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Exercise 1
P0 = 70; E(P1) = 80, so E(r) = (80-70)/70 = 14.29%
rf=7%; E(rm)=15%, so E (r) = rf+ Beta (E(rm)-rf)  14.29% = 7% + beta *(15%-7%)
 Beta = 1.0408
If the covariance doubles then Beta doubles, so the new Beta is: 2.0816
The new expected return is: E(r) = 7% + 2.0816 (15%-7%) = 23.65%
So 23.65% = (P1-70)/70  P1 = $ 86.65
Exercise 2
a. R = Rbar + Beta oil * Foil + Beta i/R*Fi/R + BetaGNP*FGNP + epsilon
The systematic risk is:
Beta oil * Foil + Beta i/R*Fi/R + BetaGNP*FGNP = 2.8*10%-1.5*2%+1.3*(-4%)+1.6*2%
= 23%
b. Rbar=5%
Epsilon = 1.5%
i.
This is the unsystematic risk
ii.
Overall return = R = 5% + 23% + 1.5% = 29.5%
c. BetaP for the interest rate= wH*BetaH+wB*BetaB=0
wH+wB=1
 -1.5*wH+.75*wB=0
wH+wB = 1
 wH=1/3
wB=2/3
The systematic risk of stock B equals:
1.2 * 10% + 0.75 * 2% + 0.8 * (-4%) + 0.5 * 2% = 11.3%
So the systematic risk of the portfolio is:
1/3 * systematic risk of stock H + 2/3 * systematic risk of stock B
= 1/3 * 23% + 2/3 * 11.3% = 15.2%
Exercise 3.
a.
Security
A
B
C
Market
Risk free asset
Expected return
12.5%
16.25%
7.5%
10%
5%
b.
Tax rate of each company:
riA = .06*(1-.3) = 4.2%
riB = .18*(1-.3)=12.6%
SD
0.06
0.18
0.02
0.04
0
Corr
1
2.25
0.5
1
0
Beta
1.5
0.75
0.25
n/a
n/a
riC = .02*(1-.3) = 1.4%
rWACC A =.042*.5+.125*.5=8.35%
rWACC B = .126*.75+.1625*.25 = 13.51%
rWACC C = .014*.25+.075*.75 = 5.98%
Exercise 4.
a. 0 = -400+ 241/(1+IRRA) + 293/ (1+ IRRA)^2  IRRA = 20.86%
0 = -200+ 131/(1+IRRB) + 172/ (1+ IRRB)^2  IRRB = 31.1%
We should select B
b. NPV A = -400+ 241/1.09+293/1.09^2 = 67.71
NPV B = -200+ 131/1.09+172/1.09^2 = 64.95
We should select A
IRR gives wrong response because cash flows are unconventional.
Another problem with IRR is that this method doesn’t work very well with
exclusive investments.
c. Crossover rate: makes two NPV equal.
NPV (A-B) = 0 = 400-200 + (241-131)/(1+IRR)+(293-172)/(1+IRR^2)
 200 = 110/(1+IRR) + 121 / (1+IRR)^2
IRR = 10%
Exercise 5
a. Beta equity of pure play: 12.4% = 6% + Beta equity * (10%-6%)
 Beta equity = 1.6
Beta asset = 1.6/ (1+ (1-.4)*.65) = 1.15
 1.15 = Beta equity of the division/(1+(1-.4)*1)
 Beta equity of the division = 1.84
 rS = 6%+ 1.84*(10%-6%) = 13.37%
b. rS’ = 12% is smaller than the return of the project, so Nexon’s current stock price
is underpriced.
c. I would buy that stock because the two indications are positive: Nexon does not
use a lot of debt compared to the average of the industry, and its stock is at the
point of beginning to go up.
Two points are violating the efficient market hypothesis: The financial statement
analysis violates the semi strong form; the chart analysis violates the weak form.
Exercise 6
rf = E(rm) – rf = 12 – 5 = 7%
E(rA) = 7% + 0.8 * 5% = 11%
E(rB) = 7% + 1.2 * 5% = 13%
E(rC) = 7% + 0.4 * 5% = 9%
14%
12%
E(r)
10%
8%
Series1
6%
4%
2%
0%
0%
10%
20%
30%
SD
SLM
14%
12%
E(r)
10%
8%
Series1
6%
4%
2%
0%
0
0.5
1
1.5
Beta
There are no inefficient securities; they
all lie on the SLM
b.
By hand
c. The market portfolio lies on the efficient set too, so we have its slope equals:
( E(rm)-rf ) / SD (rm) = 5% / 18% = 0.28
On the same CAL we have: [E(rP) – 7%] / 0.16 = 0.28  E(rP) = 11.44%
Exercise 7
P = $25
D=$2
g = 6% so r = D/P + g = 14%
SD (r) = 10%
Var (rm) = 0.00390625 so SD (rM) = 6.25%
Corr = 0.8 so cov = SD (r) * SD (rM) * corr = .005
Beta = cov / var (rm) = .005/0.00390625 = 1.28
rm = 14%
rf = 8%
So E(r) = 8%+1.28*(14%-8%) = 15.68% > 14%
So the actual expected return of the stock is higher than the return for which it is sold.
This is a good buy stock.
Exercise 8
Market efficiency implies that: If all securities are fairly priced, all must offer equal
expected rates of return.
Comment: If all securities are fairly priced, all must offer the rates of return that equal to
their expected return. But each security has its own return; the returns of different
securities do not equal.