Homeworks of financial management (MBA - OUM)

Task (1-1)r* = 3%I1 = 2%I2 = 4%I3 = 4%IP2 – Y = (2% + 4%)/ 2 = 3%IP3 – Y = (2% + 4% + 4%) = 3.3%-The yield on 2 – year Treasury securities:r2 – Y = r* + IP2 – Y + DRP + LP + MRP = 3% + 3% + 0 + 0 + 0 = 6%-The yield on 3 – year Treasury securities:r3 – Y = r* + IP3 – Y + DRP + LP + MRP = 3% + 3% + 0 + 0 + 0 = 6.3%Task (4-3)rRF = 5%RPM = 6%Expected return for the overall stock marketRM = rFR + RPM = 5% + 6% = 11%-With b = 1.2, the required rate of return on a stock r = 5% + 6% x 1.2 = 12.2%(r = rRF + RPM x b¬)

Homeworks for Financial Management

Task (1-1)

r*= 3%

I1 = 2%

I2= 4%

I3= 4%

 IP2 – Y = (2% + 4%)/ 2 = 3%

 IP3 – Y = (2% + 4% + 4%) = 3.3%

- The yield on 2 – year Treasury securities:

r2 – Y= r*+ IP2 – Y+ DRP + LP + MRP

= 3% + 3% + 0 + 0 + 0

= 6%

- The yield on 3 – year Treasury securities:

r3 – Y = r*+ IP3 – Y + DRP + LP + MRP

= 3% + 3% + 0 + 0 + 0

= 6.3%

Task (1-2)

rRF= 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%

Task (1-3)

r*= 3%

IP2 – 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%

I1 = 3%

I2= 4%

I3= 3.5% = I4 = I5 = I6= I7

MRP = 0.00005 x (t – 1)

R7– Y =?

IP7 – Y = (3% + 4% + 3.5% + 3.5% + 3.5% + 3.5% + 3.5%)/7 = 3.5%

MRP7– Y = 0.0005 x (7-1) = 0.003 = 0.3%

 r7– Y = r*+ IP + DRP + LP + MRP

= 3% + 3.5% + 0.3% + 0 + 0

= 6.8%

Task (1-5)

r*= 3%

I1 = 8%

I2= 5%

I3= 4% = I4 = I5 = …

r2 – Y = r3 – Y = 10%

MRP2 – Y =? MRP5 – Y = ?

IP2= (8% + 5%)/2 = 6.5%

IP5= (8% + 5% + 4% + 4% + 4%)/5 = 5%

MRP2 – Y = r – (r*+ IP2+ LP + DRP)

= 10% - (3% + 6.5%) = 0.5%

MRP5 – Y = r – (r*+ IP5+ LP + DRP)

= 10% - (3% + 5%) = 2%

 MRP5 – Y - MRP2 – Y = 2% - 0.5% = 1.5%

Task (1-6)

r*= 2%

I1 = 3%

I2= I3= … = I fater on > 3 %

MRP = 0

r3 – Y - r3 – Y = 2%

r*+ IP3– (r*+ IP1) = 2%

IP3– IP1= 2%

(I1+ I2+ I3)/ 3 – I1= 6

(I1+ 2I2– 3I1= 6

2I2- 2I1= 6

 I2– I1= 3 => I2= 3 + I1= 3 + 3 =6

 I2= 6%

Task (1-7)

I1 = 7%

I2= 5%

I3= … = I fater on = 3 %

r*= 2%

MRP = 0

MRP1= 0.2%

MRPt= MRPt -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 (%)

14 2 3 3 1.03 6.03

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)

(*) Probability A = [35,000/ (35,000 + 40,000)] = 0.47

Probability B = 1 – 0.47 = 0.53

 The portfolio’s beta is bp= 0.8 x 0.47 x 0.53 = 1.118

Task (4-3)

rRF= 5%

RPM= 6%

 Expected return for the overall stock market

RM= rFR+ RPM= 5% + 6% = 11%

- With b = 1.2, the required rate of return on a stock r = 5% + 6% x 1.2 = 12.2% (r = rRF+ RPMx b)

Task (4-4)

rRF= 6%

RPM= 13%

B = 0.7

- Market risk premium: RPM= rM- rRF = 13% - 6% = 7%

- Required rat eof return of a stock r

r = rRF+ RPMx B = 6% +7% x 0.7 = 10.9%

Task 4-5:

Profitability r M (%) r j (%)

a Expected rate of return for the market and stock j:

b Standard deviation for market and stock j:

c The coefficient of variation for the market and stock j:

T ask (4-6)

rRF = 5%

rM= 10%

rA= 12%

a Beta of stock A:

rA= rR+ RPMx BA = rRF+ (rM- rRF) x BA

(rM- rRF) x BA= rA- rRF

BA= [(rA- rRF)/ (rM- rRF)] = [(12% - 5%)/ (10% - 5%)] = 1.4

b Bnew = 2.0

We have rA= rRF+ (rM- rRF) x Bnew

= 5% + (10% - 5%) x 2 = 15%

Task (4-7)

rRF = 9%

rM= 14%

Bi= 1.3

a Required rate of return:

b rA= rRF+ (rM- rRF) x Bi

= 9% + (14% - 9%) x 1.3 = 15.5%

SML = rRF+ (rM- rRF) x Bi= rRF+ RPMx Bi

r RF1 = 10% r RF2 = 8%

rN1= rRF+ (rM- rRF1) x B

= 10% + (14% -10%) x 1.3

= 15.2%

RPM= rM- rRF1= 14% - 10% = 4%

SML1= 14% - 10% = 4%

With rRF= 10%

 rM= RPP+ rRF= 5% + 10% = 15%

rA= rRF+ MRPx Bi

= 10% + 5% x 1.3 = 16.5%

rN1= rRF+ (rM- rRF2) x B

= 8% + (14% - 8%) x 1.3

= 15.8%

RPM= rM- rRF2= 14% - 8% = 6% SML2= 14% - 8% = 6%

With rRF= 8%

rM= RPP+ rRF= 5% + 8% = 13%

rA= 5% + 5% x 1.3 = 14.5%

c rRF = 9% (constant)

r1= 9% + (16% - 9%) x 1.3 = 18.1% r1= 9% + (14% - 9%) x 1.3 = 14.2%

rM= 14%

rRF= 6%

- Beta of the investment:

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 = rRF+ (rM- rRF) x B = 6% + (14% - 6%) x 0.7625 = 12.1%

Task (4-11)

BR= 1.5

B3= 0.75

rRF= 7%

rˆ= 13% = rM

rRF= rM– rFR= 13% - 7% = 6%

Required rate of return:

rR= rRF+ RMPx BR= 7% + 6% x 1.5 = 16%

rS= rRF+ RMPx BS= 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%