Review Problems Solutions.doc

Problem 1 The company is selling products online. The average purchase price is 100 Lt per year. The company has profit margin of 15%. Customer acquisition costs are 75 Lt per customer. 60% of customers who bought product one year are expected to keep buying it the next year. Calculate lifetime value of a customer with 15% discount rate. Does the company have a sound business model? How many customers the company needs to acquire in order to justify initial investment needs of 25,000 Lt? Customer lifetime value = 100*15%/(10%+40%)=27,27 Lt Customer acquisition costs = 75 Lt Net value = 27,27-75=-47.73 Lt The company does not have a viable business model. No amount of customers justifies initial investment costs.

Problem 2 The company is manufacturing equipment for mobile phones. The company has made the analysis how much “item A” costs to produce. The average and incremental costs are shown in the table below: Category

Average cost per unit

Incremental costs

Direct materials Direct labor Indirect labor Depreciation of machinery Department overhead General and administrative costs

20 Lt 15 Lt 10 Lt 5 Lt 10 Lt 5 Lt

100% 100% 70% 40% 20% 10%

The company has an order to produce 10,000 items at a price of 55 Lt. Should the company sign the deal? Explain. Total average costs per unit = 65 Lt Total incremental costs per unit = 46.5 Lt If the company has spare capacity it can accept the deal since 46.5 Lt is less than 55 Lt. However if the company operates at full capacity it should seek the deal that brings more than 65 Lt per item. Only in this case the company can have profit in the long run.

Problem 3 The company is facing two investment alternatives. The payoffs depend on the expected demand. Scenario

Probability of scenario

Alternative A

Alternative B

High demand Low demand

60% 40%

100 -120

50 20

Which alternative is the best for a decision maker with a risk tolerance of 200? The company can buy information which predicts demand. The information is accurate in 80% of instances. Would you pay 30 to get the prediction? Make calculations for risk neutral individual The company should choose alternative B, it brings the value of 37.45 Lt. Value Measure

U-Value

100

0.39346934

-120

-0.8221188

50

0.22119922

20

0.09516258

0.6 high A -17.742 -0.0928

0.170785 37.45506

0.4 low

0.6 high >>> B 37.4551 0.17078

0.4 low

The value of the deal without information for risk neutral company is equal to 38 Lt: Value Measure

0.6 high 100 A 12

0.4 low

12

-120

38 38

0.6 high 50 >>> B 38

38

0.4 low 20

The value of the deal with information which is 80% accurate for risk neutral company is equal to 42.8 Lt Prediction

Decision

Result

Value Measure

0.8 high 100 >>> A 56

56

0.2 low -120

0.56 high 56

0.8 high

56

50 B 44

44

0.2 low 20

0.2 high

42.8 42.8

100 A -76

-76

0.8 low -120

0.44 low 26

0.2 high

26

50 >>> B 26

26

0.8 low 20

The value of information is 42.8-38=4.8 Lt

Problem 4 Perform first and second order dominance tests for the following alternatives: Payoff

Alternative A

Alternative B

-100 -50 0 100

20% 0%

10% 50% 40% 0%

80%

Can we say that alternative A is better regardless of risk tolerance level?

Payoff -100 -50 0 100

Alternative A 20% 0% 80%

Alternative B 10% 50% 40% 0%

CDF A 20% 20% 20% 100%

CDF B 10% 60% 100% 100%

I-Test -10% 40% 80% 0%

II-Test -10% 30% 110% 110%

No. The dominance tests are not passed. Alternative A would be better in most cases, but very risk averse individuals might choose B instead of A.

Problem 5 Explain the optimal bidding strategy in closed second price auction. We should always bet our true willingness to pay for the item.

Problem 6 You are planning the investment in a risky deal. The initial investment value is 100. The deal has 80% chance of failing and 20% chance of succeeding. In case it fails, you lose 50% of your money. In case it succeeds you earn a return of 200%. You have to make the investment today, but the fact whether the deal fails or succeeds will be seen after the research department releases their study (in about a year). If somebody gives you an option today to double your initial investment after the research department releases their study, how much would you be willing to pay for this option? The value of the deal without the option is 0: Value Measure

0.2 Success 200

0

0.8 Failure -50

The value of the deal with the option is 40: Value Measure

>>> Double investment 400 0.2 Success Don't double investment

400

200

Double investment

40

-100 0.8 Failure -50

>>> Don't double investment -50

You should be willing to pay 40 Lt for the option.