# Corporate Finance I Homework

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CORPORATE FINANCE I HOMEWORK

Problem 1:

a)

 recession normal expanding 50 40 55 60 Probability 0.1 0.8 0.1 Return -0.2 0.1 0.2 Expected R 0.08

Expected return of stock A:  E[RA] = 0.1*(-0.2)+0.8*0.1+0.1*0.2=0.08=8%

Standard deviation of stock A:

A =  = 9.8%[pic 1][pic 2]

B  = 12%[pic 3]

Beta is the measure of risk.

[pic 4]   and      [pic 5]

So

βA = ρ(A,M)* σA/ σM = 0.8 * 9.8%/10% = 0.78

βB = ρ(B,M)* σB/ σM = 0.2 * 12%/10% = 0.24

βB  < βA  so as a risk averse investor, I will prefer stock B.

b)

A portfolio with 70% of stock A and 30% of stock B

Expected return of the portfolio: E[Rp ] = 8% * 0.7 + 9% * 0.3 = 8.3%

[pic 6]

σ2 = (0.7*9.8%)2 + (0.3*12%)2  + 2*(0.7*9.8%)*(0.3*12%)*0.6 = 0.00896

σ =  = 0.0947 = 9.47%[pic 7]

c)

βp = w A * β A   + w B * β B = 0.7*0.78+0.3*0.24 = 0.62 = 62%

Problem 2:

a)

 Draw the time line of bond Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Payment 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80 1080

b)

The market price of the bond:

PV = (80/0.07)*(1-(1.07^(-20)))+1000/((1.07)^20) = \$1105.94

c) The cost of equity using the CAPM

βs = 0.048/(0.2^2) = 1.2

[pic 8]

Rs = 0.06+1.2*0.075 = 15%

d) The cost of capital using market-value weights

VB = 1000 * 1105.94 = \$1105940

Vs = 1000000*60 = \$60000000

V = 1105940 +  60000000 = \$61105940

[pic 9]

Rwacc = (60000000/61105940)*15% + (1105940/61105940)*7%*(1-0.4) = 14.8%

e)

UCF = 0.6 M

NPV = UCF/ Rwacc   - 5M = 0.6/14.8%  - 5 = -0.946M <0

So the corporation A should not invest in the considered project.

Problem 3:

1. before the recapitalization is announced:

Vu = Vs = EBIT* ( 1-0.4) / 0.2 = 50 * (1-0.4)*0.2 = 150 M

PPS = 150 / 2 = \$75

1. after the recapitalization plan is announced

VL= Vu + t*B = 150 + 0.4*25 = 160 M

Vs = 160 M

PPS = 160/2 = \$80

Shares purchases back = 25 / 80 = 0.3125 M = 312500

Outstanding shares = 2 - 0.3125 = 1.6875M = 1687500

Vs = 160 – 25 = 135M

PPS = 135/1.6875 = \$80

LCF = =50*(1-0.4) -25*0.1*0.6 = 28.5M

[pic 10]
Rs =0.2+(25/135)*0.6*(0.2-0.1) =
0.21

Vs = LCF/Rs = 28.5/0.21 = 135M

Problem 4:

a)

Value of Alpha Corporation

VA = 5000*20= \$100000

b)Value of Beta corporation

VB = VA  = \$100000

c) Beta Corporation

Vs (Beta) = 100000-25000= \$75000

d)

Buy 20% of Alpha equity: 100000*20% = \$20000

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