Homeworks of financial management (MBA - OUM)

FINANCIAL MANAGEMENT
MBAOUM -2013
HOMEWORKS Page 1
Homeworks for Financial Management
Task (1-1)
r
*
= 3%
I
1
= 2%
I
2
= 4%
I
3
= 4%
 IP
2 – Y
= (2% + 4%)/ 2 = 3%
 IP
3 – Y
= (2% + 4% + 4%) = 3.3%
- The yield on 2 – year Treasury securities:
r
2 – Y
= r
*
+ IP
2 – Y
+ DRP + LP + MRP

= 3% + 3% + 0 + 0 + 0
= 6%
- The yield on 3 – year Treasury securities:
r
3 – Y
= r
*
+ IP
3 – Y
+ DRP + LP + MRP
= 3% + 3% + 0 + 0 + 0
= 6.3%
Task (1-2)
r
RF
= r
*
+ IP = 6%
r = 8%
LP = 0.5%
DRP = ?
r = r
*
+ IP + DRP + LP + MRP
 DRP = r – (r
*
+ IP + LP + MRP)
Where r
*
+ IP = 6%

 DRP = 8% - (6% + 0.5% + 0)
= 1.5%
FINANCIAL MANAGEMENT
MBAOUM -2013
HOMEWORKS Page 2
Task (1-3)
r
*
= 3%
IP
2 – Y
= 3
MRP = ?
r = r
*
+ IP + DRP + LP + MRP
MRP = r – (r
*
+ IP + DRP + LP)
= 6.2% - (3% + 3% + 0 + 0)
= 0.2%
Task (1-4)
r
*
= 3%
I
1
= 3%
I
2

= 4%
I
3
= 3.5% = I
4
= I
5
= I
6
= I
7
MRP = 0.00005 x (t – 1)
R
7– Y
=?
IP
7 – Y
= (3% + 4% + 3.5% + 3.5% + 3.5% + 3.5% + 3.5%)/7 = 3.5%
MRP
7– Y
= 0.0005 x (7-1) = 0.003 = 0.3%
 r
7– Y
= r
*
+ IP + DRP + LP + MRP
= 3% + 3.5% + 0.3% + 0 + 0
= 6.8%
FINANCIAL MANAGEMENT
MBAOUM -2013

HOMEWORKS Page 3
Task (1-5)
r
*
= 3%
I
1
= 8%
I
2
= 5%
I
3
= 4% = I
4
= I
5
= …
r
2 – Y
= r
3 – Y
= 10%
MRP
2 – Y
=? MRP
5 – Y
= ?
IP
2

= (8% + 5%)/2 = 6.5%
IP
5
= (8% + 5% + 4% + 4% + 4%)/5 = 5%
MRP
2 – Y
= r – (r
*
+ IP
2
+ LP + DRP)
= 10% - (3% + 6.5%) = 0.5%
MRP
5 – Y
= r – (r
*
+ IP
5
+ LP + DRP)
= 10% - (3% + 5%) = 2%
 MRP
5 – Y
- MRP
2 – Y
= 2% - 0.5% = 1.5%
Task (1-6)
r
*
= 2%
I

1
= 3%
I
2
= I
3
= … = I fater on > 3 %
MRP = 0
r
3 – Y
- r
3 – Y
= 2%
 r
*
+ IP
3
– (r
*
+ IP
1
) = 2%
 IP
3
– IP
1
= 2%
FINANCIAL MANAGEMENT
MBAOUM -2013
HOMEWORKS Page 4

 (I
1
+ I
2
+ I
3
)/ 3 – I
1
= 6
 (I
1
+ 2I
2
– 3I
1
= 6
 2I
2
- 2I
1
= 6
 I
2
– I
1
= 3 => I
2
= 3 + I
1
= 3 + 3 =6

 I
2
= 6%
Task (1-7)
I
1
= 7%
I
2
= 5%
I
3
= … = I fater on = 3 %
r
*
= 2%
MRP = 0
MRP
1
= 0.2%
MRP
t
= MRP
t -1
(1+0.2) increase up to 1%
a. r for 1-year, 2-year, 3-year, 5-year, 10-year and 20- year Treasury securities,
as the following table:
Year
r
*

(%)
Inflation
(%)
IP (%)
MRP (%)
r (%)
1
2
7
7
0.20
9.20
2
2
5
6
0.24
8.24
3
2
3
5
0.29
7.29
4
2
3
5
0.35
6.85

5
2
3
4
0.41
6.61
6
2
3
4
0.50
6.50
7
2
3
4
0.60
6.45
8
2
3
4
0.72
6.47
9
2
3
4
0.86
6.53

10
2
3
4
1.03
7.03
11
2
3
3
1.03
6.03
12
2
3
3
1.03
6.03
13
2
3
3
1.03
6.03
FINANCIAL MANAGEMENT
MBAOUM -2013
HOMEWORKS Page 5
14
2
3

3
1.03
6.03
15
2
3
3
1.03
6.03
16
2
3
3
1.03
6.03
17
2
3
3
1.03
6.03
18
2
3
3
1.03
6.03
19
2
3

3
1.03
6.03
20
2
3
3
1.03
6.03
FINANCIAL MANAGEMENT
MBAOUM -2013
HOMEWORKS Page 6
CHAPTER 4: RISK AND RETURN
Task (4-1):
- Expected return:
= [0.1 x (-0.5)] + [0.2 x (-0.05)] + [0.4 X 0.16] + [0.2 x 0.25] + [0.1 x 0.6]
= 0.114 = 11.4%
- Standard Deviation:
= 0.2669
- Coefficient of variation:
Task (4-2)
Stock
b
Probability (*)
A: $35,000
0.8
0.47
B: $40,000
1.4
0.53

(*) Probability A = [35,000/ (35,000 + 40,000)] = 0.47
FINANCIAL MANAGEMENT
MBAOUM -2013
HOMEWORKS Page 7
Probability B = 1 – 0.47 = 0.53
 The portfolio’s beta is b
p
= 0.8 x 0.47 x 0.53 = 1.118
Task (4-3)
r
RF
= 5%
RP
M
= 6%
 Expected return for the overall stock market
R
M
= r
FR
+ RP
M
= 5% + 6% = 11%
- With b = 1.2, the required rate of return on a stock r = 5% + 6% x 1.2 = 12.2%
(r = r
RF
+ RP
M
x b)
Task (4-4)

r
RF
= 6%
RP
M
= 13%
B = 0.7
- Market risk premium: RP
M
= r
M
- r
RF
= 13% - 6% = 7%
- Required rat eof return of a stock r
r = r
RF
+ RP
M
x B = 6% +7% x 0.7 = 10.9%
Task 4-5:
Profitability
r
M
(%)
r
j
(%)
0.3
15

20
0.4
9
5
0.3
18
12
a. Expected rate of return for the market and stock j:
b. Standard deviation for market and stock j:
FINANCIAL MANAGEMENT
MBAOUM -2013
HOMEWORKS Page 8
c. The coefficient of variation for the market and stock j:
T
ask (4-6)
r
RF
= 5%
r
M
= 10%
r
A
= 12%
a. Beta of stock A:
r
A
= r
R
+ RP

M
x B
A
= r
RF
+ (r
M
- r
RF
) x B
A
 (r
M
- r
RF
) x B
A
= r
A
- r
RF
 B
A
= [(r
A
- r
RF
)/ (r
M
- r

RF
)] = [(12% - 5%)/ (10% - 5%)] = 1.4
FINANCIAL MANAGEMENT
MBAOUM -2013
HOMEWORKS Page 9
b. B
new
= 2.0
We have r
A
= r
RF
+ (r
M
- r
RF
) x B
new
= 5% + (10% - 5%) x 2 = 15%
Task (4-7)
r
RF
= 9%
r
M
= 14%
B
i
= 1.3
a. Required rate of return:

b. r
A
= r
RF
+ (r
M
- r
RF
) x B
i
= 9% + (14% - 9%) x 1.3 = 15.5%
SML = r
RF
+ (r
M
- r
RF
) x B
i
= r
RF
+ RP
M
x B
i
r
RF1
= 10%
r
RF2

= 8%
r
N1
= r
RF
+ (r
M
- r
RF1
) x B
= 10% + (14% -10%) x 1.3
= 15.2%
RP
M
= r
M
- r
RF1
= 14% - 10% = 4%
SML
1
= 14% - 10% = 4%
With r
RF
= 10%
 r
M
= RP
P
+ r

RF
= 5% + 10% = 15%
r
A
= r
RF
+ MR
P
x B
i
= 10% + 5% x 1.3 = 16.5%
r
N1
= r
RF
+ (r
M
- r
RF2
) x B
= 8% + (14% - 8%) x 1.3
= 15.8%
RP
M
= r
M
- r
RF2
= 14% - 8% = 6%
SML

2
= 14% - 8% = 6%
With r
RF
= 8%
r
M
= RP
P
+ r
RF
= 5% + 8% = 13%
r
A
= 5% + 5% x 1.3 = 14.5%
c. r
RF
= 9% (constant)
r
M1
= 16%
r
M2
= 13%
r
1
= 9% + (16% - 9%) x 1.3 = 18.1%
r
1
= 9% + (14% - 9%) x 1.3 = 14.2%

Stock
Investment ($)
Beta
Probability (%)
A
400,000
1.50
10
B
600,000
(0.50)
15
C
1,000,000
1.25
25
D
2,000,000
0.75
50
r
M
= 14%
r
RF
= 6%
- Beta of the investment:
FINANCIAL MANAGEMENT
MBAOUM -2013
HOMEWORKS Page 10

B = 1.5 x 0.1 + (-0.5) x 0.15 + 1.25 x 0.25 + 0.75 x 0.5 = 0.7625
- Require rate of retun of the dund:
r = r
RF
+ (r
M
- r
RF
) x B = 6% + (14% - 6%) x 0.7625 = 12.1%
Task (4-11)
B
R
= 1.5
B
3
= 0.75
r
RF
= 7%
rˆ = 13% = r
M
r
RF
= r
M
– r
FR
= 13% - 7% = 6%
Required rate of return:
r

R
= r
RF
+ RM
P
x B
R
= 7% + 6% x 1.5 = 16%
r
S
= r
RF
+ RM
P
x B
S
= 7% + 6% x 0.75 = 11.5%
 The required rate of return on the risker srock exceed the required return on
the less risky stock: = 16% - 11.5% = 4.5%