Unformatted text preview: AEM 424 PS #1 Answer Key 1. Software marketing. a. See attached decision tree. You have already developed the software, so that $2 million is a sunk cost (assuming you can’t see the software). Forget about it. The expected value of marketing the software is $3,350,000, which is greater than the expected value of not marketing, which is $0. So, not knowing whether or not Linux will succeed, the best you can do is to get $3,350,000 on average. Now suppose you know whether or not Linux will succeed. If Linux does succeed, a situation you will face with probability 0.7, you will chose to market with a profit of $5,000,000. If Linux does not succeed, a situation you will face with probability 0.3, you will chose not to market with a payout of $0. So, on average, you will get 0.7($5,000,000)+0.3($0)=3,5000,000. The value of knowing the information is thus the difference between the best you can do knowing and the best you can do not knowing: $3,500,000-$3,350,000=$150,000. If you could go back in time and reconsider the decision to develop the software, the value of the information would increase to $750,000. Use the same procedure to see this. 2. VC Decision Tree a. See attached decision tree. The highest EV is to prepare lightly with an average outcome of $12,000. b. The question asks what the option value of waiting to see the outcome of the first meeting before deciding how much to prepare for the second meeting. Obviously, if you prepare heavily for the first meeting, then there is no option value (nothing gained from delaying). So, you need to consider only the case in which you prepare lightly, and then prepare heavily if the first meeting fails. To do this, just change the probabilities and payouts in the “prepare light” VC#2 decision branch to the same as that of the “prepare heavy” VC#2 branch. The expected outcome of the VC#2 branch then rises from zero to $5,000 and the “light preparation” decision rises from $12,000 to $15,500 (0.3*$40,000+0.7*$5,000). Hence, you would pay up to $3,500 for the option to have the second meeting a week later. 3. Acme Steel Research (a) See figure 3a. (b) For the project to be successful, each of the three independent steps must be completed. Since the probability of success in each stage is 0.8 and the probabilities are independent (uncorrelated), the probability of three successes is pr = 0.8 ! 0.8 ! 0.8 = 0.8 3 = 0.512 , just over one-half. (c) E [gain] = 0. 512 *$4, 000, 000 + 0.488 * 0 = $2, 048, 000 (d) Yes. As shown by the decision tree, the payoff from investing is positive, $828,000. The expected cost of the project is 0.2*$500,000+0.8*0.2*$l,000,000+0.8*0.8*$1,500,000=$1,220,000. The first term is the probability of a failure in the first step (.2) times the cost of a failure in the first step ($500,000). The second term is the cost of proceeding through two steps ($1,000,000) times the probability only getting that far—the probability of success in the first step (.8) times the probability of failing in the second step (.2). The third term is the cost of proceeding through three steps ($1,500,000) times the probability of getting that far—the probability of success in the first step (.8) times the probability of success in the second step (.8). Note that the success or failure in the third step does not affect the cost of the project, just the gain from it. Summarizing, the expected cost ($1,220,000) is less than the expected gain ($2,048,000). Since the company is not risk averse, it should begin the project. (e) The answer is no, to both questions. Obviously, if one stage fails, then the project cannot be completed successfully (remember, all three stages are required for success), so any additional expenditures on the project after a stage failure is wasted. However, at each decision node, if all previous stages have succeeded, then the expected benefit of proceeding is always greater than the expected cost. Moreover the expected benefits of proceeding grow relative to the costs as the project moves forward. (f) See figure 3f. (g) The alternate process would be used only if step three of the current project failed, which has a 0.2 probability. (h) There is a 0.2 probability that the alternate process would be used and a $1,000,000 value if it is used, so the option value of having a costless alternate process available would be $200,000. ( i) Since the option value of the alternate process is greater than the cost of having this option, the alternate process should be developed even if one continues with the three-step project. The net value of developing this option is $200,000 - $150,000 = $50,000. Of course, the alternate process should also be developed if the three-step project is dropped, since the net value of the alternate process would then be $850,000. The remaining question is whether Acme should drop the three-step project rather than attempting the third step. Given that the alternate process will be developed, the extra (or marginal) value of successfully completing the three-step project would be $3,000,000, because it would save $3,000,000 more than the alternate process. The expected value of attempting the third step is then 0.8 ! $ 3,000,000 = $2,400,000. This is greater than the $500,000 cost of the third step, so Acme should proceed with the three-step project as well as the alternate process. ( j) We know that Acme should pursue the alternate process: It was worth doing after successful completion of steps one and two (see (i)) and would have greater expected value if the probability of the three-step project failing were higher. The question is whether Acme should pursue the three-step project given that it will have the alternate process available with certainty. As in (i), the marginal value of successfully completing the three-step project would be $3,000,000, because it would save $3,000,000 more than the alternate process. The expected value of attempting the three-step project is then 0.512*$3,000,000 = $1,536,000. This is greater than the expected cost of pursuing the three-step project, which is 0.2*500,000+0.8*0.2*1, 000, 000 + 0.8* 0.8 *1,500,000 = 1,220,000, so Acme should proceed with the three-step project as well as the alternate process. (Note that the probability that you get to the third stage is 0.8*0.8, which is the probability of succeeding in the first and second stage. Whether you succeed in the third stage has no effect on the cost of the project, just the benefit.) Software Development/Marketing Problem New platform fails [p=0.3] -500,000 Market for new platform EV=3,350,000 -1,000,000 Develop software for new platform New platform succeeds [p=0.7] 5,000,000 6,000,000 500,000 Do not market for new platform 0 0 Value of learning platform success before marketing is $150,000 Venture Capital Financing Decision Tree VC#1 - Yes [p=0.3] 20,000 50,000 Heavy Preparation
EV=9,500 -30,000 VC#1 - No [p=0.7] VC#2 - Yes [p=0.7] 20,000 50,000
EV=5,000 VC#2 - No [p=0.3] -30,000 0 VC#1 - Yes [p=0.3] 40,000 50,000 Light Preparation
EV=12,000 -10,000 VC#1 - No [p=0.7] VC#2 - Yes [p=0.2] 40,000 50,000
EV=0 VC#2 - No [p=0.8] -10,000 0 Stick with Rich Uncle Financing 0 0 0 Figure 3a Success in Step 3 [p=0.8] 2,500,000 Success in Step 2 [p=0.8] EV=1,700,000 -500,000 Failure in Step 3 [p=0.2] Success in Step 1 [p=0.8] EV=1,160,000 -500,000 R&D Failure in Step 2 [p=0.2] -500,000 -1,500,000 3,500,000 -500,000 EV=828,000 -500,000 -1,000,000 Failure in Step 1 [p=0.2] EV=828,000 -500,000 -500,000 NO R&D 0 0 Figure 3f Success in Step 3 [p=0.8] 2,500,000 Do Step 3 only EV=1,700,000 Failure in Step 3 [p=0.2] -1,500,000 -500,000 Success in Step 3 [p=0.8] Success in Step 2 [p=0.8] EV=1,750,000 -500,000 Do Step 3 & Alternate EV=1,750,000 Failure in Step 3/Use Alternate [p=0.2] -650,000 350,000 Success in Step 1 [p=0.8] EV=1,200,000 -500,000 Do Alternate Proj only Use Atlernate Process -150,000 850,000 R&D EV=860,000 Failure in Step 2 [p=0.2] -1,000,000 -500,000 EV=860,000 Failure in Step 1 [p=0.2] -500,000 -500000 NO R&D 0 3,350,000 2,350,000 3,500,000 -500,000 AEM 4240: Management Strategy
Additional Problem Set Answer Key
No Leak: [.6] $16 mm Buy Machine: - $13 mm EV = $1.2 mm Leak: [.4] $11.5 mm - $1.5 mm $3 mm The EV of purchasing the new machine is $1.2 million. Since you must finance $10 million of the purchase of the new machine through a one-year loan from the bank, you would be willing to accept an interest rate of up to 12% because $10 million x 12% = $1.2 million. b)
No Leak: [.9] $16 mm Buy Machine: - $13 mm EV = $2.55 mm Leak: [.1] $11.5 mm - $1.5 mm $3 mm The added value of the services provided by the security consulting firm is $1.35 million ($2.55 mm – $1.2 mm). Therefore, since the added value of $1.35 million is less than $1.5 million cost of the services, you should not take this offer. 2. a)
Pass [.6] $60,000 Pass [.7] - $10,000 Pass [.8] - $10,000 Attempt Test - $10,000 EV = $0 $0 EV = - $3,440 $0 Fail [.2] - $10,000 EV = - $1,800 $0 Fail [.3] - $20,000 EV = $6,000 $0 Fail [.4] - $30,000 $30,000 Do Not Attempt Test b) .8 x .7 x .6 = .336 c) No, you should not take your boss up on his offer because the EV of doing so is -$3,440. The minimum bonus you would be willing to accept for passing the CFA exams is $70,000: .2(-$10,000) + (.8)(.3)(-$20,000) + (.8)(.7)(.4)(-$30,000) + (.8)(.7)(.6)(X) X = $40,000 ! this is equal to a $70,000 bonus d) Since you already took the first two tests and will study for the third test no matter what, the cost of a forgone bonus is a sunk cost. Therefore, you would be willing to pay up to $32,000 ($80,000 – $48,000) to take this class.
Take Class $80,000 Pass [.6] $80,000 Don’t Take Class EV = $48,000 $0 Fail [.4] $48,000 e) You should attempt the third test because $38,000 > $35,000 (and the first two tests are sunk costs).
Pass [.6] $80,000 Third Test - $10,000 EV = $38,000 $0 Fail [.4] $35,000 - $10,000 $70,000 Other Offer 3. a)
Receive [.4] $10 mm Purifier - $1 mm Pass [.5] - $3 mm Overhaul EV = - $1 mm Tax Credit [.5] EV = $1 mm - $3 mm $7 mm Doesn’t Receive [.6] - $3 mm EV = - $2 mm No Tax Credit [.5] - $3 mm Doesn’t Pass [.5] Speedy should install the air purifier because - $1,000,000 > - $2,000,000. b) Speedy should overhaul the factory and be willing to pay up to $500,000 for the guarantee. Purifier -$1,000,000 and the overhaul EV = -$500,000. Purifier - $1 mm Pass [.5] - $3 mm Overhaul Tax Credit [.5] $7 mm EV = $2 mm - $3 mm EV = - $.5 mm No Tax Credit [.5] - $3 mm Doesn’t Pass [.5] ...
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- Fall '07
- Probability theory, sunk costs, alternate process