Advanced corporate finance - publié le 02/05/2008

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Advanced corporate finance - publié le 02/05/2008

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Résumé du document

X = $100 kRF = 8% 50% P1 = $120 P0 = $80 50% P1' = $60 En utilisant l?approche par portefeuille de réplication, déterminez la valeur de l'option. Quel est le ratio de couverture? Que signifie le ratio de couverture? HR = options / actions HR = (120 ? 100) / (120 ? 60) HR = 1/3 Le ratio de couverture signifie le nombre d'actions de stocks qui sont nécessaires pour reproduire une option. Vc = HR [Stock price ? PV(Loan)] Vc = HR [P0 ? P1? / (1+kRF)] Vc = 1/3 [80 ? 60 / (1+8%)] Vc = 8.15 La valeur de l'option de réplication en utilisant une approche par portefeuille est de $ 8.15. X = $100 kRF = 8% 50% P1 = $120 P0 = $80 50% P1' = $60 En utilisant l?approche par portefeuille de réplication, déterminez la valeur de l'option. Quel est le ratio de couverture? Qu'est-ce que signifie le ratio de couverture? HR = options / actions HR = (120 ? 100) / (120 ? 60) HR = 1/3 Le ratio de couverture signifie le nombre d'actions de stocks qui sont nécessaires pour reproduire une option. Vc = HR [Stock price ? PV(Loan)] Vc = HR [P0 ? P1? / (1+kRF)] Vc = 1/3 [80 ? 60 / (1+8%)] Vc = 8.15 La valeur de l'option de réplication en utilisant une approche par portefeuille est de $ 8.15.

Sommaire

Exercice 1
1. a) Using the replicating portfolio approach, determine the value of the option. What is the hedge ratio? What does the hedge ratio signify?
2. b) Now using the risk-neutral approach, determine the probability that the stock will increase in price (or decrease in price). Now determine the value of the option using the risk-neutral approach
3. c) Why is the value of the option the same using either the replicating portfolio approach or the risk-neutral approach?
Exercice 2
1. Determine the value of a call option on the stock
2. What is the value of a put option?
3. What is the value of the call option if the time to maturity drops to 0.30?
Exercice 3
1. What is the value of Bagamery's stock, debt, and the default option held by the shareholders?
2. What is the new value of Bagamery's stock, debt, and the default option? Explain your results
3. What is the new value of Bagamery's stock, debt, and the default option? Explain your results
Exercice 4
Exercice 5
1. If only corporate taxes exist, what is the new total value of the firm and the gain from leverage?
2. b) With both corporate and personal taxes, what is the gain from leverage and the total value of the firm if it issues the debt?
3. Why is the gain from leverage and the total value of the firm less in (b) than in (a)?
Exercice 6
1. What is the stock capitalization rate SDC?
2. Construct a table that shows the relevant transactions and arbitrage profit
3. Calculate how much debt you must buy or issue on personal account in order to carry out the arbitrage process and the return or payment it will generate
Exercice 7
Exercice 8
1. What is the maximum price Steve should pay for the service station?
2. How much is the maximum amount he should pay?

Extraits

[...] Advanced corporate finance Exercise 1 X = $100 kRF = Using the replicating portfolio approach, determine the value of the option. What is the hedge ratio? What does the hedge ratio signify? HR = (options / (actions HR = (120 100) / (120 60) HR = 1/3 ( The Hedge Ratio signifies the number of shares of stocks that are needed to replicate one option. Vc = HR [Stock price PV(Loan)] Vc = HR [P0 P1' / Vc = 1/3 [80 60 / Vc = 8.15 ( The value of the option using the replicating portfolio approach is $ Now using the risk-neutral approach, determine the probability that the stock will increase in price (or decrease in price). [...]

[...] Step There will be no growth in after-tax cash flows for 3 years: CF1 = CF2 = CF3 = $ Step 10% growth for years 4 and CF4 = 20 000( 1.10 ) = $ CF5 = 20 000( 1.10 = $ Step growth from year 6 to infinity: CF6 = 24 200( 1.03 ) = $ P5 = CF6 / = / - = $ Step We discount all after-tax cash flows back to P0 = (20 000/( 1.15 + (20 000/( 1.15 + (20 000/( 1.15 + (22 000/( 1.15 200/( 1.15 + (207 717/( 1.15 $ P0 = ( The maximum price Steve should pay for the service station is $ Bibliography CFA Level I 2007, Volume Corporate Finance and Portfolio Management (CFA) R. A. Brealey, S.C. [...]

[...] B(riskless) = X / ekRFt B(riskless) = / e8%x5 B(riskless) = 670 B = B(riskless) Default option Default option = B(riskless) - B Default option = 670 673 Default option = ( The default option is ( The shareholders loss 80$ and the bondholders gain 80$. The equity becomes less valuable as the volatility of the firm's assets decreases. Exercise 4 Original NPV = kRF = ( = 0.70 Should the project be undertaken? Why or why not? For t = 0.5 = 0.70 0.5 0.5 = 0.70 P0 / (X/ekRFt) = (200) / (150 / e9%x1) P0 / (X/ekRFt) = 1.46 Voption1 = 0.106 x P0 with Table B.7 because the option to abandon is a put. [...]

[...] B(riskless) = X / ekRF't B(riskless) = / e13%x5 B(riskless) = 522 B = B(riskless) Default option Default option = B(riskless) - B Default option = 522 462 Default option= 60 ( The default option is $60. ( The shareholders gain 132$ and the bondholders loss 132$. The equity becomes more valuable as the interest rates increase. What is the new value of Bagamery's stock, debt, and the default option? Explain your results 0.5 = 0.25 0.5 = 0.56 V / (X/ekRFt) = / 000/e8%x5) V / (X/ekRFt) = 2.1 S = 0.519 V with Table B.6 S = 0.519 x S = 727 ( The value of stock is $727. [...]

[...] B(riskless) = X / ekRFt B(riskless) = / e8%x5 B(riskless) = 670 B = B(riskless) Default option Default option = B(riskless) - B Default option = 670 594 Default option= 77 ( The default option is $77. What is the new value of Bagamery's stock, debt, and the default option? Explain your results 0.5 = 0.40 0.5 = 0.89 V / (X/ekRF't) = / 000/e13%x5) V / (X/ekRF't) = 2.7 S = ( V S = 0.670 x with Table B.6 S = 938 ( The value of stock is $938. [...]

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