1. Suppose New Ghana Brewing Company’s property losses have the following distribution.
Loss |
Probability |
$6,500,000 |
0.01 |
$4,000,000 |
0.01 |
$2,000,000 |
0.04 |
$700,000 |
0.08 |
0 |
0.86 |
a. What is the expected value of New Ghana’s property losses (aka, the actuarially fair value of insurance)?
b. What is the standard deviation of New Ghana’s expected property losses?
c. Suppose PC Inc, New Ghana’s insurance carrier, charges a 40% load when determining its property and casualty insurance premiums. What would they charge New Ghana for property insurance, i.e., what will the premium be?
d. Assume that New Ghana’s property losses are normally distributed (they aren’t, of course) with mean and standard deviation equal to the expected value and standard deviation you calculated in a. and b. What is New Ghana’s probable maximum loss (PML) at the 95% level?[1] (critical value = 1.645)
e. Suppose New Ghana’s CRO makes this assumption. Would the estimated PML underestimate or overestimate New Belgian’s true PML? Why?
2. Bird Song Industries makes a bird seed that sets native song birds singing all day long. Its product has been discovered by the back-to-nature crowd around the world. As a result, Bird Song’s executives expect free cash flow (FCF) to grow rapidly over the next 4 years. The forecast FCFs are 20, 40, 75 and 90 in years 2016 – 2019, respectively. However, by 2020 Bird Song expects growth to slow to 3% per year in perpetuity. Bird Song’s weighted average cost-of-capital (WACC) is 9%. What is Bird Song’s fundamental value?
3. Briefly explain the relationship between capital structure, insurance and strategic risk management. When do insurance and risk management add to firm value? When do they not add to firm value?
[1] There is a fair amount of confusion (including mine) about MPL (maximum possible loss), MPL (maximum probably loss) and PML (probable maximum loss. According to IRMI.org, MPL (maximum possible loss) is the most that could be lost; MPL (maximum probably loss) and PML are one in the same and represent the greatest the loss will be some percent (e.g., 95%) of the time. To confuse matters still further, sometimes the term ‘Maximum Probable Loss’ is used. This term is just another way of saying ‘Probable Maximum Loss.’
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