Corporate Finance I Homework
Essay by Oanh_Pham • May 9, 2018 • Coursework • 762 Words (4 Pages) • 862 Views
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:
- 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
- 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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