3. (7 points- The value of risk management on perfect financial markets) Steel I

Question

3. (7 points- The value of risk management on perfect financial markets) Steel Inc. (SI) has the following end-of-year cash flows per share: $200 with a probability of 0.8 when there is no severe workplace accident, $150 with a probability of 0.2 in case of a severe workplace accident. The risk-free rate is 3%, the expected return of the market is 5% and SI's beta factor is given by 0.8. a. Find the expected return on SI stock. (2 points) b. Find the value of SI stock. If you buy SlI stock at this price, what are the two possible end-of-year returns? (3 points) Determine the value of SI stock if the company buys workers' comp insurance that fully reimburses losses. Distinguish in your answer between a scenario where the premium is actuarially fair and a scenario with a 15% loading. (2 points) c.

Explanation / Answer

a. Expected return on Si stock as per CAPM = Rf + beta*(Rm - Rf) = 3% + 0.8(5%-3%) = 4.6%

b. Value of SI stock = Expected year end cash flow/ expected return

Expected year end cash flow = 200*0.8 + 150*0.2 = 190

Value of SI stock = 190/0.046 = $4,130.43

The two possible year end values are 200/0.046 or 150/0.046 which result in 4,347.83 or $3,260.87

Possible returns are (4347.83-4130.43)/4130.43 or (3260.87-4130.43)/4230.43 which would result in 5.12% or -21.05%

Two possible end of year returns = +5.12% or -21.05%

c. Since there are no losses, the value of SI stock would be = 200/0.046 = 4,347.83

Now, we consider the loading of 15%

Additonal cost = 15% *200 = $30

so, Year end cash flows = $200-$30 = $170 (There is no possibility of loss)

Value of SI stock with 15% loading = 170/0.046 = $3,695.65

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