EBK CORPORATE FINANCE
EBK CORPORATE FINANCE
11th Edition
ISBN: 8220102798878
Author: Ross
Publisher: YUZU
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Chapter 24, Problem 16QP
Summary Introduction

To determine: Number of warrant, company should issue.

Warrant:

Warrant is given to the security holder those who purchase the shares. It is not the obligation of the share holder it’s a right of the share holder to purchase the share at a fixed price.

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Explanation of Solution

Formula to calculate the number of the warrants,

Presentvalueofliability=AW(CommonstockCommonstock+AW)×Call(Valueofstockmarket),$95

Where,

  • AW is the number of the warrant.
  • Call(S, E) is the call option.

Substitute $17,468,019.6 for the PV liability, $2,700,000 for the common stock, $88.89 for the value of the stock market.

17,468,019.6=(AW)[2,700,0002,700,000+AW]×Call($88.89,$95)AW=3,756,683

Working notes:

Calculate the present value of the liability,

Presentvalueofliability=Presentvalueoftheshare0.6(Periodtime)=$18,000,000e0.06(0.5)=$17,468,019.60

Calculate the value of the stock price,

Stockprice=MarketvalueoftheassetsCommomstock=$240,000,0002,700,000=$88.89

Calculate the value of the single warrant,

W=[AA+AW]×Call{S=(VA),E=EW}

Where,

  • A is the number of shares.
  • AW is the number of warrants.
  • Call(S, E) is the call option.
  • V is the value of the debt.
  • EW is the strike price of each debt.

W=[2,700,0002,700,000+AW]×Call{($240,000,0002,700,000),E=$95}=[2,700,0002,700,000+AW]×Call{($88.89),E=$95}

Since the firm must raise $17,468,019.60 as a result of the warrant issued, and AW×W must equal $17,468,019.60.

So,

$17,468,019.60=(AW)(W)$17,468,019.60=(AW)(2,700,000(2,700,000+AW))×Call($88.89,$95)

Calculate the value of the warrant by using the black schools, for the call option,

Calculate the D1 ,

D1=[In(SK)+(R+σ22)×tσ2×t]

Where,

  • S is the value of the stock.
  • K is the exercise price.
  • R is the risk rate.
  • T is the tenure of the option.
  • σ is the standard deviation.

Calculate D1,

D1=[In($88.89$95)+(.06+0.502)×.5(0.50×52)]=0.736

Calculate the D2,

D2=D1(σ×t2)=0.736(0.5×0.52)=0.611

Calculate the N(d1) ,

N(d1)=N(0.736)=0.27004

Calculate the N(d2) ,

N(d2)=N(0.611)=0.378162

Black scholes formula to calculate the value of one option,

C=Sx×N(D)K×e-Rt×N(D2)=($88.89)(0.27004)($95)×0.06(0.5)(0.378162)=$24.004$1.078=$22.92

Conclusion

Hence, the number of the warrants is 3,756,683.

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Chapter 24 Solutions

EBK CORPORATE FINANCE

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