In: Finance
You are considering a merger of two companies:
Company A Company B
Value of Assets (MV) $ 10 Billion $ 100 Billion
Debt (MV) $ 5 Billion $ 10 Billion
Maturity of Debt 5 years 5 years
Volatility 35% 40%
Rf 2% 2%
If company B wants to buy Company A’s equity and pay off its debt as part of the merger,
(a) use the Black-Scholes model to analyze the market value of the equity and the debt of A and B before the merger
(b) If the two firms are merged and there is no synergy, and the combined firm has volatility of 32%, use the Black-Scholes model to analyze the market value of the equity and the debt of B of the combined firm
(c) does this merger makes sense for the stockholders of A and B? Explain
Using Black scholes Equation,
Where,
S = the current price of the asset
K = the strike price
r = risk free rate
T = time to maturity
σ = standard deviation(volatility)
C= value of equity.
A.Equity value of company A ltd.=
Value is finded out by excel-
Today's Date |
1/1/2015 |
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Expiry Date |
12/31/2019 |
The Date which the contract expires |
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Historical Volatility |
35.00% |
The Historical Volatility of the asset's returns |
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Risk Free Rate |
2.00% |
The current risk free interest rate i.e. your return on cash held in the bank |
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Dividened Yield |
0.00% |
The Annualized Dividend Growth Rate of the Stock |
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DTE (Years) |
5.00 |
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d1 |
1.4048 |
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Nd1 |
0.1487 |
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d2 |
0.6221 |
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Nd2 |
0.7331 |
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Value of equity(A)= |
5.8830 |
Equity value of company B ltd.=
Underlying Price |
100.00 |
The current base price of the instrument, eg, the closing price of Microsft Stock |
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Exercise Price |
10.00 |
The price at which the underlying instrument will be exchanged. Also called Strike Price |
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Today's Date |
1/1/2015 |
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Expiry Date |
12/31/2019 |
The Date which the contract expires |
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Historical Volatility |
40.00% |
The Historical Volatility of the asset's returns |
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Risk Free Rate |
2.00% |
The current risk free interest rate i.e. your return on cash held in the bank |
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Dividened Yield |
0.00% |
The Annualized Dividend Growth Rate of the Stock |
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DTE (Years) |
5.00 |
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d1 |
3.1334 |
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Nd1 |
0.0029 |
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d2 |
2.2390 |
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Nd2 |
0.9874 |
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Value of equity(B) |
90.9790 |
B. Value of combined firm
Underlying Price |
110.00 |
The current base price of the instrument, eg, the closing price of Microsft Stock |
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Exercise Price |
15.00 |
The price at which the underlying instrument will be exchanged. Also called Strike Price |
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Today's Date |
1/1/2015 |
|||||||
Expiry Date |
12/31/2019 |
The Date which the contract expires |
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Historical Volatility |
32.00% |
The Historical Volatility of the asset's returns |
||||||
Risk Free Rate |
2.00% |
The current risk free interest rate i.e. your return on cash held in the bank |
||||||
Dividened Yield |
0.00% |
The Annualized Dividend Growth Rate of the Stock |
||||||
DTE (Years) |
5.00 |
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d1 |
3.2820 |
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Nd1 |
0.0018 |
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d2 |
2.5665 |
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Nd2 |
0.9949 |
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Value of combined firm |
96.4405 |
C. Impact to merger
The combined value of the equity prior to the merger is $ 96.862 million and it declines to $96.4405 million after.