Question 1. A firm used to have productive assets that generated an income stream with a present value of 3,000. However, fire occurred and most of those assets were destroyed. The remaining, undamaged assets produce an income stream that has a present value of only 1,000. Therefore, the fire has led to reduction in the value of the firm from 3,000 to 1,000. The firm could undertake a reconstruction of the damaged asset for a capital cost of 1,500, which would restore the income stream to its pre-loss level (PV = 3000). The firm has existing debt of 2,000 which is a senior claim.
a. Would the shareholders choose to reinvest by issuing new equity to pay for the loss or are they better off walking away from the firm?
b. Would the decision made by the shareholders be in the best interest of the bondholders?
In answering this question remember that the shareholders have limited liability and therefore the share value cannot be negative.
Question 2. Some people are good drives and others are bad drives. The former have a 10% chance of crashing their cars and the later have a 30% chance. All have a total wealth of 400 but this will fall to 100 if they crash their cars. In other words, each will lose 300 of wealth if crash. You’re an insurance company who wishes to offer a pair of policies to all drivers. Each policy is designed to break even (zero profit) given the people that choose to buy that policy. The first policy has a premium of 90 and covers all losses (i.e. will pay 300 in the event of a crash). The second policy has a premium of 5 and will pay 50 in the event of a crash. Each person has a utility function of Utility = (Wealth)0.5
a. Who will buy which policy?
b. Will the insurance company make a profit, break even or lose money?
Each person has a utility function as follows:
Utility = (wealth)^0.5