal payments in period i
D = initial proceeds from the debt issue
C0 = initial investment outlays
kE = cost of equity
Present value of savings in operating
costs due to leasing
i = 1, …, n

C 1 g 

 1  n 

t
n
r

g



 
t 1 1 r 
1 r   
n
PV  
Firm valuation using operating cash
flows with WACC
OCFt

OCF 1 g 
 
1
n



t
n

t 11 WACC

WACC  g
1 WACC 

n

OCFt

C 1 g 
 C
 1  n 

0
t
n

t 1 1 r 

 r  g 
1 r 

n
NPV  
OCFt = operating cash flow after tax,
including cash flow from (non-cash)
depreciation for period t
r = discount rate
n = period of initial cash flow
forecasting
Cn = OCFn = cash flow of the last
forecast period
g = perpetual growth rate after period n
NPV of acquisition using operating cash
flows (with WACC as the required
return)
OCFt
C0 = cost of the acquisition in terms of
new debt and share purchases
NPV = value to debtholders, preferred
shareholders, and common equity
shareholders
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 13 of 21
OCFt
n
PVequity  
t 1
1  r  t
 1   C n 1  g  

  B 0  P0
n 
 1  r    r  g  
Firm value to equity shareholders using
operating cash flows
B0 = PV of debt
P0 = PV of preferred shares
n
PV  
t 1
FCFFt
1  r  t
 1

n
 1  r 
OCFt
n

t 1
n

1  WACC t
t 1
  FCFFn 1  g  


  r  g  
NCI t
1  WACC t
Firm valuation using free cash flows to
the firm and WACC method

1

n
 1  WACC
FCFF = free cash flow to the firm
NCI = net capital investments
  FCFFn 1  g  

 g = perpetual growth rate of free cash
  WACC  g   flow to the firm after period n
n
 1   FCFFn 1  g 
FCFFt
IT
  t C t 

n
t
t 11  rD 
t 11  rU 
 1  rU    rU  g 
Firm valuation using free cash flows to
the firm and APV method
n
PV  
n

t 1
OCFt
1  kU 
n
 1
  FCFFn 1  g 
NCIt
IT
  t C t 

t
n
t 11  k U 
t 11  k D 
 1  kU    k U  g 
n
t

ItTC = period income tax shield on
interest from long-term debt
rU = kU = unlevered cost of equity
rD = kD = after-tax cost of long-term debt
g = perpetual growth rate of free cash
flow to the firm after period n
(For perpetual funding with debt, the
debt tax shield could become a
perpetuity.)
n
PV  
t 1
n


1

n
 1  k E 
FCFE t
1  k E  t
OCFt
1  k E 
n

NCI t
  FCFE n 1  g  


  k E  g  
n

I t (1  TC )  PDiv t
1  k E  t 1
1  k E 

  FCFE n 1  g  
1

  B 0  P0
n  
 1  k E    k E  g  
t 1
t
t 1
EFN2D10 [FN2.1011]
t
t
Firm valuation using free cash flows to
equity and ERM method
n

t 1
B t  Pt
1  k E  t
CGA-Canada, 2010
FCFE = free cash flow to equity
kE = return to levered equity
OCFt = operating cash flow for period t
NCIt = net capital investment for period t
It = interest payment on debt for period t
TC = effective corporate tax rate
PDivt = preferred share dividend for
period t
Bt = bond repayment for period t
Pt = preferred share repayment for period
t
B0 = initial bond amount
P0 = initial preferred share amount
g = perpetual growth rate of free cash
flow to equity after period n
Attachment 14 of 21
PV0 
D 1  g 
D1
 0
r  g  r  g 
Valuation using dividend cash flows and
ERM method
PV0 = present value at the current time
(end of period 0)
D1 = cash dividend payment at the end
of period 1
D0 = cash dividend payment at the end
of period 0
r = discount rate = kE
g = perpetual growth rate in dividends
n
PV0  
Dt
t 1
1  r  t
n
Dt
or
PV0  
t 1
1  r 
t
 1   D n 1 


n  
 1  r    r  g  
Valuation using dividend cash flows and
ERM method with initial period of
specific dividend amounts
 1   D n 1  g  


n 
 1  r    r  g  
n = number of periods of specific
dividend amounts
 D1   1  g 1  n   1   D n 1 
PV0  


 1 

1  r  n   1  r  n   r  g 2  
 r  g 1   
or
 D1   1  g 1  n   1   D1 1  g 1  n 
PV0  



 1 
1  r  n   1  r  n   r  g 2  
 r  g 1   
 CFt
n
D
  (1  i)
t 1
t

 t

g1 = initial high growth rate
g2 = perpetual growth at the market rate
Duration of a security
CFt = cash flow expected at time t
t = number of periods until cash flow
payment
i = yield to maturity
n = number of anticipated cash flows
 CFt 

t 
 (1  i) 
t 1 
n

 V 


 V  D

i
r
1
m
EFN2D10 [FN2.1011]
Valuation using dividend cash flows and
ERM method with initial period of high
dividend growth
Volatility (percentage change) of a
security’s value from changes in the
required yield (stated per year)
D = duration measured in years
V = market value of the security
V = change in market value of the
security
r = change in interest rates
i = yield to maturity
m = number of compounding periods per
year
CGA-Canada, 2010
Attachment 15 of 21
V 
D  V  r
D  V
 r or
i
i
1
1
m
m
Change in market (dollar) value of a
security for a given change in interest
rate (stated per year)
NII = r  gap
Change in net interest income due to gap
r = expected change in interest rates
DP 
D1V1  D i Vi    D n Vn
VP 
Duration of a portfolio
V1  Vi    Vn
Di = durations of i securities
(i = 1, …, n)
Vi = market values of i securities
(i = 1, …, n)
 D P  VP  r
 D P  VP
 r or
1 dW
1 d W
Change in a portfolio’s value as a
function of a weighted average expected
change in individual yields
Dp = portfolio’s duration
r = change in interest rates
dW = weighted average discount rate,
where the component rate for an asset is
the yield to maturity per compounding
period
i1
i2
in
m1 V1  m2 V2  ...  mn Vn
dw 
V1  V2  ...  Vn
Weighted average interest rate for a
portfolio
Price index = 100 – id
Price index
i = quoted interest rate for a bond
m = number of compounding periods per
year for the bond
V = market value of the bond
id = annual discount rate in percent
F0,T = S0 (1 + Rf0,T – Rh0,T)
Futures price for financial futures
F0,T = futures price at time 0 for delivery
at time T
S0 = spot price at time 0
Rf0,T = rate at time 0 on the risk-free
asset maturing at time T
Rh0,T = rate of cash payments expected
to be paid by the underlying asset
between time 0 and time T
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 16 of 21
F0,T = S0 (1 + Rf0,T – Rh0,T) + H0,T
Futures price for non-financial or general
assets
H0,T = holding costs from time 0 to time
T
F0,T = S0 [1 + Rf0,T – E(D0,T)]
General pricing formula for index
futures prices
E(D0,T) = opportunity loss for the
contract holder from the loss of
dividends during the contract period
F0,T
MN

R D  D
1 +

N D 

 S0
MN

R F  F
1
+


N F 

HR   
Forward exchange rate using the interest
rate parity relationship
F0,T = forward rate at time 0 quoted in
domestic currency at which the foreign
currency can be purchased for delivery
at time T
S0 = spot rate at time 0 quoted in
domestic currency at which the foreign
currency can be purchased for immediate
delivery
RD = annual interest rate on the domestic
currency
RF = annual interest rate on the foreign
currency
ND = number of compounding periods
per year for the domestic interest rate
NF = number of compounding periods
per year for the foreign interest rate
M = number of years until the forward
contract matures
Hedge ratio
V MC

FF M F
EFN2D10 [FN2.1011]
V = market value of assets/liabilities to
be hedged
FF = face value of the security
underlying the futures contract
MC = maturity of the assets/liabilities to
be hedged
MF = maturity of the security underlying
the futures contract
 = correlation of the change in volatility
of the rate to be hedged in relation to the
change in volatility of the rate on the
security underlying the futures contract
CGA-Canada, 2010
Attachment 17 of 21
TB =   BA
Price 
Change in value of T-bill rates as a
function of the bankers’ acceptance
futures rates
$100

days to maturity 
1 yield 



365
Price of a short-term, pure discount
security
C = SN(d1) – EN(d2) e–rT
Black-Scholes option-pricing model for
a call
S
ln   rT
T ½
E
d1 

2
T ½
S = share price
E = exercise price
r = continuously compounded risk-free
rate
T = time to expiration measured in years
 = standard deviation of the share’s
continuously compounded rate of return
N(d) = probability that a standardized,
normally distributed, random variable
will be less than or equal to d
d2 = d1 – T½
 d * d L

 N d U   Nd L  
N d * Nd L   

d
d
L
 U

Interpolation formula to determine N(d1)
or N(d2)
N(d*) = probability that an outcome will
be less than or equal to d*
dL = value of d in the normal curve table
that is smaller than and nearest to d*
dU = value of d in the normal curve table
that is greater than and nearest to d*
Present value = Ee – rT
Present value of the exercise price at the
expiry date
C + Ee – rT = S + P
Put-call parity relationship
P = put premium
C = call premium
S = share price
E = cash exercise price on option
expiration
r = risk-free rate
T = time to expiration of the options
P = C + Ee – rT – S
Value of a put option in terms of the putcall parity relationship
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 18 of 21
P = [1 – N(d2)] Ee – rT – S[1 –N(d1)]
Value of a put option using the BlackScholes formula
Security value = value of straight security + option value
Value of a security with built-in options
RX = RFX X – RFL X
Change in degree of risk from borrowing
in fixed-rate market compared with the
floating-rate market
RFX X = risk to lenders from lending to X
in the fixed-rate market
RFL X = risk to lenders from lending to X
in the floating-rate market
RY = RFL Y – RFX Y
Change in degree of risk from borrowing
in the floating-rate market compared
with the fixed-rate market
RFL Y = risk to lenders from lending to Y
in the floating-rate market
RFX Y = risk to lenders from lending to Y
in the fixed-rate market
r
eff, ann
e
r cnt,ann
Conversion of annual continuously
compounded rate to annual effective rate
and vice versa
1
rcnt,ann  ln1 reff,ann 
reff,ann = effective annual return
rcnt,ann = continuously compounded
annual return
IC = average inventory / (COGS/365)
RC = average accounts receivable / (CS/365)
PD = (average accounts payable + average accruals) / (COGS/365)
Cash conversion period = IC + RC – PD

COGS  
CS 
NWC  (IC  PD) 
 RC 
 AC  ANP  CPLD


365  
365 
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Cash conversion cycle and net working
capital
IC = inventory conversion period
RC = receivables conversion period
PD = payables deferral period
COGS = cost of goods sold
CS = annual credit sales
NWC = net working capital
AC = average cash level
ANP = average notes payable
CPLD = current portion of long-term
debt
Attachment 19 of 21
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 20 of 21
EFN2D10 [FN2.1011]
CGA-Canada, 2010
Attachment 21 of 21
CGA-CANADA
ADVANCED CORPORATE FINANCE [FN2] EXAMINATION
December 2010
SUGGESTED SOLUTIONS
Marks
12
Time: 4 Hours
Question 1
Note:
2 marks each
Sources:
a.
b.
c.
d.
e.
f.
18
4)
3)
2)
3)
1)
1)
Topic 1.4 (Level 2)
Topic 1.8 (Level 1)
Topic 2.7 (Level 1)
Topic 7.6 (Level 1)
Topic 10.5 (Level 1)
Topic 10.3 (Level 1)
Question 2
Note:
3 marks each
a.
3) Source: Topic 2.4 (Level 1)
PB = 3 + (75,000 – 10,000 – 25,000 – 30,000) / 15,000 = 3.667
b. 3) Source: Topic 3.1 (Level 1)
0.07
 8.43%
1  0.07  0.1
c.
4) Source: Topic 3.7 (Level 1)
Number of shares the minority group needs to ensure the election of 3 directors:
3  12M
 1  4,000,001 shares
8 1
The minority group will have 4,000,001  8 = 32,000,008 votes.
The number of votes required per director is 32,000,008 / 3 = 10.667 million
Continued...
SFN2D10
©CGA-Canada, 2010
Page 1 of 9
d. 1) Source: Topic 9.2 (Level 1)
E = $20, r = 0.02, σ = 0.15, S = $17, T = 120 / 365
First calculate d1 and d2:
S
ln    rT
T1/2
E

d1 =  1/2
2
T
=
=
120
 $17 
ln 
  0.02 
$
20
365


 120 
0.15  

 365 
1/ 2
 120 
0.15  

 365 

2
1/ 2
0.1625  0.0066 0.086

0.086
2
= 1.77
d2 = d 1  T 1/2  1.77  0.086  1.856
N(d1) = 0.0384
The d2 value is between –1.85 and –1.86.
Calculate N(d2) using linear interpolation:
N(d2) = 0.0314 + [(–1.856 + 1.86) / (–1.85 + 1.86)]  (0.0322 – 0.0314) = 0.0317
Calculate the call option premium:
C = SN(d1) – EN (d2)e-rT = $17  0.0384 – $20  0.0317  e (-0.02120/365) = $0.023
e.
2) Source: Topic 7.9 (Level 1)
95% normal z-statistic (one-tail) is 1.645.
VaR = z × Standard deviation × Value of portfolio
VaR = $50 million  0.2  1.645 = $16.45 million
Continued...
SFN2D10
©CGA-Canada, 2010
Page 2 of 9
f.
1) Source: Topic 10.4 (Level 1)
Cash conversion period = Inventory conversion period + Receivables conversion period –
Payables deferral period
Inventory conversion period:
=
=
inventory
 cost of goods sold 


365


$18M
 $200M  (1  0.30) 


365


= 46.93 days
Receivables conversion period:
=
=
accounts receivable
 annual credit sales 


365


$15M
 $200M  0.85 


365


= 32.21 days
Payables deferral period:
=
=
=
accounts payable  accruals
 cost of goods sold 


365


$20M
 $200M  (1  0.30) 


365


52.14 days
The cash conversion period:
= 46.93 + 32.21 – 52.14
= 27 days
SFN2D10
©CGA-Canada, 2010
Page 3 of 9
20
Question 3
Source: Topics 1.7, 2.7, 5.1, and 5.4 (Level 1)
2
a.
APV should be used because this project involves a financial side effect.




Debt used to finance the project is significantly different from the firm’s other debt arrangements.
The project has different risk characteristics from the firm’s other projects.
Security issuing costs have the benefit of tax savings.
Some cash flows are stable over time, which makes calculations easier without compromising
accuracy.
Note:
Any one of these factors is acceptable for 1 mark.
5
b. The discount rates that would be used are the unlevered cost of equity for calculating the base-case
NPV and the after-tax cost of debt for calculating the present value of financing-related cash flows.
To compute the first discount rate, we need the new division’s beta. However, it is a new division and
we are unable to estimate its beta directly with the given information. Since we are given industry
information, we will use it to estimate the new division’s beta. The first step is to “un-lever” the given
levered beta.
Unlevered beta:  U 
L
1  (1  T ) 
D
E
1.6

1  (1  35%) 
35%
65%
 1.1852
Unlevered cost of equity: kU = 5% + 1.1852  (12% – 5%) = 13.3%
After-tax cost of debt: 10% (1 – 40%) = 6%
5
c.
Annual after-tax operating cash flows:
$5B  (1 – 80%)  (1 – 40%) = $0.6B
Present value of these cash flows, discounted at the unlevered cost of equity:
$0.6B  PVIFA (13.3%, 20) = $4,139,998,318
Present value of CCA tax shield on initial investment:
൥
(2 + 13.3%)
$7 B  30%  40%
൩×൥
൩ = $1,826,090,679
(1 + 13.3%)
2  (30% + 13.3%)
The base-case NPV:
NPVB = $4,139,998,318 + $1,826,090,679 – $7,000,000,000 = –$1,033,911,003 < 0
This negative number indicates that the project is not financially feasible if only shareholders’ equity
(retained earnings) is used.
Continued...
SFN2D10
©CGA-Canada, 2010
Page 4 of 9
4
d. This project is financed with a debt-to-equity ratio of 50% to 50%, that is, $3.5 billion debt and
$3.5 billion equity.
Flotation costs for new equity: $3.5B  1% = $35M
Net flotation costs for new equity issue: $35M – [$35M / 5  40%  PVIFA (6%, 5)] = $23,205,381
Tax shield on bank loan interest: $3.5B  10%  40%  PVIFA(6%, 20) = $1,605,788,971
Adjusted NPV including financing side effects:
–$1,033,911,003 – $23,205,381 + $1,605,788,971 = $548,672,587 > 0
Since the NPV is positive, the project is financially feasible without the governments’ financial
support when financed with a debt-to-equity ratio of 50% to 50%.
4
e.
If FSC takes the maximum low-interest loan ($1 billion) from the provincial government, it needs to
borrow only another $2.5 billion from the bank.
Tax shield on the debt financing interest (both bank loan and the government low-interest loan):
($2.5B  10%  40% + $1B  6%  40%)  PVIFA (6%, 20) = $1,422,270,231
Value of low-interest loan:
$1B – $1B  6%  (1 – 40%)  PVIFA(6%, 20) – $1B  PVIF(6%, 20)
= $1B – $412,917,164 – $311,804,727 = $275,278,109
Alternatively, it can be calculated as $1B  (10% – 6%)  (1 – 40%)  PVIFA (6%, 20)
= $275,278,109
Present value of the after-tax operating cost subsidies from the federal government over the first
5 years: $1M  (1 – 40%)  PVIFA (6%, 5) = $2,527,418
Adjusted NPV with government subsidy:
–$1,033,911,003 – $23,205,381 + $1,422,270,231 + $275,278,109 + $2,527,418 = $642,959,374 > 0
With the financial support from both the provincial and the federal governments, FSC should accept
the project, since the NPV is positive.
SFN2D10
©CGA-Canada, 2010
Page 5 of 9
15
Question 4
Source: Topics 2.1, 4.1, 4.3, and 4.8 (Level 1)
3
a.
The current price per share = $100M/5M = $20 per share
The cost of equity: ku = EBIT(1 – Tc) / Vu = $25M  (1 – 40%) / $100M = 15%
For an all-equity firm, WACC = ku = 15%
10
b. Let D be the amount of loan that DFY should take on and VL be the value of the firm (total assets)
after the share repurchase.
D = 30%  VL
VL = $100M + Tc  D = $100M + 40%  30%  VL = $100M + 0.12 VL
(2)
Solve for VL = $100M / (1 – 0.12) = $113.64M
(1)
D = 30%  $113.64M = $34.09M
(1)
The value of equity: EL = $113.64M – $34.09M = $79.55M
(2)
The cost of equity: kE = kU + (kU – kB)  (D / E)  (1 – Tc)
= 15% + (15% – 5%)  (30% / 70%)  (1 – 40%)
= 17.57%
Alternatively, the cost of equity: kE = (EBIT – I) (1 – Tc) / EL
= ($25M – $34.09M  5%)(1 – 40%) / $79.55M
= 17.57%
(1)
WACC = kB  (1 – Tc)  D/V + kE  E/V
= 5%  (1 – 40%)  30% + 17.57%  70%
= 13.2% < 15%
(1)
The change in the value of the firm = $113.64M – $100M = $13.64M or 40%  $34.09M = $13.64M,
which should be shared among the original shareholders.
(1)
The share price should rise by $13.64M / 5M shares = $2.728 per share, from $20 to $22.728.
(1)
The number of shares outstanding after the share repurchase = 5M – $34.09M / $22.728
= 3.5M shares.
To verify, the number of shares outstanding = $79.55M / $22.728 = 3.5M shares.
Alternatively, let N be the number of shares repurchased and P be the share price after the share
repurchase.
$34.09M = N  P
(5M – N)  P = $79.55M
Solving these two equations simultaneously, we have N = 1.5M and P = $22.728.
2
SFN2D10
c.
The share repurchase increases DFY’s earnings per share, may increase the market price, and serves
as an alternative to a cash dividend.
©CGA-Canada, 2010
Page 6 of 9
10
Question 5
Source: Topics 6.3 and 6.11 (Level 1)
2
a.
This is an example of a vertical merger. Reasons why CMI would want to acquire GBC:






Acquiring an existing network of distributors of its products and services
Internalizing the distribution process
Obtaining operating economies of scale and/or scope
Pursuing effective strategic motives
Increasing market power and control
Allowing faster growth
Note:
Any one of these reasons is acceptable for 1 mark.
8
b. EXHIBIT S5-1
Key Income Statement and Balance Sheet Items of GBC
Item Considered
Level of GBC Item
Price per share
Earnings per share
Cash flow per share
Book value per share
Replacement cost per share
$170M / 10M = $17
$20M / 10M = $2
($50M – $25M – $15M) / 10M = $1
($20M + $30M + $50M) / 10M = $10
$150M / 10M = $15
EXHIBIT S5-2
Ranges of possible offer prices for GBC shares
Item Considered
Level of GBC Item
Price per share
Earnings per share
Cash flow per share
Book value per share
Replacement cost per share
$ 17
$ 2
$ 1
$ 10
$ 15
Minimum
Prior
Offer
Ratio
Price
15%
5.0
5.5
1.5
1.5
$ 19.55
$ 10.00
$ 5.50
$ 15.00
$ 22.50
Maximum
Prior
Offer
Ratio
Price
55%
18.0
28.0
5.5
2.0
$ 26.35
$ 36.00
$ 28.00
$ 55.00
$ 30.00
A reasonable range of share prices should be $22.50 to $26.35.
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Page 7 of 9
25
Question 6
Source: Topics 3.4, 7.1, 8.3, 8.4, and 9.4 (Level 1)
9
a.
Call premium = 15%  $100 million = $15 million
Flotation cost = 2.5%  $100 million = $2.5 million to be amortized over 5 years. Thus, the firm can
claim an annual flotation cost of $2.5 million / 5 = $500,000 over the next 5 years. Each year the firm
will realize tax savings equal to:
$500,000  40% = $200,000
The pre-tax cost of the new debt is 8% per annum compounded semi-annually. The semi-annual rate is
8% / 2 = 4%.
The pre-tax effective annual rate is (1 + 0.04)2 – 1 = 8.16%.
The after-tax effective rate on new debt is 8.16%  (1 – 40%) = 4.896%.
Present value of the flotation cost future tax savings is $200,000  PVIFA (4.896%, 5) = $868,390.
Therefore, net flotation cost = $2,500,000 – $868,390 = $1,631,610.
Net additional interest expense during the overlap period:
$100 million  [(12% – 2%) × 1/12]  (1 – 40%) = $500,000
Incremental semi-annual after-tax interest savings:
= $100 million  [(12% – 8%) / 2]  (1 – 40%) = $1.2 million
Semi-annual after-tax cost of debt is (1 + 4.896%)½ – 1 = 2.42%.
Present value of semi-annual interest savings:
$1.2 million  PVIFA (2.42%, 28) = $24,200,894
NPV = $24,200,894 – $15,000,000 – $1,631,610 – $500,000 = $7,069,284 > 0
Decision: GMI should refinance the old bond issue with the new issue as the NPV is positive. The
interest rate level is now low enough to make refinancing financially feasible.
2
b. In using short-term financing, GMI is exposed to interest-rate risk. There are two possible negative
consequences of using such a strategy. First, GMI may not be able to renew its short-term financing.
Second, short-term interest rates have high volatility. Although the short-term rates are generally
lower than the long-term rates, short-term rates have occasionally been higher than long-term rates.
GMI is also incurring the additional cost of refinancing regularly.
Continued...
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Page 8 of 9
7
c.
(3)
GMI can use futures contracts, forward contracts, options, and interest-rate swaps to manage its
interest-rate risk.
GMI can sell BA futures contracts. This type of contract works as follows: If interest rates rise in the
coming months, the futures price for BA will fall and GMI will make a profit by selling high and
buying back low. The profit on the futures position will be used to offset the increased interest
expense. If interest rates drop in the coming months, GMI will incur a loss on the futures position, but
the loss will be offset by the lower interest expense. The short position in BA futures contracts helps
GMI lock in interest rates at the current level.
Forward contracts work almost in the same way as futures contracts do. GMI could customize the size
of the contract, which is not possible with a futures contract.
(2)
GMI could also buy put options on BA futures contracts. If the interest rates go up, the price of BA
futures contracts will go down. GMI could exercise its put options and gain a profit, which would
reduce its loss from financing at higher interest rates. If the interest rates go down, the price of BA
futures contracts will go up. GMI would let its put options expire without execution and take
advantage of the lower financing rates.
(2)
If GMI uses an interest-rate swap, GMI will pay a fixed rate to receive the floating rate. Combined
with its existing position — paying floating rates — GMI would pay a fixed rate in the end.
7
(3)
d.
GMI should sell BA futures contracts. The number of futures contracts GMI should sell would be:
0.92  $40M  1
 147.6 rounded to 148
91
$1M 
365
(1)
One month later, if the short-term interest rates increase to 7% (approximately corresponding to the
futures price of 93), GMI will have to pay (7% – 4.5%)($40M) = $1 million more in interest expense.
But GMI will gain from its futures contracts:
(1)
148 contracts  (95.5 – 93)  100  $25 = $925,000
This profit will reduce GMI’s interest payment almost to the current 4.5% level.
(2)
On the other hand, if the short-term interest rates decrease to 2%, GMI will gain by paying lower
interest expenses, but will incur a loss on its futures contracts. The gain and loss will approximately
cancel out each other. GMI will still pay the current 4.5% rate. Selling BA futures contracts will help
GMI lock in its short-term interest rate at the current level.
100
SFN2D10
END OF SOLUTIONS
©CGA-Canada, 2010
Page 9 of 9
CGA-CANADA
ADVANCED CORPORATE FINANCE [FN2] EXAMINATION
December 2010
EXAMINER’S COMMENTS
General Comments
Overall performance on this examination was satisfactory.
The examination covered a variety of topics, both quantitative and qualitative, with questions based on real
world experience. The best results were on Questions 2 and 3. Performance was also satisfactory on
Questions 1 and 4. However, candidates struggled with Questions 5 and 6.
Candidates showed the same strengths and weaknesses as on previous examinations. While they were
good at quantitative questions (Question 2, consisting of pure quantitative questions, and Question 3),
results were weaker for questions integrating both quantitative and qualitative aspects of topics. Question 5
was a case in point. It was about identifying the type of merger and determining a range of share prices
that might be paid by the acquirer to the target in the merger. Few candidates recognized that this was
based on a real-world event — BCE acquired the Source store chain — and correctly identified this as an
example of a vertical merger. While candidates’ incorrect answers to part (a) suggested that they did not
have a good understanding of the qualitative side of this topic, the unsatisfactory performance in part (b)
revealed a weakness in problem-solving skills. Part (b) tested the ability to extract information from a
large set of data and calculate some numbers. The required calculations were basic arithmetic operations
(addition, subtraction, multiplication, and division), yet many candidates were unable to find the share
price number and unable to find relevant numbers used to calculate earnings per share, book value of
common equity, and cash flow per share.
In brief, candidates are strongly encouraged to spend time and effort reading the course materials and
understanding basic concepts. Before attempting the previous examinations, they must understand and be
able to finish the assignment questions without any help from peers or instructors. While working on the
assignment questions, candidates should calculate all the numbers on their calculators even though an
EXCEL spreadsheet is used to do all the calculations.
Specific Comments
Question 1 Multiple choice (Level 1)
This question included six qualitative multiple-choice items. The overall performance was almost
satisfactory. The best performance was on parts (b) (unethical behaviour) and (d) (hedging strategy for a
bank with a negative gap when interest rates are expected to increase). Performance on parts (f) (cash
budget) and (e) (financing strategy benefiting from an expected decline in interest rates) was also
satisfactory. Candidates struggled with parts (a) (market efficiency) and (c) (beta).
Question 2 Multiple choice (Level 1)
Performance on this question was satisfactory and the best on the examination, indicating that candidates
were strong in solving standard quantitative questions. This question consisted of six quantitative multiplechoice items. The poorest performance was on parts (c) (cumulative voting) and (d) (the Black-Scholes
option-pricing model). Results were excellent on parts (a) (payback period), (b) (a discount interest term
loan with a compensating balance), (e) (value at risk), and (f) (cash conversion period).
Continued...
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©CGA-Canada, 2010
Question 3 Capital budgeting (Level 1)
Performance on this question was satisfactory. This was a quantitative analysis question, designed to test
candidates’ understanding of the adjusted present value (APV) method and their ability to apply it to
analyze a project. The majority of candidates were able to explain what APV is and why it was the most
appropriate in this situation, and to arrive at the two discount rates to be used in the analysis. Then many
of them were able to identify and calculate the cash flows relevant in two scenarios — without and with
financial aid from the government — and make the correct accept/reject decision.
However, a few candidates were unable to differentiate among the three methods. Some candidates
calculated and used the weighted-average cost of capital (WACC) in their analysis although in part (a)
they had clearly specified that the APV method was the most appropriate. Some other candidates
converted the cost of equity into an after-tax basis or calculated the after-tax cost of debt using the rate on
the government loan, showing an inability to differentiate between the APV, WACC, and equity residual
(ERM) methods. Some candidates mixed up part (c) (the base case with shareholders’ equity — retained
earnings only) with part (d) (the adjusted case with external debt and equity financing) and part (d)
(without government help) with part (e) (with government help). Some of them calculated the same cash
flows in parts (c) and (d) but used the different discount rates. This shows that they did not really
understand the features of APV.
Other common mistakes were: (1) some candidates were unable to distinguish between the tax savings from
interest and the after-tax interest payment, (2) some candidates did not know the comparative method to
estimate the new project’s beta, (3) some candidates calculated the issuing cost for the bank loan or for
retained earnings, and (4) few candidates set up the amortization schedule for the bank loan in order to
calculate the tax savings from the interest payments. They clearly missed the piece of information about
this loan being an interest-only loan.
Question 4 Capital structure (Level 1)
Performance on this question was satisfactory. This question was based on the real-world practice of
corporations increasing their debt load to replace equity during a post financial-crisis period. It required
candidates to analyze borrowing new debt to substitute equity capital so as to raise the debt-to-asset ratio to be
in line with the industry norm. Many candidates were able to calculate the value of the firm and the share
price/equity value before (a) and after (b), the recapitalization, demonstrating their solid understanding of
value — the fundamental concept in finance — and their competence in calculating the value of a firm and
share price. Yet quite a number of candidates incorrectly calculated the per-share value of a firm (debt plus
equity) as the share price.
Some common problems remained: (1) Many candidates did not quite understand the MM proposition with
tax scenario — they did not recognize that several things would change at the same time in part (b), where the
firm issued new debt to substitute equity capital, including the total value of the firm, the value of equity, and
the risk measured by a higher cost of equity. They incorrectly calculated the amount of new debt by
multiplying the change in debt ratio (from 0 to 30%) by the value of the firm from part (a) (before the
recapitalization). While they did not apply the correct formula (VL = VU + T × D) in part (b) to calculate the
value of the firm after the debt issue, the same formula was used incorrectly in part (a) by many candidates to
find the value of equity. Besides, another formula — the leverage-indifference EBIT Level — was incorrectly
used by some candidates to calculate the number of shares outstanding after the restructuring in part (b).
(2) Many candidates did not identify the two purposes that a share repurchase served in this particular
situation.
Continued...
FN2D10
©CGA-Canada, 2010
Question 5 Mergers and acquisitions (Level 1)
Performance on this question was unsatisfactory and the weakest on the examination. This was a pure
quantitative analysis question, designed to test candidates’ understanding of a common practice during a
financial crisis (mergers and acquisitions) and their ability to apply the comparison with previous
acquisition cases method to analyze an acquisition case.
In addition to the problems identified in the general comments section, two other common mistakes were:
(1) instead of calculating the maximum and minimum share prices for each ratio across the five cases,
many candidates incorrectly calculated the maximum and minimum share prices for each case; and (2)
some candidates did not understand that the numbers in Exhibit 5-1 were the ratios already, and therefore
they calculated the five ratios using the numbers in this exhibit.
The unsatisfactory performance on this question underlines the importance of understanding basic finance
concepts. Finance is not only about numbers and calculations. Without a good understanding of some
basic concepts, it is difficult to calculate some very simple numbers, such as the book value in this
question.
Question 6 Bond refinancing, working capital and treasury risk management (Level 1)
Performance on this question was unsatisfactory. This integrated question combined two real-world
practices during a financial crisis: issuing new low-interest bonds to replace existing high-interest bonds
and managing treasury risk of increasing interest rates.
Part (a) was designed to test candidates’ understanding of bond valuation and their competence in
analyzing bond refinancing. The majority of candidates were able to identify the appropriate discount rate
and the cash outflows and inflows associated with the refunding of a bond issue, including the interest
income the firm may earn during the one-month overlap period by investing proceeds from issuing new
bonds in T-bills. However, some candidates mixed up the calculation of the flotation costs with the
calculation of the call premium. Quite a few candidates incorrectly calculated the call premium as 2.5% of
the total face value, though the question clearly stated that the call premium was 15% of the total face
value. Some other candidates calculated the effective annual rate of the coupon rate before calculating the
call premium. As well, a few candidates calculated the call premium at the after-tax base.
Part (c) tested candidates’ understanding of the financial contracts available on the market and their ability
to design three hedging strategies by using these contracts. While many candidates were able to name and
describe futures/forward contracts, options, and swaps, fewer designed correct hedging strategies (selling
BA futures/forwards, buying puts, paying a fixed rate to receive the floating rate). Some candidates simply
listed and repeated the definitions of the three financial contracts. Others suggested that the firm should
speculate rather than manage the risks, saying they would advise the firm to buy futures if interest rates are
expected to fall and to sell futures if rates are expected to rise. Finally, some incorrectly provided the three
approaches to short-term and long-term financing decisions: conservative, aggressive, maturity-matching
strategies as the three hedging strategies.
Part (d) was a quantitative question on this topic. While more candidates were able to provide some
calculations, a common mistake was to treat the short-term bank loan as commercial paper and therefore
they incorrectly calculated the value of liability to be hedged. This meant they had to do much more
complicated calculations to illustrate that the hedging strategy would work under the two opposite (rate
increase and decline) scenarios: the implicit cost of financing would be locked in at the current level.
FN2D10
©CGA-Canada, 2010