You own a small networking startup. You have just received an offer to buy your

Question

You own a small networking startup. You have just received an offer to buy your firm from a large, publicly traded firm, JCH Systems. Under the terms of the offer, you will receive 1 million shares of JCH. JCH stock currently trades for $24.22 per share. You can sell the shares of JCH that you will receive in the market at any time. But as part of the offer, JCH also agrees that at the end of one year, it will buy the shares back from you for $24.22 per share if you desire. Suppose the current one-year risk-free rate is 6.44%, the volatility of JCH stock is 30.5%, and JCH does not pay dividends. Round all intermediate values to five decimal places as needed

a. Is this offer worth more than $24.22 million? Explain.

b. What is the value of the offer?

Explanation / Answer

a)

offer is worth more than 24.22. Because it is At the money put option.

hence option premium should be included.

b)

Option calculation done in

d1 = (LN(S / PV(X))/SD*SQRT(T) + SD*SQRT(T)/ 2

d2 = d1 - SD*SQRT(T)

PV(X) = 24.22 / (1+6.44%) = 22.7546

d1 = (LN(24.22 / 22.7546)/30.5%*SQRT(1) + 30.5%*SQRT(1) / 2)) = 0.357127

d2 = 0.357127? - 30.5%*SQRT(1)? = 0.052127

N(d1) = N(0.357127?) = 0.639502

N(d2) = N(0.052127?) = 0.520786

Put = PV(X)*(1-N(d2)) - S*(1-N(d1))

Put = 22.7546*(1-0.520786?) - 24.22*(1-0.639502?) = 2.173048

Value of the offer = 24.22 + 2.173048 = 26.39305

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