Question

In: Finance

You are considering a merger of two companies:                                   &nb

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

Solutions

Expert Solution

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

Expiry Date

12/31/2019

The Date which the contract expires

Historical Volatility

35.00%

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

d1

1.4048

Nd1

0.1487

d2

0.6221

Nd2

0.7331

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

Exercise Price

10.00

The price at which the underlying instrument will be exchanged. Also called Strike Price

Today's Date

1/1/2015

Expiry Date

12/31/2019

The Date which the contract expires

Historical Volatility

40.00%

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

d1

3.1334

Nd1

0.0029

d2

2.2390

Nd2

0.9874

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

Exercise Price

15.00

The price at which the underlying instrument will be exchanged. Also called Strike Price

Today's Date

1/1/2015

Expiry Date

12/31/2019

The Date which the contract expires

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

d1

3.2820

Nd1

0.0018

d2

2.5665

Nd2

0.9949

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.


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