Question

In November 2018, Lyft acquired America’s largest bikeshare service Motivate. Assume that next year’s earnings before interest payments for the bikeshare division are estimated at $10 million. Lyft designs the bikes and then contracts to manufacture using third-party suppliers and manufacturers. The company faces risk associated with design or manufacturing defects which could result in a product liability lawsuit. The probability of a lawsuit is .05, and if a lawsuit occurs, it will cost $5 million. From its $10 million in earnings, Lyft expects to pay $6 million on its interest and principal payments, leaving $4 million for shareholders as long as the company does not lose a product liability suit.

1. What is the expected value of loss associated with the product liability lawsuit?

2. Imagine Lyft operates in a perfect market without transaction costs (taxes are among potential transaction costs). Assume that Lyft does not benefit from insurer services. What is the most Lyft’s shareholders want the company to pay for $5 million product liability insurance?

3. Would an insurer be willing to provide the policy for the price Lyft should be willing to pay? Why or why not? Spring 2020Continued on next page

Recognizing that Lyft does not in fact operate in a perfect market, Lyft’s risk manager uses risk management concepts and tools learned in RMI 300 to analyze how risk management adds value to the company. Evaluate each scenario independently (i.e. do not use information in question 4 to answer question 5).

4. Suppose Lyft’s insurer has an in-house legal expert who can reduce the probability of losing a lawsuit from .05 to .025. If the insurer’s premium loadings add an additional amount to the premium equal to 20% of the losses and loss adjustment expense, how much is the premium for $5 million of coverage? Should Lyft be willing to purchase this insurance?

5. Assume Lyft has a $2,000,000 per year purchase contract with Shimano, a supplier of unique bicycle pedals. Shimano faces counterparty risk since it does not have perfect information about Lyft’s ability to uphold the contract. If Lyft purchases product liability insurance, the company can negotiate better contract terms with Shimano and reduce the cost to purchase the pedals by 8%. How much should Lyft be willing to pay for the insurance?

6. If Lyft has not transferred risk associated with a product liability lawsuit, the firm will have to seek external capital to pay for losses (i.e. Lyft has insufficient internal funds to cover the entire cost of the lawsuit). Lyft will take out a loan for the entire $5 million, and legal and administrative costs will equal $100,000.

a. Should Lyft purchase $5 million of insurance coverage for a premium $255,000? Explain.

b. Would the tax status of premiums affect your answer to the previous question (6.a.)? Explain

Answer 1

1.Expected value of loss associated with the product liability lawsuit=

Cost of lawsuit*Probability of it occuring =5 mln.*0.05=

0.25

Mlns.

2. The most Lyft’s shareholders would want the company to pay for $5 million product liability insurance=

the expected value of loss associated with the product liability lawsuit calculated as above, ie. 0.25 mlns.

3. NOT SURE.The insurer will have his own premium ranges commensurate to the risks & probablities , of the said event(losing the lawsuit ) happening.But premiums can be negotiated by Lyft , by explaining & under-playing the loss- probablity.

4,.Premium amt.=Expected Losses+(20% *Loss)=

(Cost of lawsuit*Probability of it occuring )+ (20% * expected loss)

(5*0.025)+(5*0.025*20%)=

0.125+0.025=

0.15

mlns.

YES. As it is less costlier than 0.25 mlns. As in 1 above

5.In case of contract with Shimano, the given Lyft be willing to pay for the insurance

as the cost reduced by 2 mln.*0.08%= 0.16 mln.

Lyft should be willing to pay for the insurance= 0.25 (expected loss as in 1. above)+0.16 (savings in costs) 0.41   mlns.

6.a. In case of Lyft taking out a loan for the entire $5 million, still with the given probability of losing the lawsuit , of 0.05

the costs will be   expected loss, 0.25 mln. + legal & admn. Costs ,0.1 mln.= total = 0.35 mln.

a.So, Lyft should purchase $5 million of insurance coverage for a premium $255,000----

as   0.255 mln. < 0.35 mln. Calculated in the above line.

b. YES. It needs to be seen , if taxes such as Goods & Services Tax , added up to the above premium amount of 0.255 mln., exceeds the 0.35 mln. as calculated for option 6.a.