Problems on Warrants and Convertibles

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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.
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