# Problems on Warrants and Convertibles

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• Published : October 5, 2010

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Chapter - 24: Warrants and Convertibles

Problem # 24-6: Warrant Value
A warrant right to purchase 3 shares of common stock at an exercise price of \$32 per share. The current price of the stock is \$39. What is the minimum value of the warrant! The intrinsic value = 39-32 = \$7.00 per share (3x7 = \$21.00 for 3 shares) Value of a warrant = n/n+nw (call price)

= (1/1+3)*32 = \$8.00 (!)
Where:
n = the original number of shares
nw = the number of warrants
However, the minimum or lower bound should be: \$7.00 (current price – exercise price)

Chapter - 25: Derivatives and Hedging Risk

Problem # 25-4: Marking to Market

In long futures contracts, you gain when the price increases, and lose when the price declines. The cash flow at the initial settle price = 10(100)(\$480)= \$480,000

The following four days, the gold settles at \$473, \$479, \$482, and \$486 Day 1 account value = 10(100)(\$473) = \$473,000
Day 1 cash flow = 473,000-480,000= - \$7,000

Day 2 account value = 10(100)(\$479) = \$479,000
Day 2 cash flow = 479,000-473,000 = \$6,000

Day 3 account value = 10(100)(\$482) = \$482,000
Day 3 cash flow = 482,000-479,000 = \$3,000

Day 4 account value = 10(100)(\$486) = \$486,000
Day 4 cash flow = 486,000-482,000 = \$4,000

Total profit (loss) = \$486,000-480,000 = \$6,000

Problem # 25-12: Duration

What is the duration of a bond with two years to maturity if the bond has a coupon rate of 8% paid semiannually, and the market rate is 7%? Semiannual interest amount = 8%/2 (1000) = \$40.00

YearsCash FlowPV of pymtYears X PV
/Bond price

0.54038.650.019
14037.340.037
1.54036.070.053
21,040906.31.780
Price of bond =1018.36Duration = 1.889 years

The duration is 1,889 years.