7.3 Expected returns: You have chosen biology as your college major because you

Question

7.3 Expected returns: You have chosen biology as your college major because you would like to be a medical doctor. However, you find that the probability of being accepted into medical school is about 10 percent. If you are accepted into medical school, then your starting salary when you graduate will be $300,000 per year. However, if you are not accepted, then you would choose to work in a zoo, where you will earn $40,000 per year. Without considering the additional educational years or the time value of money, what is your expected starting salary as well as the standard deviation of that starting salary?

Explanation / Answer

1) Expected returns: Probability of being accepted into medical school is P(A) = 0.10 (10 percent) If you are accepted into medical school, Salary S(A) = $300,000 per year. However, if you are not accepted, P(Not A) = 1-0.10 , let us write that P(R) = 0.90, and S(R) = $40,000 per year. (1a) Expectation of salary based on these probabilities is: E(Salary) = P(A).S(A) + P(R).S(R) E(Salary) = 0.10 x 300,000 + 0.90 x 40,000 E(Salary) = 30,000 + 36,000 E(Salary) = $66,000 (1b) Standard deviation: This is “s” the square root of the variance “V” which is the sum of the squares of the expected distance to the expected return (!!!) OR V = expected [return – expected return]^2 V = 0.10 x (300000 – 66000)^2 + 0.90 x (40000 – 66000)^2 V = 0.10 x 54756x10^6 + 0.90 x 676x10^6 V = 54756x10^5 + 6084x10^5 V = 6084 x 10^6 or 6084000000 And s = 78000

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