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

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.

jeff jeffy answered 5 months ago

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