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SOLUTIONS EXAM 2013-10-25
Instructions
1.
Only one problem should be treated on each sheet of paper and only one side
of the sheet should be used.
2.
The solutions folder must be handed in before you leave (even if it contains no
solution sheets).
3.
State on the folder the number of solution sheets that it contains.
About the test
1.
Aids allowed:
- Calculator (all admitted, but empty memory).
- Dictionary to English language if necessary, free of notes and calculations.
No other aids are allowed.
2.
At each problem is stated the number of points that a correct solution is given.
To pass the test the total points should be 18 or higher.
3.
It is important that the solution method and arguments leading to a conclusion
are clearly stated. Answers without motivation are not accepted
WRITE AS CLEARLY AND DISTINCTLY AS POSSIBLE!
GOOD LUCK!
Problem 1 (10 points)
a) Explain the following concepts:
i. The inherent conflict (dysfunctionality) of Corporate Governance in typical large public
firm (1pts.)
ii. The effect of market interest rates on Bond Prices and Yield (1pts.)
b) Explain why maximizing the NPV is the correct decision rule in comparison to the IRR. (2pts.)
c) Do you think a stable historical growth rate in dividends leads to a constant price of the firm’s stock?
Explain. (2 pts.)
d) Suppose that a young couple just had their first baby and they wish to insure that enough money will be
available to pay for their child's college education. They decide to make deposits into an educational savings
account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational
savings account will return a constant 7.5%. The parents deposit $2500 the first year and plan to increase
the size of their deposits by 4.5% each year. What is the amount available for their daughter's college
expenses on her 19th birthday, give that the parents made the final deposit on her 19th birthday? (2pts.)
e) You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current
mortgage. The current monthly payment is $2500 and you have made every payment on time. The original
term of the mortgage was 30 years, and the mortgage is exactly four years and eight months old. You have
just made your monthly payment. The mortgage interest rate is 6.38% (APR). How much do you owe on the
mortgage today? (2pts.)
Problem 2 (10 points)
a) Explain the following concepts:
i. Systematic and unsystematic risk (1pts.)
b) Write down the assumptions of the CAPM. Derive the CAPM mathematically. Explain the efficient
portfolio and the capital market line. (Draw necessary diagrams and equations to justify of your answer)
(1+2.5+1.5=5pts.)
c) A hedge fund has created a portfolio using just two stocks. It has shorted $45,000,000 worth of Volvo
stock and has purchased $75,000,000 of Toyota stock. The correlation between Volvo’s and Toyota’s
returns is 0.65. The expected returns and standard deviations of the two stocks are given in the table
below:
Expected Return
Standard Deviation
Volvo
10%
40%
Toyota
15%
45%
i.
What is the expected return of the hedge fund’s portfolio?
ii. What is the standard deviation of the hedge fund’s portfolio?
(1+1.5=2.5 pts.)
d) The ABC Mutual Fund has an expected return of 25% and a volatility of 20%. ABC claims that no other
portfolio offers a higher Sharpe ratio. Suppose this claim is true, and the risk-free interest rate is 4.5%.
I.
II.
Problem 3 (10 points)
What is ABC’s Sharpe Ratio?
If eBay’s stock has a volatility of 45% and an expected return of 15%, what must be its
correlation with the ABC fund?
(.5+1=1.5pts.)
a) Explain the following concepts:
i. Direct and Indirect Bankruptcy costs
(2 pts.)
b) What are the assumptions underlying the Modigliani-Miller theorem? Mathematically derive the MM1
Proposition in the presence of corporate taxes and show that value of the levered firm is equal to the
value of the unlevered firm plus present value of the tax shield. (1+2=3pts.)
c) The valuation model of a growing firm seems to validate the theory of dividend policy irrelevance.
Explain this model and show how it ignores dividend policy. Prove that dividend policy is irrelevant at a
discount rate of 12 percent, if a firm with two million shares decides to trade-off dividend between two
periods by paying 20 percent less in the current period as against the policy of constant $50m in all
periods.
(3 pts.)
d) ABC maintains a debt-equity ratio of 0.85, and has an equity cost of capital of 12.5%, and a debt cost of
capital of 7.5%. ABC’s corporate tax rate is 40%, and its market capitalization is $220 million. If ABC’s
free cash flow is expected to be $10 million in one year, what constant expected future growth rate is
consistent with the firm’s current market value? Estimate the value of ABC’s interest tax shield.
(1+1= 2pts.)
Problem 4 (10 points)
a) Explain the following concepts:
I.
Clientele effect and the Signaling hypothesis? (1pts.)
II.
Risk neutral Probabilities
(1pts.)
III.
Public and Private debt
(1 pts.)
IV.
Convertible Bond and Warrant (1pts.)(=4 pts.)
b) Write down the assumption of the Black-Scholes option pricing model. What is the unknown factor in
valuation of options? Why would an investor be interested in creating a long strangle position? (1+2=3
pts.)
c) Consider an option on TBX share with an exercise price (X) of $50.00 and maturing in 60 days. A call
option is selling at a premium of $5.00 while a put option is selling at a premium of $3.00. The current
market interest rate is 12% per annum while a TBX share is selling at $50.50
I.
II.
III.
Estimate, with supporting explanations, the intrinsic and time values of the call and put options.
Using the put-call parity relationship, explain if the options are appropriately priced.
If the options are not appropriately priced explain how you are going to take advantage of the
mispricing. Show and explain any profit position arising from your strategy in a diagram.
(1+1+1 =3 pts.)
ANSWER:
Problem 1 (10 points)
(A) Explain the following concepts:
a. The inherent conflict (dysfunctionality) of Corporate Governance in typical large public
firm (1pts.)
The dysfunctionality of corporate governance such as
-a lack of transparency and of managerial accountability: investors are imperfectly informed of managers actions
- a level of compensation that is not always related to performance
-accounting manipulations
- managerial accountability,
-corporate governance failures
(B) Explain why maximizing the NPV is the correct decision rule in comparison to the IRR. (3pts.)
Sometimes firms must decide among mutually exclusive projects. The manager must rank the projects and
choose the best one. In this case, NPV again yields the correct decision. Suppose a project with a positive
NPV is being compared with another project that is identical in all respects, except that the size is double.
Then the larger project will have an NPV that is double that of the first, meaning it is clearly the better
project. However, the IRRs for the two projects will be the same. Hence IRR cannot be used to evaluate
mutually exclusive projects of different scales. By the same token, IRR cannot be used consistently to
evaluate two projects with different timing or different risk. One improvement of IRR is included here. The
incremental IRR investment rule applies the IRR rule to the difference between the cash flows of the two
mutually exclusive alternatives. This approach will give the same answer as NPV. However, incremental IRR
still has some problems. First, the incremental IRR could not exist, or there could be several. The fact that
the incremental IRR exceeds the cost of capital does not imply that the NPV of either project is positive. In
addition, it is sometimes difficult to keep track of which project is the incremental project.
(C) Do you think a stable historical growth rate in dividends leads to a constant price of the firm’s
stock? Explain. (2 pts.)
The assumption that the growth rate in dividends has to be constant over time is a difficult assumption to
meet, especially given the volatility of earnings. If a firm has an average growth rate that is close to a stable
growth rate, the model can be used with little real effect on value. Thus, a cyclical firm that can be expected
to have year-to-year swings in growth rates, but has an average growth rate that is 5%, can be valued using
the Gordon growth model, without a significant loss of generality. There are two reasons for this result.
First, since dividends are smoothed even when earnings are volatile, they are less likely to be affected by
year-to-year changes in earnings growth. Second, the mathematical effects of using an average growth rate
rather than a constant growth rate are small.
(D) Suppose that a young couple has just had their first baby and they wish to insure that enough money will be
available to pay for their child's college education. They decide to make deposits into an educational savings
account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational
savings account will return a constant 7%. The parents deposit $2000 on their daughter's first birthday and
plan to increase the size of their deposits by 5% each year. Assuming that, the parents have already made
the deposit for their daughter's 18th birthday. Then, what is the amount available for their daughter's college
expenses on her 18th birthday.? (2pts.)
Explanation: growing annuity
$2,000 ×
18 

  1+ .05  
1 − 
  (1.07)18 = $97,331

 1+ .07  

(E) You have decided to refinance your mortgage. You plan to borrow whatever is outstanding on your current
mortgage. The current monthly payment is $2356 and you have made every payment on time. The original
term of the mortgage was 30 years, and the mortgage is exactly four years and eight months old. You have
just made your monthly payment. The mortgage interest rate is 63⁄8% (APR). How much do you owe on the
mortgage today? (2pts.)
To find out what is owed, compute the PV of the remaining payments using the loan interest rate to
compute the discount rate:
Discount Rate =
PV =
2, 356
6.375
12

1 −
0.0053125 
= 0.53125%
1

 = $354, 900
(1.0053125 )304 
Problem 2 (10 points)
(A) Explain the following concepts:
(a)Systematic and unsystematic risk (1pts.)
Usually stock prices fluctuate due to two types of news. Firm specific: news about the company itself. The
risk associated is then called firm-specific, unsystematic or diversifiable. Market-wide: news about the whole
economy, affecting the whole market. The risk associated is then called systematic, undiversifiable. If firms
are only affected by firm-specific risk, then it is possible to reduce the risk significantly through
diversification, adding more and more stocks in the portfolio, so that returns offset each other. Therefore
no compensation is needed for that. In reality firms are linked to both types of risk. The point is, only
systematic risk must be compensated, since it is the only risk that cannot be canceled away through
diversification.
(B) Write down the assumptions of the CAPM. Derive the CAPM mathematically. Explain the efficient
portfolio and the capital market line. (Draw necessary diagrams and equations to justify of your answer)
(1+2.5+1.5=5pts.)
Note: Gazi Lecture+Seminar-02+Note for CAPM
(C) A hedge fund has created a portfolio using just two stocks. It has shorted $35,000,000 worth of Oracle
stock and has purchased $85,000,000 of Intel stock. The correlation between Oracle’s and Intel’s returns
is 0.65. The expected returns and standard deviations of the two stocks are given in the table below:
a.
What is the expected return of the hedge fund’s portfolio?
b. What is the standard deviation of the hedge fund’s portfolio?(1+1.5=2.5 pts.)
Answer:
a. The total value of the portfolio is $50m = (–$35 + $85). This means that the weight on Oracle is
–70% and the weight on Intel is 170%. The expected return is
Expected return = −0.7 × 12% + 1.7 × 14.5%
= 16.25%.
Variance = (−0.7 ) × (0.45) + (1.7 ) × (0.40 )
2
2
2
2
+ 2 × (−0.7 )× (1.7 )× 0.65 × 0.45 × 0.40
b.
= 0.283165
Std dev = (0.283165)0.5 = 53.2%
(D) The ABC Mutual Fund has an expected return of 20% and a volatility of 20%. ABC claims that no other
portfolio offers a higher Sharpe ratio. Suppose this claim is true, and the risk-free interest rate is 5%.
a.
III.
What is ABC’s Sharpe Ratio?
IV.
If eBay’s stock has a volatility of 40% and an expected return of 11%, what must be its
correlation with the ABC fund?
(.5+1=1.5pts.)
Optima’s Sharpe Ratio = (20% – 5%)/20% = 0.75
b. eBay’s Sharpe Ratio = (11% – 5%)/40% = 0.15, It’s correlation must be 0.15/0.75 = 0.2
(Note: Text Book: Using equation 11.18)
Problem 3 (10 points)
(A) Explain the following concepts:
a. Direct and Indirect Bankruptcy costs
(2 pts.)
The costs of bankruptcy:
_ Direct costs. Administrative and legal costs.
_ Indirect costs. They are much larger than direct costs:
1. The perception on the part of customers that the firm is in trouble. Customers may stop purchasing the
product or service.
2. Suppliers start demanding stricter terms as protection against default, leading to an increase in working
capital.
3. Firms may .nd it di¢ cult to raise fresh capital (equity and debt) leading to the rejection of good investment
projects.
_ Indirect costs are higher for:
1. Firms selling durable products with long lives that require replacement parts and services. (ex a computer
manufacturer)
2. Firms selling goods and services where quality is an important atttribute (ex if a car maker is in trouble its
customers may be uncertain of the quality of its cars)
3. Firms producing products whose value to customer depends on services and complementary products
supplied by independent .rms (If Apple computer gets into trouble, companies producing software for its
computers may stop producing.)
4. Firms that sell products that require continuous service (A manufacturer of copying machines is more
accepted than a furniture manufacturer.)
(B)What are the assumptions underlying the Modigliani-Miller theorem? Mathematically derive the MM1
Proposition in the presence of corporate taxes and show that value of the levered firm is equal to the value
of the unlevered firm plus present value of the tax shield. (1+2=3pts.)
Note: Seminar-2 note (Both assumption and Derivation).
(C)The valuation model of a growing firm seems to validate the theory of dividend policy irrelevance.
Explain this model and show how it ignores dividend policy. Prove that dividend policy is irrelevant at a
discount rate of 12 percent, if a firm with two million shares decides to trade-off dividend between two
periods by paying 20 percent less in the current period as against the policy of constant $50m in all periods.
(3 pts.)
Presentation and analysis of a valuation model for a growing firm, such as;
∞
V0 = EBIT(1-tc)/(1+ku) + ∑ It(rt - ku)/ku(1+ku)
t=2
In this model, growth is driven by constant differential between return on investment
and cost of capital ((rt - ku)).
The components of this model need to be carefully explained. It does not contain any
factor that depicts the influence of dividend policy on value of the firm. The relevant
factors contributing to value of the firm are;
return on investment
cost of capital
The information provided can be used to prove that dividend policy is irrelevant.
With constant amount of dividend payout the value of firm and equity are;
Value of firm: VF = DIV0 + DIV1/(1+r) = 50 + 50/1.12 = $94.643m
Value of equity: VE =94.643/2 = $47.32
With the trade-off in dividend payout the value of the firm and equity are;
Value of firm: VF = DIV0 + DIV1/(1+r) = 40 + 61.2/1.12 = $94.643m
Value of equity: VE =94.643/2 = $47.32
The values remain the same, indicating that dividend policy is irrelevant.
(B)
Restex maintains a debt-equity ratio of 0.85, and has an equity cost of capital of 12%, and a debt
cost of capital of 7%. Restex’s corporate tax rate is 40%, and its market capitalization is $220 million. If
Restex’s free cash flow is expected to be $10 million in one year, what constant expected future growth
rate is consistent with the firm’s current market value? Estimate the value of Restex’s interest tax shield.
(1+1= 2pts.)
a.
b.
1
0.85
12% +
7% (1 − 0.40 ) = 8.42%
1.85
1.85
FCF
10
=
V L = E + D = 220 × 1.85 = 407 =
WACC − g 0.0842 − g
10
g = 0.0842 −
= 5.96%
407
1
0.85
pretax WACC =
12% +
7% = 9.70%
1.85
1.85
FCF
10
VU =
=
= $267 million
pretax WACC − g 0.0970 − 0.0596
WACC =
PV ( Interest Tax Shield ) = 407 − 267 = $140 million
Problem 4 (10 points)
(A) Explain the following concepts:
a) Clientele effect and the Signaling hypothesis? (1pts.)
Clientele Effect: Different groups of investors, or clienteles, prefer different dividend policies. Firm’s past
dividend policy determines its current clientele of investors. Clientele effects impede changing dividend
policy. Taxes & brokerage costs hurt investors who have to switch companies due to a change in payout
policy.
Signaling Hypothesis: Investors view dividend changes as signals of management’s view of the future.
Managers hate to cut dividends, so won’t raise dividends unless they think raise is sustainable. Therefore, a
stock price increase at time of a dividend increase could reflect higher expectations for future EPS, not a
desire for dividends.
b) Risk neutral Probabilities
(1pts.)
• If all market participants are risk neutral, then all financial assets (including options) have the same cost
of capital, the risk-free rate of interest. The Binomial and Black-Scholes models give the same option
price no matter what the actual risk preferences and expected stock returns are.
– In the real world, investors are risk averse and require a positive risk premium to compensate
for risk, while in a hypothetical risk-neutral world, investors do not require compensation for
risk.
c) Public and Private debt
(1 pts.)
Public Debt
Domestic bonds are issued by a local entity, traded in a local market, but purchased by foreigners.
Domestic bonds are issued by a local entity, traded in a local market, but purchased by foreigners.
– Foreign bonds are issued by foreign entity, traded on local markets, intended for local investors.
– Eurobonds are international bonds denominated in a foreign currency. Consequently there is no connection
between the physical location of the trading market and the location of the issuing entity.
– Global bonds combine the features of the others and are offered on different markets simoultaneously.
Private Debt
– Bank loans are an example of private debt, not publicly traded. A syndicated loan is financed by a group of
banks instead of only one. Term loan indicates a loan that lasts for a pre-specified period.
– A revolving line of credit is a credit commitment for a specific time period up to some limit, which a
company can use if needed.
– A private placement is a bond issue that does not trade on public market but is sold to a small group of
investors. It is less costly to issue.
• Sovereign debt is debt issued by national governments. US government issues Treasury bills (up to 26 weeks)
and bonds of various maturities (2, 3, 5, 10 years). Moreover long bonds with maturities 20 years and 30 years.
d) Convertible Bond and Warrant (1pts.)(=4 pts.)
A convertible bond is a bond which can be converted before maturity into a predetermined number of shares
of the issuing company. Basically it is like a normal bond with an embedded warrant which represents a call
option on the stock.
e) Write down the assumption of the Black-Scholes option pricing model. What is the unknown
factor in valuation of options? Why would an investor be interested in creating a long strangle
position? (1+2=3 pts.)
Black-Scholes Option Pricing Model: A technique for pricing European-style options when the stock can be
traded continuously. It can be derived from the Binomial Option Pricing Model by allowing the length of
each period to shrink to zero and letting the number of periods grow infinitely large.
Assumption:
The short selling of securities with full use of proceeds is permitted
There are no transaction costs or taxes. All securities are perfectly divisible
There are no dividends during the life of the derivative
There are no riskless arbitrage opportunities.
Securitiy trading is continuous
The risk-free rate of interest, r, is constant and the same for all maturities.
Why would an investor be interested in creating a long strangle position? (2 marks)
An investor would be interested to create a long strangle position if he believes that the price of the
underlying security is likely to fluctuate significantly such that the future price will be at a significant
deviation from some predetermined level. On the other hand the investor is uncertain of the direction.
In the above illustration the investor believes that the stock’s price will fluctuate by C+P+0.5(E2 – E1)
around the value 0.5(E2 + E1). Come the expiration day, the investor believe that one of the options will
be in the money (hence have an intrinsic value) by at least the magnitude of the fluctuation. A strangle
allows for wider fluctuation than a straddle (which allows a fluctuation of only C+P around the exercise
price E).
A short position (a strangle or a straddle) assumes the opposite: that the price is not going to move
outside a certain band. An investor taking the position profits by pocketing the proceeds from the call
and put options sold while believing that the intrinsic value of any of the option at expiration (i.e. the
one that will be in the money hence exercised) will at most equal the proceed from the options sold..
(f) Consider an option on TBX share with an exercise price (X) of $50.00 and maturing in 60 days. A
call option is selling at a premium of $5.00 while a put option is selling at a premium of $3.00. The
current market interest rate is 12% per annum while a TBX share is selling at $50.50
(i)Estimate, with supporting explanations, the intrinsic and time values of the call and put options.
(ii) Using the put-call parity relationship, explain if the options are appropriately priced.
(iii) If the options are not appropriately priced explain how you are going to take advantage of the
mispricing. Show and explain any profit position arising from your strategy in a diagram.
(1+1+1
=3 pts.)
Answer:
(i)Estimate, with supporting explanations, the intrinsic and time values of the call and put
options.
Since a TBX share is selling at $50.50 which is above the strike price for the two options then the call
option is in the money and the put is out of money. Exercising the call option the holder will be buying TBX
stock at $50.00 which can be sold at $50.50. The intrinsic value of the call option is $0.50 and the time value is
$4.50. The put option is out of the money and the entire premium is time value.
(ii)Using the put-call parity relationship, explain if the options are appropriately priced
From part (b) the Put-Call Parity has the form: C 0 − P0 = S 0 − E (1 + r ) −T
The LHS is $0.20 (i.e. $0.50-$0.30)
The RHS is $0.148 (i.e. $50.50-$50.00x0.980392)
The LSH is higher meaning that the call option is overpriced relative to the put option.
(iii)If the options are not appropriately priced explain how you are going to take advantage of the mispricing. Show any profit position arising from your strategy.
To exploit the mis-pricing one has to engage in riskless arbitrage as follows:
• Borrow $49.02 at 12% interest per annum for two months
• Sell a call option for $0.50 and buy a put option for $0.30.
• Use the total funds raised from the three transactions (i.e. $51.02) to buy the stock at $50.50. This leaves
a balance of $0.52.
• At the end of the 60 days the proceeds from the stock will always be $50.00 which will be used to repay
the borrowed funds.
(Notice that if the price is below $50.00 the put that you’re holding will be in the money and the call that
you sold out of money). You exercise the put by disposing the stock at $50.00. If the price is above
$50.00, the put that you’re holding will be out of money and the call that you sold in the money). The
call will be exercised and you’ll be ‘forced’ to give up the stock for only $50.00)
TPPE17 Corporate Finance
10(5)
THE CUMULATIVE NORMAL DISTRIBUTION
Table gives N(x). To obtain N(-x) use N(-x) = 1-N(x).
Use interpolation, e.g. N(0.6278) = N(0.62)+0.78*(N(0.63)-N(0.62))=0.7350
x
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
1,9
2,0
2,1
2,2
2,3
2,4
2,5
2,6
2,7
2,8
2,9
3,0
3,1
3,2
3,3
3,4
3,5
3,6
3,7
3,8
3,9
4,0
0
1
2
3
4
5
6
7
8
9
0,5000
0,5040
0,5080
0,5120
0,5160
0,5199
0,5239
0,5279
0,5319
0,5359
0,5398
0,5438
0,5478
0,5517
0,5557
0,5596
0,5636
0,5675
0,5714
0,5753
0,5793
0,5832
0,5871
0,5910
0,5948
0,5987
0,6026
0,6064
0,6103
0,6141
0,6179
0,6217
0,6255
0,6293
0,6331
0,6368
0,6406
0,6443
0,6480
0,6517
0,6554
0,6591
0,6628
0,6664
0,6700
0,6736
0,6772
0,6808
0,6844
0,6879
0,6915
0,6950
0,6985
0,7019
0,7054
0,7088
0,7123
0,7157
0,7190
0,7224
0,7257
0,7291
0,7324
0,7357
0,7389
0,7422
0,7454
0,7486
0,7517
0,7549
0,7580
0,7611
0,7642
0,7673
0,7704
0,7734
0,7764
0,7794
0,7823
0,7852
0,7881
0,7910
0,7939
0,7967
0,7995
0,8023
0,8051
0,8078
0,8106
0,8133
0,8159
0,8186
0,8212
0,8238
0,8264
0,8289
0,8315
0,8340
0,8365
0,8389
0,8413
0,8438
0,8461
0,8485
0,8508
0,8531
0,8554
0,8577
0,8599
0,8621
0,8643
0,8665
0,8686
0,8708
0,8729
0,8749
0,8770
0,8790
0,8810
0,8830
0,8849
0,8869
0,8888
0,8907
0,8925
0,8944
0,8962
0,8980
0,8997
0,9015
0,9032
0,9049
0,9066
0,9082
0,9099
0,9115
0,9131
0,9147
0,9162
0,9177
0,9192
0,9207
0,9222
0,9236
0,9251
0,9265
0,9279
0,9292
0,9306
0,9319
0,9332
0,9345
0,9357
0,9370
0,9382
0,9394
0,9406
0,9418
0,9429
0,9441
0,9452
0,9463
0,9474
0,9484
0,9495
0,9505
0,9515
0,9525
0,9535
0,9545
0,9554
0,9564
0,9573
0,9582
0,9591
0,9599
0,9608
0,9616
0,9625
0,9633
0,9641
0,9649
0,9656
0,9664
0,9671
0,9678
0,9686
0,9693
0,9699
0,9706
0,9713
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