Chapter 4 Solutions - 4-1 a Purchasing an op/on ...

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Unformatted text preview: 4-1 a) Purchasing an op/on is probably strategic. The op/on is an asset that will lose value over /me, as the expira/on date approaches. Because it is adjacent to the nursery, the land probably would be less valuable to others so that the op/on would not be readily transferable to others (it is not reversible). Acquiring the op/on gives the nursery owner the flexibility to expand (it is consequen/al and non- rou/ne). b) For similar reasons, the acquisi/on of the land is probably strategic. A counter argument would be if the op/on were exercised for the purpose of acquiring the land to resell to someone else. In that case, the acquisi/on is unrelated to the core business and, in itself, is not strategic. However, by doing this, the nursery owner would be giving up the op/on to use the land to develop the nursery. If that op/on was important, then even the acquisi/on for resale would have a strategic dimension. c) The decision to carry palm trees is probably not strategic. If the trees do not sell, the nursery owner can stop carrying them. Carrying palm trees could be strategic if the nursery sought to develop an image or brand related to them, but simply selling them would not be strategic. d) Expanding staff is strategic if it would be costly to terminate the employees and if the employees were being added to expand the business. e) Building a greenhouse is strategic because it is costly to reverse, is consequen/al as a specific investment that prevents the land from being use in other ways, and finally, it is not a rou/ne decision. 4-2 a) Compared to large- scale entry, small- scale entry would be more valuable to the entrepreneur if rapid, pre- emp/ve entry is not important, the entrepreneur has limited resources, and outside investors would be overly nega/ve about the growth propects of the venture. b) Rapid growth would be favored if the venture is subject to significant economies of scale and would be consuming cash un/l achieving substan/al sales volumes. If pre- emp/on is important to discourage compe//ve entry and if outside investors are willing to finance the growth on terms favorable to the entrepreneur, rapid growth would be preferred. c) Ver/cal integra/on into manufacturing and distribu/on would be favored if the venture would otherwise be dependent on a manufacturer or distributor in a market that was not compe//ve, where the quality of performance by the manufacturer or distributor was hard to evaluate, or where the manufacturer or the distributor who was not integrated could hold up the venture. d) Equity would tend to be favored over debt in cases when the venture does not generate the cash flows necessary for debt service and when the venture has not taxable earnings that would enable it to take advantage of the tax deduc/bility of interest payments. In addi/on, equity is favored in cases where debt financing could result in a conflict of interest between the creditors and shareholders. 4-3 If the share price is $547 at expira9on, the value of the call op9on will be $27. The profit with an op9on premium of $9.50 is $17.50 ($27 - $9.50). option value $27 $520 $547 share price 4-4 a) As the exercise price goes up, the value of a call op5on decreases. A higher exercise price reduces the probability the op5on will be in the money at expira5on. b) As the value of the underlying asset increases, so does the probability the op5on will be in the money at expira5on. Thus, the value of a call op5on also increases. c) More 5me to expira5on means more chance the underlying asset value will move above the exercise price. This increases the value of the call op5on. d) As the vola5lity of the underlying asset price increases, so does the value of the call op5on. More vola5lity means more outcomes where the asset price exceeds the strike price. 4-5 If the share price is $22 at expira;on, the call op;on has no value, i.e., it is out of the money. At a $16.50 share price, the value of the op;on is $3.50. With an op;on premium of $1.50, the profit is $2.00 ($3.50 - $1.50). option value $3.50 $16.50 $20 $22 share price 4-6 a) As the exercise price goes up, the value of a put op5on increases A higher exercise price increases the probability the put op5on will be in the money at expira5on. b) As the value of the underlying asset increases, the probability the put op5on will be in the money at expira5on decrease. Thus, the value of a put op5on also decreases. c) More 5me to expira5on means more chance the underlying asset value will move below the exercise price. This increases the value of the put op5on. d) As the vola5lity of the underlying asset price increases, so does the value of the put op5on. More vola5lity means more outcomes where the asset price is below the strike price. 4-7 An abandonment op5on is the op5on to stop inves5ng in a venture and to liquidate any of the venture's remaining assets. An entrepreneur can benefit from an abandonment op5on in a variety of ways. For one, if the venture is abandoned, the entrepreneur can stop commiDng effort and resource to the venture and refocus them on other ac5vi5es that may be more valuable. Another poten5al benefit is that abandoning may give the entrepreneur the liquida5on return on any exis5ng assets invested in the venture which could have a higher value in alterna5ve use. 4-8 Based on the decision tree below, the preferable best decision is to expand the store. 20.0% Upturn FALSE Build New 1.9 0.0% 1.9 Economy 0.46 60.0% Stable 0.3 20.0% Downturn -0.5 0.0% 0.3 0.0% -0.5 Decision Building Supply Store 0.54 20.0% Upturn Expand TRUE 1.5 1.5 Economy 0.54 60.0% Stable 0.5 20.0% Downturn -0.3 20.0% Upturn Do nothing 20.0% FALSE 0.5 60.0% 0.5 20.0% -0.3 0.0% 0.5 Economy 0.08 Stable Downturn 60.0% 0 20.0% -0.1 0.0% 0 0.0% -0.1 4-9 The expected NPV of making the acquisiDon is - $75,000, so it would be inadvisable to make the acquisiDon. 40.0% High FALSE Make acquisiDon $3,000,000 Chance ($2,000,000) ($75,000) 25.0% Moderate $1,500,000 35.0% Low AcquisiDon decision $1,000,000 Decision 0 Do nothing TRUE 0 0.0% $1,000,000 100.0% 0 0.0% ($500,000) 0.0% ($1,000,000) 4-10 Expansion Option TRUE Expand High Demand 40.0% 1500000 NPV = -$2,500,000 + $4,000,000 = $1,500,000 Decision 1500000 Do Not Expand Invest/Expand 40.0% 1500000 FALSE 0.0% 1000000 1000000 NPV = -$2,000,000 + $3,000,000 = $1,000,000 Chance 250000 TRUE Expand Moderate Demand 25.0% 0 NPV = -$2,500,000 + $2,500,000 = $0 Decision 0 Expand 35.0% FALSE 0.0% -500000 -500000 FALSE Do Not Expand Low Demand 25.0% 0 0.0% -1500000 -1500000 NPV = -$2,000,000 + $1,500,000 = -$500,000 NPV = -$2,500,000 + $1,000,000 = -$1,500,000 Decision -1000000 Do Not Expand TRUE -1000000 35.0% -1000000 NPV = -$2,000,000 + $1,000,000 = -$1,000,000 Expanding dominates continuing in high and moderate demand states. The NPV of the venture with expansion option is the following: NPV = 0.4 x $1,500,000 + 0.25 x $0 + 0.35 x $1,000,000 = $250,000 The value of the expansion option: NPV with expansion = $325,000 compared to negative NPV of accept/reject decision NPV with expansion = $250,000 compared to not doing the venture 4-11 Abandonment Option Con5nue High Demand 40.0% 40.0% 1000000 NPV = -$2,000,000 + $3,000,000 = $1,000,000 Decision 1000000 Abandon Invest/Abandon TRUE 1000000 FALSE 0.0% -200000 -200000 NPV = -$2,000,000 + $1,800,000 = -$200,000 Chance 280000 Con5nue Moderate Demand 25.0% 0.0% -500000 NPV = -$2,000,000 + $1,500,000 = -$500,000 Decision -200000 Abandon Con5nue Low Demand FALSE -500000 35.0% TRUE 25.0% -200000 -200000 FALSE NPV = -$2,000,000 + $1,800,000 = -$200,000 0.0% -1000000 -1000000 NPV = -$2,000,000 + $1,000,000 = -$1,000,000 Decision -200000 Abandon TRUE -200000 35.0% -200000 NPV = -$2,000,000 + $1,800,000 = -$200,000 Abandoning dominates continuing in moderate and low demand states. The NPV of the venture with abandonment option is the following: NPV = 0.4 x $1,000,000 + 0.25 x -$200,000 + 0.35 x -$200,000 = $280,000 The value of the abandonment option: NPV with abandonment = $355,000 compared to negative NPV of accept/reject decision NPV with abandonment = $280,000 compared to not doing the venture 4-12 Complex Real Options TRUE Expand High Demand 40.0% 1500000 NPV = -$2,500,000 + $4,000,000 = $1,500,000 Decision 1500000 Do Neither Abandon Invest/Complex 40.0% 1500000 FALSE 1000000 0.0% 1000000 FALSE -200000 -200000 NPV = -$2,000,000 + $3,000,000 = $1,000,000 0.0% NPV = -$2,000,000 + $1,800,000 = -$200,000 Chance 530000 TRUE Expand Moderate Demand 25.0% 0 0 NPV = -$2,500,000 + $2,500,000 = $0 Decision 0 Do Neither Abandon Expand Low Demand 25.0% 35.0% FALSE 0.0% -500000 -500000 FALSE 0.0% -200000 -200000 FALSE 0.0% -1500000 -1500000 NPV = -$2,000,000 + $1,500,000 = -$500,000 NPV = -$2,000,000 + $1,800,000 = -$200,000 NPV = -$2,500,000 + $1,000,000 = -$1,500,000 Decision -200000 Do Neither Abandon FALSE -1000000 TRUE -200000 0.0% -1000000 NPV = -$2,000,000 + $1,000,000 = -$1,000,000 35.0% -200000 NPV = -$2,000,000 + $1,800,000 = -$200,000 Expansion dominate in high and moderate demand, abandoning in low demand states. The NPV of the venture with expansion and abandonment options is the following: NPV = 0.4 x $1,500,000 + 0.25 x $0 + 0.35 x -$200,000 = $530,000 The value of the complex options: NPV with abandonment = $605,000 compared to negative NPV of accept/reject decision NPV with abandonment = $530,000 compared to not doing the venture 4-13 Accept/Reject No Success No Success 60.0% 70.0% Invest $3 million 20.0% 40.0% 30.0% 4000000 Probability of not succeeding: P(no) = 0.7 x 0.6 * 0.8 = 0.336 Probability of succeeding: P(success) = 1 - P(no) = 1 - 0.336 = 0.664 Expected value of investment: PV = P(success) x $4,000,000 = 0.664 x $4,000,000 = $2,656,000 Net Present Value: NPV = -$3,000,000 + $2,656,000 = -$344,000 Do not undertake the project 4000000 Chance Success 4000000 Chance 2656000 30.0% 4000000 33.6% 0 800000 2080000 Success 0 Chance Success No Success 80.0% 28.0% 4000000 8.4% 4000000 4-14 Staging of Investment Decision a. No Success Invest $1,000,000 FALSE -1000000 No Success 0 20.0% Invest $1,000,000 TRUE -1000000 TRUE 600000 40.0% Success No Success 70.0% 0 Chance -1000000 4000000 28.0% 3000000 Decision 0 600000 FALSE Abandon -1000000 0.0% -1000000 Chance Invest $1 million 1620000 Success 30.0% 4000000 30.0% 4000000 b. Conditional Value in Stage 1 Expected Value of Success: Conditional Value in Stage 2 Expected Value of Success: Conditional Value in Stage 3 Expected Value of Success: E(x) = 0.3 * ($4,000,000) E(x) = $1,200,000 E(x) = 0.4 * ($4,000,000) E(x) = $1,600,000 E(x) = 0.2 * ($4,000,000) E(x) = $800,000 Expected Value of failure: NPV of Conditional Investment: NPV of Conditional Investment: E(x) = (0.7)*(NPV of Stage 2) E(x) = (0.7)*($600,000) E(x) = $420,000 NPV = -$1,000,000 + $1,600,000 NPV = $600,000 NPV = -$1,000,000 + $800,000 NPV = -$200,000 Invest in Stage 2 Do not invest in Stage 3 Total Present Value of Stage 1 Investment: Exp. Value of Success + Exp. Value of Failure $1,200,000 + $420,000 = $1,620,000 NPV of Stage 1 Investment: NPV = -$1,000,000 + $1,620,000 NPV = $620,000 Invest in Stage 1 4000000 Decision Abandon 0 0.0% -2000000 -1200000 Success 60.0% 80.0% Chance 42.0% -1000000 0.0% 2000000 4-15 The NPV in Problem 13 is nega4ve; the NPV in Problem 14 is posi4ve. This result is due to the abandonment op4ons, which allows the infusions to be staged in three, $1 million investments rather than an up- front, $3 million investment. The total difference in NPV between Problems 13 and 14 is $964,000 (from - $344,000 to $620,000). However, since the nega4ve NPV means the opportunity would not be pursued as presented in Problem 13, the value added by the op4ons is $620,000. This simple example illustrates that op4on values are not addi4ve. More generally, because some op4ons can only be exercised if others are exercised (in this case, the third stage cannot be exercised without the second stage) the op4on values are not addi4ve. 4-16 a) See tree diagrams and calcula1ons below. b) Accept- Reject Decision: The large restaurant has the highest NPV for the entrepreneur at $204,500. This compares with $191,500 using the probabili1es in the text. Op1on to Delay: Wai1ng is worth $226,000 to the entrepreneur. Compared with the simple accept- reject decision, the op1on is worth $21,500. The book probabili1es yielded an op1on value of $213,500. Op1on to Expand: With this op1on, the small restaurant is worth $280,000, which makes the op1on value $75,500 compared to the accept- reject decision. It is worth $54,000 more than the op1on to delay. The op1on to expand based on the text probabili1es is $278,000. Abandonment op1on: The op1on to abandon makes the large restaurant worth $263,000, but adds no value to the small restaurant. In the text, the large restaurant with an op1on to abandon was worth $230,500. c) The best strategy is to build the small restaurant with the op1on to expand. Adding the op1on to abandon does not add to the value of the small restaurant. The cost of the abandonment op1on for the large restaurant is not relevant since the best choice is to build small with the op1on to expand if demand is high. If expansion were not an op1on, then the op1on to abandon the large restaurant would be worth $58,500, or $37,000 more than the op1on to delay. d) The new probabili1es make the value of the restaurant less certain. e) As with financial op1ons, uncertainty adds to the value of real op1ons. Accept-Reject Decision Conditional Value State Probability Weighted Value $575.000 0.4 $230.000 Intermed. Demand $120.000 0.3 $36.000 Low Demand Large Restaurant State of Nature High Demand Strategy ($205.000) 0.3 ($61.500) $96.000 High Demand $240.000 0.4 Intermed. Demand $240.000 0.3 $72.000 Low Demand Small Restaurant ($80.000) 0.3 $204.500 ($24.000) High Demand $0.000 0.4 $0.000 0.3 $0.000 $0.000 0.3 $0.000 State of Nature Conditional Value State Probability Weighted Value High Demand $575.000 0.4 $230.000 Intermed. Demand $120.000 0.3 $36.000 Low Demand ($205.000) 0.3 $144.000 $0.000 Intermed. Demand Low Demand Do Not Enter Value of Strategy ($61.500) $96.000 $0.000 Option to Delay Strategy Large Restaurant High Demand $240.000 0.4 Intermed. Demand $240.000 0.3 $72.000 Low Demand Small Restaurant ($80.000) 0.3 $204.500 ($24.000) High Demand $445.000 0.4 $160.000 0.3 $48.000 $0.000 0.3 $0.000 State of Nature Conditional Value State Probability Weighted Value High Demand $575.000 0.4 $230.000 Intermed. Demand $120.000 0.3 $36.000 Low Demand ($205.000) 0.3 ($61.500) Expand $580.000 0.4 $232.000 Do Not Expand $240.000 0.4 $96.000 Intermed. Demand $240.000 0.3 $72.000 Low Demand ($80.000) 0.3 $144.000 $178.000 Intermed. Demand Low Demand Wait Value of Strategy ($24.000) Demand Info. $226.000 Expansion Option Strategy Large Restaurant Value of Strategy $204.500 High Demand Small Restaurant High Demand 0.4 $0.000 $0.000 0.3 $0.000 Low Demand Do Not Enter $0.000 Intermed. Demand $0.000 0.3 $280.000 $0.000 $0.000 Abandonment Option Aband. Value Conditional PV State Probability Weighted Value $390.000 $975.000 0.4 $390.000 Intermed. Demand $390.000 $520.000 0.3 $156.000 Low Demand Large Restaurant State of Nature High Demand Strategy $390.000 $195.000 0.3 $117.000 High Demand $240.000 $640.000 0.4 $240.000 $640.000 0.3 $192.000 $240.000 $320.000 0.3 $96.000 High Demand Do Not Enter $263.000 $256.000 Intermed. Demand Low Demand Small Restaurant NPV of Strategy $0.000 0.4 $0.000 Intermed. Demand $0.000 0.3 $0.000 Low Demand $0.000 0.3 $0.000 $144.000 $0.000 4-17 a) If the investor is willing to accept 1% of equity per $20,000 invested instead of 1% per $10,000, the entrepreneur's share of the large restaurant with wai?ng (in Figure 4.4) is 82.5% instead of 65%. The entrepreneur's share of the small restaurant is 90% instead of 80%. The resultant NPV increases to $316,750, up from $213,500. b) With these assump?ons about how risk reduc?on affects the investor's willingness to invest, the wai?ng op?on becomes the best alterna?ve. Note that a similar argument could be made for the cost of expansion. If expansion is warranted, the investor might be willing to accept a smaller ownership share for the incremental investment. Also, as having an abandonment op?on reduces risk (for the large restaurant), the investor might accept a lower share of large- restaurant equity with the abandonment op?on. Option to Delay Weighted Value $575.000 0.3 $172.500 Intermed. Demand $120.000 0.5 $60.000 ($205.000) 0.2 ($41.000) $240.000 0.3 $72.000 Intermed. Demand $240.000 0.5 $120.000 Low Demand ($80.000) 0.2 ($16.000) High Demand Wait State Probability High Demand Small Restaurant Conditional Value Low Demand Large Restaurant State of Nature High Demand Strategy $672.500 0.3 $201.750 Intermed. Demand $230.000 0.5 $115.000 Low Demand $0.000 0.2 $0.000 Demand Info. Value of Strategy $191.500 $176.000 $316.750 4-18 a) If you bet 2,000 points, the rival should bet enough so that the outcome if you lose and the rival wins is such that the rival has more than 5,000 points. The rival must bet at least 1,001 - if the rival bets less, you always win. The game tree illustrates this. By beBng at least 1,001, the rival has a 25% chance of winning. Your Outcome Rival Action Rival Outcome Payoff Win 1001 Net 5001 You Win Lose 1001 Net 2999 You Win Win 999 Net 4999 You Win Lose 999 Net 3001 You Win Win 1001 Net 5001 You Lose Lose 1001 Net 2999 You Win Win 999 Net 4999 You Win Lose 999 Net 3001 Your Action You Win Bet 1001 Win 2000 Net 9000 Bet 999 Bet 2000 Hold 5000 Bet 1001 Lose 2000 Net 5000 Bet 999 b) If your rival bets 4,000 points, you need to bet at least 1,001 to end up with more than 8,000 points. If you bet less, the rival wins half of the Fme. The game tree illustrates this. By beBng at least 1,001, you have a 75% chance of winning. Rival Outcome Your Action Your Outcome Payoff Win 1001 Net 8001 You Win Lose 1001 Net 5999 You Lose Win 999 Net 7999 You Lose Lose 999 Net 6001 You Lose Win 1001 Net 8001 You Win Lose 1001 Net 5999 You Win Win 999 Net 7999 You Win Lose 999 Net 6001 Rival Action You Win Bet 1001 Win 4000 Net 8000 Bet 999 Bet 4000 Hold 0 Bet 1001 Lose 4000 Net 0 Bet 999 c) The offer to split is only valuable if half of the prize with certainty is worth more to you than a 75 percent chance of winning (and the associated 25% chance of losing). Assuming it is, you might sFll be concerned that the rival will cheat on the agreement. If so, you would want to move last so you can guarantee the rival does not bet. If you both bet at the same Fme, the rival could sFll cheat. d) In this case, with no agreement in place, as long as you do not care about the other prize, it does not maLer whether you are first or last. If there is an agreement, you would want to be last to protect against cheaFng by the rival. These answers all assume that you and the rival bet on opposite colors. 4-19 As the game tree below shows, if SPF enters, Jolax's best strategy is to maintain the high price, even if they lose market share. This would give them $3 million versus $0 if they pursue the low- price strategy. Knowing what Jolax will do if SPF enters, SPF compares their expected payoff from entering ($2 million) with the payoff from not entering ($0). In this case, they are beLer off by entering, with the knowledge that Jolax will keep the price high. Enter Mover Jolax: Expected Payoff $3 million $2 million Low price Action Action High price Mover SPF: Expected Payoff $0 million -$1 million High price $5 million $0 million Jolax SPF Stay out Jolax 4-20 As the game tree below shows, if SPF enters, Jolax's best strategy is to reduce the price. This would give them $4 million versus $3 if maintain the high price. Knowing that Jolax will cut the price if SPF enters, SPF compares their expected payoff from entering (- $3 million) with the payoff from not entering ($0). In this case, they are beLer off staying out. Enter Mover Jolax: Expected Payoff $3 million $2 million Low price Action Action High price Mover SPF: Expected Payoff $4 million -$3 million High price $5 million $0 million Jolax SPF Stay out Jolax 4-21 a) Assuming Erin has a 70% chance of selec6ng her best course of ac6on, Erin is more likely to stay out if Kelly enters with a large bar and is rela6vely likely to enter if Kelly enters with a small bar. If Kelly waits, Erin has a 70% chance of entering. As shown in the game tree below, regardless of whether Erin enters, Kelly's best ac6on is to enter with a large bar, with an expected payoff of $411,500. This is less than Kelly would get if Erin behaved op6mally, i.e., if she stayed out, yielding Kelly an expected payoff of $425,000 (from Figure 4.6). Kelly's expected payoff from entering with a small bar is $295,000, which is more than she would get if Erin behaved op6mally ($250,000 from Figure 4.6). The gain occurs because there is a 30% chance that Erin will incorrectly decide to enter. If Kelly waits, her expected return is $111,000, which is based on entering with a large bar, regardless of what Erin selects. Therefore, Kelly's best decision is s6ll to enter now with the large bar. b) Assuming Erin has a 70% chance of entering, no maQer what Kelly does, Kelly's best strategy con6nues to be to enter with a large bar. As shown in the second game tree below, her expected payoff is $393,500. In this case, Erin's ignoring Kelly's ac6on is analogous to a chance outcome in a decision tree, i.e., Erin's decision is like a state of nature. With a game tree and with Erin behaving ra6onally, as in Figure 4.6, Kelly's payoffs hav the widest variance. This is because Kelly can pre- empt Erin's decision to enter, know what Erin's response will be. Assuming There is a 70 Percent Chance That Erin Selects the Right Action $425.000 $0.000 $250.000 $200.000 $400.000 $0.000 Large $300.000 $100.000 Small $190.000 $210.000 Stay Out $0.000 $300.000 Large $370.000 $0.000 Small $350.000 $0.000 Stay Out $0.000 $0.000 Kelly's Conditional Payoff Erin's Conditional Payoff Erin Enters $380.000 ($100.000) Erin Stays Out $425.000 $0.000 Erin Enters $250.000 $200.000 Erin Stays Out $400.000 $0.000 Large $300.000 $100.000 Small $190.000 $210.000 Stay Out Small ($100.000) Erin Stays Out Kelly's Bar $380.000 Erin Enters Large Mover Erin's Conditional Payoff Erin Stays Out Action Kelly's Conditional Payoff Erin Enters Mover $0.000 $300.000 Large $370.000 $0.000 Small $350.000 $0.000 Stay Out $0.000 $0.000 Stay Out Kelly's Bar Kelly's Expected Payoff Erin's Expected Payoff ($70.000) $140.000 $321.000 Erin' Pub $210.000 $295.000 Kelly's Bar $60.000 $393.500 Erin' Pub ($30.000) $111.000 Erin' Pub Enter Wait Action Erin's Expected Payoff $295.000 Mover Kelly's Expected Payoff $411.500 Action $70.000 Assuming Erin Enters with 70 Percent Probability, No Matter What Kelly Does Mover Mover Large Kelly's Bar Action Erin' Pub Small Action Action Erin' Pub Enter Wait Mover Kelly's Bar Erin' Pub Stay Out Kelly's Bar ...
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