 The famous black school or BS model can also be used to price a warrant in modern corporate finance Let's see how Does this model work? before going into the the model, let's see a general understanding on the Value of a call and value of a warrant in terms of gain for the investor As we have seen in our earlier Discussion we see that per share gain on a call was $300 whereas per share gain on a warrant was $200 and if we rearrange these two terms, we have an other term in which the first part is s over s minus sw Where s is basically equal to the number of outstanding shares before issuing warrant and s plus sw is the total number of shares Outstanding after the issuance of warrant now this ratio is Always equal to less always less than one Because the number of shares have now been increased so the earliest version of shares as outstanding are lesser than the number of Newell new total shares This means that the gain on warrant is less than gain on Call without the issuance of warrant As we have seen that now there is a case where the ratio of Existing capital with the new capital is Equal to 2 by 3 as there is the inflow of our new partner into the firm The new partner was earlier earning the gain of $300 on the call Per share whereas his gain under warrant is $200 per share because The amount of capital has been increased from two shares to three shares so this Decline in earning per share or gain per share is termed as a dilutive effect due to the issuance of warrant now, let's see an example how BS model works for Pricing a warrant we have a company named as omega airline whose capital structure is composed of 3.2 million outstanding shares and 18 million dollars of Zero coupon bond with six months to maturity the firm is announcing The issuance of a warrant with the exercise price of 75 dollars each With the right to buy one new share against one existing share with the expiration date of six months as a expiry period Now if there is a buying of six percent tables from the proceed of this warrant issue, then the fund can be used to pay the Existing that of 18 million dollars The effect of this announcement of the company will be that The asserts market value is at present 210 million dollars Company is not paying any dividend The standard deviation on the return of these companies asserts is 50 percent So using this data we can determine the number of amounts that warrant can be Issued by the company using PS model So first we need to determine the amount to raise through the warrant issue In fact, we can determine the present value of the maturing debt in order to declare the amount of the amount of Fund to be raised through the issuance of a warrant and if we Determine the present value of 18 million which is the debt the amount is equal to 17.468 million so the firm must need of must raise this amount to retire its present date the proceeds from this warrant and The debt payment will be equal to each other as the firm is raising amount through the issuance of warrant the same amount is used to pay Repay the amount of debt this means there is no effect on the firm's balance sheet at all So the ambiguous current stock price if we want to determine we need to divide the amount of 210 million over its existing shares of 3.2 million the resulting figure is 65.63 dollars per share that is the per share stock price in the market The value of the single warrant we can determine so our way w is equal to s plus S over s plus w into call Into Stock price and the exercise price so in this particular equation. We are missing only the value of call This means that omega must raise 17.463 million dollars in warrant so the SW Means total number of outstanding shares after the warrant has been issued in multiplying with the per share warrant value should be equal to 17.468 million Therefore, it can be stated that 17.468 million is equal to number of total shares after the issuance of warrant multiplied with the per share warrant value But in this equation, we are missing the number of total shares after the warrants are issued So this SW or the number of total new shares can be determined using PS model this base model as we know that it works in three steps at first step We need to determine the amount value of D1 and D2 then using these values of D1 and D2 in the next step We can determine the value of N D1 and N D2 these values of N D1 and N D2 can be determined the normal distribution function given in Excel Once we have calculated these values in the third and the last step we can determine the value of C which is basically the value of the call and putting the computed values in The model of BS we can determine the value of C and that is 6.54 and in our case This is a per share value of the warrant Now we have the equation where the value of call was missing if we put this value of 6.54 dollars in place of call the resulting figure is equal to 16.569 million So with the help of BS model we have determined the number of shares that the firm must sell to warrants in order to raise the amount of 17.68 million that can be used right now To pay off the debt existing debt of 18 million dollars