Q1
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The discount rate for the value of the option is the expected return on the
stock:
E(s) =r=0.02+3(0.1-0.02)=0.26
The call option has a positive value if (up, up) occurs. This happens with
probability:
Pr(up,up)=0.6^2=0.36
The present value of the option is:
PV=0.36[50(1.15^2)-55]/(1.262)=2.52
Q2
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The present value of the cost for r=EAIR=(1.005)^12-1=0.061678 is:
PV=80/(1+r)21+80/(1+r)22+80/(1+r)23+80/(1+r)24
+90/(1+r)24+90/(1+r)25+90/(1+r)26+90/(1+r)27
=161.84
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The present value of the deposits for the same discount rate:
PV=100/(1+r)2+x/(1+r)10
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Set the present value of the cost equal to the value of the deposits and solve of x
161.84=88.19+x/(1+r)10
X=133,052
Q3
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Calculate the present value of the cash value of dividends for each year and add
them together:
PV1/2=5.5/1.161/2 +
PV3/2 =5.5(1.15)/1.163/2 +
PV5/2=5.5(1.15)2/1.165/2 +
PV7/2 =5.5(1.15)3/1.167/2
PV9/2=5.5(1.15)4/1.169/2 +
PV11/2=5.5(1.15)5/1.1611/2 +
PV13/2=5.5(1.15)5/(0.16*1.1611/2)
=60.55
Q4
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You can find the covariance of the portfolio by multiplying the correlation by the
standard deviations of both stocks:
Cov(x,y)=0.04*0.12*0.18=0.000864
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Then use the formula for the portfolio variance and take the square root to find
the portfolio’s standard deviation:
Varp=0.82*0.122+2*0.8*0.2*0.000864+0.22*0.182=0.010788
Std=(0.010788)1/2=0.10387
Q5
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Use the weighted cost of capital equation from Modigliani and Miller (1958)
proposition II:
RS  R0 
B
( R0  RB )
S
RS=0.12+0.4/0.6(0.12-0.3)=0.18
Q6
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Use the condition that IRR is the discount rate (r) that would make the projects
NPV=0. Then solve for r using the quadratic formula.
1.Let x=1+r
NPV=0
-500-600/x+1500/x2=0
5x2+6x-15=0
2. Using the quadratic formula x is either
x1= 1.233
x2=-2.34
3.Ignore any negative rates of return
r=x1-1=0.23
Q7
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The yield on a bond is the discount rate (r) that would make the NPV of the bond
equal to zero. Use that condition and solve for r using the quadratic formula.
1.Let x=1+r
NPV=0
1320/x2+120/x+120-800=0
17x2-3x-33=0
2. Using the quadratic formula x is either
x1= 1.484
x2=-1.307
3.Ignore any negative rates of return
4.Currently r is the 6 month discount rate. Transform it to an effective annual interest
rate:
EAIR=(x1)2-1=0.203 = 20.3%