∙Company stock is selling for $80 and risk
free is 6%. Convertible bond w a conversion
price $100, FV of $1000, coupon rate 8%, 10
yr to maturity. Similar bond w/o conversion
have yield of 7%. Convertible bond sells for
$1100.
Conversion ratio = 1000/100 = 10
Conversion premium = 100/80 1=.25
Conversion value = $80 x 10 = $800
Straight Bond value. n=10 r=7 fv=1000
pmt=1000x.08 pv=?=$1070.23
Value of conversion opt = 1100  1070.23
∙Stock A has expected return of 8% and std dev
of 12%. Stock B expec ret 10% and std dev
15%. Correlation .3.
60% invested in A and 40% in B. Rf 5%
Er = .6x8 + .4x10= 8.8%
Variant Rp = (.6² x 12²)+(.4² x 15²)
+ (2 x .3 x .6 x .4 x 12 x 15)
Std dev
=√variant =10.7%
Sharpe ratio = (8.8  5) / 10.7= .355
∙Preferred stock pays quarterly dividend of
$2.30. Sells for $92, what is req ret for holding
stock?
R = (2.3 / 92) x 4 = 10%
∙Asset worth $35 or $60 in 1 year. Current price
is $40. Risk free rate 5%. Call option w strike
price $50.
Possible payoffs for option= 10 or 0
construct risk free portfolio using only options
and underlying asset.
(100) / (6035) = .4
Buy .4 shares, write 1
option
PV of portfolio: hi: (60x.4) 10= $14
lo: (35x.4)0= $14
PV= 14 / 1.05 = $13.33
Value of option = (.4 x $40) –c= $13.33
C= $2.67
Beta 2.5 and residuals
1.1
Risk premium of 8% and riskfree 5% What is
risk premium of stock and Er?
RiskP = 2.5 x 8 = 20%
Er =.05 + .2 = 25%
Market goes up 1% next month, what is
expected change in stock?
5/12 + 2.5(1 5/12) = 1.875%
stock actually goes up 2% what is idio. Risk?
21.875= .125%
Std dev of ret is 1.5. What are syst risk, idio
risk, total risk?
Sys=1.5x2.5=3.75%
Idio= 1.1 (residuals)
Total =√1.1² + 3.75² = 3.91%
What range expect mnt ret to fall in 95% of the
time?
25/12 + 2(3.91) = [5.732 , 9.899]
Given $1000, how to construct a
portfolio w B=2. What is annual Er?
2 = 2.5w + (1w)0
W=.8
$800 stock and $200 riskfree
Er= (2x8) + 5= 21%
Company wants to start project. 4
yrs and initial start of $50,000 depric
str line to 0 over 4 yrs. No salvage
value. Ann. Costs expected to be
$10k per year.Tax 35% d rate 12%
OCF required ea yr to break even at
end? (NPV=0)
N=4 pv=50k r=12 fv=0
pmt=?=16,461.72
Min. bid that should be offered?
OCF=(bidcost) x .65 +depr x .35
Bid=(ocf+costs x .65depr x.35)/.65
=(16,461.72+65004375) / .65
= $28594.95
Comp. consider prjt w initial cost
$120k. depric over 5 yr strt line. Proj
end after 4 yrs and assets have
salvage value of $15k. Ann. Costs
are $30k, sales $50k. Proj require
$20k in NWC that will be recovered
at end. Tax 35%. Cpt CF for ea yr.
depr = 120k/5= 24k
ocf =(salescost) x (1t) + depr x T
= (50k30k)x.65 + 24k x .35
= 13k + 8400 = 21.4k
atsv= btsv x(1t) + endBV x T
=15k x .65 + 24k x .35
= 9750 + 8400 = 18,150
Yr
0
1
2
3
4
ocf
0
21.4k
21.4k 21.4k 21.4k
∆nwc 20k
0
0
0
20k
ncs
120k
0
0
0
18.15k
ttl
140k 21.4k 21.4k 21.4k 59.55k
consider these CF
Yr
0
1
2
3
4
5
CF
20k
4k
5k
6k
4k
4k
Discount rate= 12%
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 Fall '07
 DONCHEZ,RO
 Capital Asset Pricing Model, Corporate Finance, Net Present Value, Convertible bond

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