Mid Exam FINC 5880- Shanghai
Advanced Corporate Finance
VERSION A - ANSWERS
2013 - 23 November
Multiple Choice Questions: 20 points (4 points each)
Q1) You have been asked to assess the dividend policy of HULTIMO, an Education
services company that has been in existence only 3 years. The firm has provided you with
its last three years of financial data:
Year : 3 years ago (2010)
Net Income
$ 100 million
Capital Expenditures
$ 50 million
Depreciation
$ 50 million
Non-cash Working Capital -$ 15 million
Total Debt
$0
2 years ago (2011)
$ 120 million
$ 130 million
$ 60 million
$ 15 million
$ 40 million
Most recent year (2012)
$ 150 million
$ 145 million
$ 70 million
$ 30 million
$ 30 million
(Note: You have been given total non-cash working capital each year, not the change)
You are also told that the firm had $ 20 million in cash, no non-cash working capital and
no debt when it started operations three years ago.
If the current cash balance is $ 30 million, the firm bought back no stock and the firm
maintained a constant dividend pay-out ratio over the 3 years, calculate this average
dividend pay-out ratio.
A: The average pay out ratio over these 3 years was about 62%
B: The average pay out ratio over these 3 years was about 42%
C: The average pay out ratio over these 3 years was about 58%
D: Non of the above 3 years average pay out ratio’s is correct
Q2) An investor is executing the following Arbitrage;
Action
Buy 3 call options
Short sell 1 share
Cash Flow t=0
- $ 16.50
$100
St=$90 (t=1)
$0
- $90
St=$120 (t=1)
$30
-$120
(repay in t=1)
Lend $83.50 at 10%
interest rate
TOTAL
- $83.50
$ 91.85
$ 91.85
$0
$ 1.85
$ 1.85
If the fair value of the call option was $ 6.00 what must be the market price of the call
option given above arbitrage?
A)
B)
C)
D)
$ 4.21
$ 5.44
$ 5.50
Non of the above
Answer:
$ 1.85/3 calls= $ 0.6166 mis pricing per call so Pv of this $ 0.6166/1.10=$ 0.56
Thus $6.00-$0.56=$5.44 Note the calls are bought indicating that they are under priced.
However the information provided is somewhat contradicting; the arbitrage starts with
buying 3 calls for $5.50 each so C is also correct and most students choose this answer
without doing the calculation.
Q3) Suppose that a commodity sells for $280 (today’s spot price), inflation is 2% per year
and the risk free interest rate is 0.5% per month. What should be the fair value of the 6
months (maturity) Futures contract (Fo)?
A)
B)
C)
D)
$297.27
$288.51
$285
Non of the above
Answer: $280*(1+0.005)^6=$288.51
Q4) A company considers and investment of $100 M; the asset is depreciated over 3 years
MACRS method respectively 45% (year one), 35%(year two) and 15%(year three). The
residual value is estimated at $ 10 M and the tax rate 35%; if the company buys the asset
and borrows the money the interest is 10% per year.
A guideline lease requires a yearly lease fee of $ 40 M
If this Company makes the decision entirely based on the cost over the 3 year usage of the
asset and you have no other information then the above then the Company would choose;
A: Leasing since the cost is more than $ 10M lower over 3 years
B: To borrow the money and buy the asset since the cost is more than $ 5 M lower over 3
years
C: To borrow the money and buy the asset although the difference with Leasing is really
small over the 3 years
D: The Company can choose since the Costs will be exactly the same under Leasing or if
the Company borrows the money and buys the asset
Answer: B
Q5) In 2010 Apple Inc’s Beta is estimated to be 0.9 (lower than the market). If you know
that Apple’s Firm value is $ 280 Billion and it has about $ 180 Billion in Cash (and
equivalents). You further know that the Company has about $ 5 billion debt. If the Firm
value of $ 280 Billion includes that cash amount and $ 5 Billion debt what is the
“Unlevered Business Beta” of Apple Inc.? Assume a tax rate of 35%.
A: Apple’s Business Beta excluding cash based on 100% Equity financing must be: close
to the Market beta
B: Apple’s Unlevered Business Beta excluding cash must be about 1.4
C: Apple’s Unlevered Business Beta excluding cash must be about 1.9
D: Apple’s Unlevered Business Beta excluding cash must be over 2.0
Answer: B
Open Question1) Black Scholes Option Valuation (20 points)
Assume we know the following for calculating the value of an option:
The annual standard deviation of the return of the underlying security is
27.83%, the maturity is exactly half a year, the risk free rate (annual) is 6%,
the underlying stock (spot) price is $100 and the strike price of the option is
$105 no dividend is paid on the stock.
REQUIRED:
a) What is the value of the Call Option and Put Option according to the Black
Scholes Option Valuation Model? (5 points)
b) Use the Call-Put Parity to show that the Parity results in the same Put
option value (5 points)
c) If the Call option is actually selling for $8 in the market; how much is it’s
implied volatility (Standard Deviation of return of the underlying
security)? (10 points)
ANSWER:
a) Call Value $ 7.00 Put Value $ 8.8968
b) P=C-So+PV(X) or: P= $7.00-$100+$105/1.03= $8.94 however with
continuous interest; P=$7.00-$100+$105*e^-0.06*0.5=$7.00$100+0.970445534*$105=$8.8968 EXACTLY
c) Try out or use GOAL seeker: The volatility should of course be higher;
0.3138 (31.38%) exceeding the original 27.83%.
Open Question 2) Binomial Option Valuation and Arbitrage (20 points)
a) For a call option on SUFE Food. (strike price = $40) with 1 year upon expiration,
calculate its theoretical price if you know:
The underlying SUFE Food’s stock sells for $30 per share now. In 1 year, we know the
stock can be traded at either $60 or $15.
You are able to borrow or lend at the risk-free rate of 5% per annum. (10 points)
b) If this Call option is trading at a price of $6 now. Please set up the arbitrage and “get”
the risk-free benefit. (Show your process) (10 points)
ANSWER
a)
b)
Open Question 3) Futures and Arbitrage (20 points – 10 points each)
a) How should we value a “Long “ Future Contract (Fo) on Gold today if you
know:
Current Sport Price of Gold (So); $ 1,775
Inflation (I): 2% per year
Risk free rate (Rf) : 0.1% per month
Maturity Future contract (t): 6 months (October 2012)
GDP growth US in 2012 estimate: 1.5% per year
ANSWER: Fo= So*(1+Rf)^t thus Fo= $1,775*(1+0.1%)^6= $ 1,785.68
b) If above Future contract is traded today for $ 1,782.50 how could you make a
risk free profit through arbitrage. Show your calculations, explain your
symbols and assumptions.
ANSWER: Arbitrage: Buy the Under Priced Future Contract (Long
position)
Strategy: (note t=6 means 6 months later)
Sell Gold Today + $ 1775 Buy back in t=6 for -St (future spot price cash
out)
Buy the Future no cash today future t=6 pay off: St- 1782.50 (Fo)
Invest - $ 1775 and get back plus interest in t=6 $ 1785.68
Net pay off: $ 1785.68 - $ 1782.50= $ 3.18 Risk Free
Note this is exactly the amount of the miss pricing!
Open Question 4) Plain Vanilla Interest SWAPS (20 points – 10 points each)
Two companies want to enter into a plain vanilla interest SWAP.
Their current financing conditions are:
Company A
Company B
Fixed Rate 5%
Fixed Rate 6.5%
Floating Rate IBOR+0.1%
Floating Rate IBOR+0.4%
Company A is currently Financed with Fixed rate Debt and Company B with floating rate
Debt. You are the SWAP dealer and you take 0.2% dealer fee.
a) Assume that A and B perfectly equally share the benefit of this SWAP what will be
the interest % (in Floating rate for A and Fixed rate for B) after the SWAP?
Answer
Company A: IBOR-0.4% and Company B: 6%
b) DRAW and set up the SWAP deal:
Open Question 5) Bottom Up Beta’s (20 points)
You have been asked to analyze GenCorp, a corporation with food and tobacco
subsidiaries.
The tobacco subsidiary is estimated to be worth $ 15 billion and the food
subsidiary is estimated to have a value of $ 10 billion.
The firm has a debt to equity ratio of
1.00.
You are provided with the following information on comparable firms:
Business
Average Beta
Average D/E Ratio
Food
0.92
25%
Tobacco
1.17
50%
All firms are assumed to have a tax rate of 40%. If the current long-term bond rate is 6%,
estimate the Levered Beta for this company
Answer
Unlevered Beta for Food Business = 0.92/(1+(1-.4)(.25)) =
Unlevered Beta for Tobacco Business = 1.17/(1+(1 - .4)(.5)) =
0.8
0.9
Unlevered Beta for the Company = 0.8 (10/25) + 0.9 (15/25) =
0.86
Levered Beta for the Company = 0.86 (1 + (1-.4)(1.00)) =
0.86
! Weighted by values of each division
END OF MID EXAM FINC 5880 NOV 2013
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