Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

A swap contract is an agreement between parties to

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Unformatted text preview: owned by the CEO will be: New percentage of stock = 750,000 / 5,882,352.94 New percentage of stock = .1275 or 12.75% 12. a. Before the warrant was issued, the firm’s assets were worth: Value of assets = 9 oz of platinum($850 per oz) Value of assets = $7,650 So, the price per share is: Price per share = $7,650 / 8 Price per share = $956.25 b. When the warrant was issued, the firm received $850, increasing the total value of the firm’s assets to $8,500 (= $7,650 + 850). If the 8 shares of common stock were the only outstanding claims on the firm’s assets, each share would be worth $1,062.50 (= $8,500 / 8 shares). However, since the warrant gives warrant holder a claim on the firm’s assets worth $850, the value of the firm’s assets available to stockholders is only $7,650 (= $8,500 – 850). Since there are 8 shares outstanding, the value per share remains at $956.25 (= $7,650 / 8 shares) after the warrant issue. Note that the firm uses the warrant price of $850 to purchase one more ounce of platinum. If the price of platinum is $975 per ounce, the total value of the firm’s assets is $9,750 (= 10 oz of platinum × $975 per oz). If the warrant is not exercised, the value of the firm’s assets would remain at $9,750 and there would be 8 shares of common stock outstanding, so the stock price would be $1,218.75. If the warrant is exercised, the firm would receive the warrant’s $1,000 strike price and issue one share of stock. The total value of the firm’s assets would increase to $10,750 (= $9,750 + 1,000). Since there would now be 9 shares outstanding and no warrants, the price per share would be $1,194.44 (= $10,750 / 9 shares). Since the $1,218.75 value of the share that the warrant holder will receive is greater than the $1,000 exercise price of the warrant, investors will expect the warrant to be exercised. The firm’s stock price will reflect this information and will be priced at $1,194.44 per share on the warrant’s expiration date. c. 13. The value of the company’s assets is the combined value of the stock and the warrants. So, the value of the company’s assets before the warrants are exercised is: Company value = 15,000,000($25) + 1,000,000($7) Company value = $382,000,000 When the warrants are exercised, the value of the company will increase by the number of warrants times the exercise price, or: Value increase = 1,000,000($19) Value increase = $19,000,000 So, the new value of the company is: New company value = $382,000,000 + 19,000,000 483 CHAPTER 24 B-484 New company value = $401,000,000 This means the new stock price is: New stock price = $401,000,000 / 16,000,000 New stock price = $25.06 Note that since the warrants were exercised when the price per warrant ($7) was above the exercise value of each warrant ($6 = $25 – 19), the stockholders gain and the warrant holders lose. Challenge 14. The straight bond value today is: Straight bond value = $68(PVIFA9%,25) + $1,000/1.0925 Straight bond value = $783.90 And the conversion value of the bond today is: Conversion value = $35.50($1,000/$150) Conversion value = $236.67 We expect the bond to be called when the conversion value increases to $1,250, so we need to find the number of periods it will take for the current conversion value to reach the expected value at which the bond will be converted. Doing so, we find: $236.67(1.12)t = $1,250 t = 14.69 years. The bond will be called in 14.69 years. The bond value is the present value of the expected cash flows. The cash flows will be the annual coupon payments plus the conversion price. The present value of these cash flows is: Bond value = $68(PVIFA9%,14.69) + $1,250/1.0914.69 = $895.03 15. The value of a single warrant (W) equals: W = [# / (# + #W)] × Call{S = (V/ #), K = KW} where: # #W Call{S, K} V KW = the number of shares of common stock outstanding = the number of warrants outstanding = a call option on an underlying asset worth S with a strike price K = the firm’s value net of debt = the strike price of each warrant Therefore, the value of a single warrant (W) equals: W = [# / (# + #W)] × Call{S = (V/ #), K = KW} = [6,000,000 / (6,000,000 + 750,000) × Call{S = ($105,000,000 / 6,000,000), K = $20} = (.8889) × Call(S = $17.50, K = $20) 484 CHAPTER 24 B-485 In order to value the call option, use the Black-Scholes formula. Solving for d1 and d2, we find d1 = [ln(S/K) + (R + ½σ 2)(t) ] / (σ 2t)1/2 d1 = [ln($17.50/20) + {0.07 + ½(0.15)}(1) ] / (0.15×1)1/2 d1 = 0.0296 d2 = d1 – (σ 2t)1/2 d2 = 0.0296 – (0.15 × 1)1/2 d2 = –0.3577 Next, we need to find N(d1) and N(d2), the area under the normal curve from negative infinity to d 1 and negative infinity to d2, respectively. N(d1) = N(0.0296) = 0.5118 N(d2) = N(–0.3577) = 0.3603 According to the Black-Scholes formula, the price of a European call option (C) on a non-dividend paying common stock is: C = SN(d1) – Ke–RtN(d2) C = ($17.50)(0.5118) – (20)e–0.07(1) (0.3603) C = $2.24 Therefore, the price of a single warrant (W) eq...
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