6-20. A private equity firm is evaluating two alternative investments. Although

Question

6-20. A private equity firm is evaluating two alternative investments. Although the returns are random, each investment's return can be described using a normal distribution. The first investment has a mean return of $2,000,000 with a standard deviation of $125,000. The second investment has a mean return of $2,275,000 with a standard deviation of $500,000 a. How likely is it that the first investment will return $1,900,000 or less? return $1,900,000 or less? return being less than $1,750,000, which investment b. How likely is it that the second investment will c. If the firm would like to limit the probability of a should it make?

Explanation / Answer

(a) Pr(first investmennt < $1,900,000 ; $2,000,000 ; $125,000)

Z = (1900000 - 2000000)/ 125000 = -0.8

Pr(first investmennt < $1,900,000 ; $2,000,000 ; $125,000) = (-0.8) = 0.2118

(b)

Pr(Second investmennt < $1,900,000 ; $2,275,000 ; $500,000)

Z = (1900000 - 2275000)/ 500000 = -0.75

Pr(first investmennt < $1,900,000 ; $2,000,000 ; $125,000) = (-0.75) = 0.2266

(c) For firm 1 :

Pr(first investmennt < $1,750,000 ; $2,000,000 ; $125,000)

Z = (1750000 - 2000000)/ 125000 = -2

Pr(first investmennt < $1,750,000 ; $2,000,000 ; $125,000) = (-2) = 0.0228

For firm 2:

Pr(first investmennt < $1,750,000 ; $2,275,000 ; $500,000)

Z = (1750000 - 2275000)/ 500000 = -1.05

Pr(first investmennt < $1,750,000 ; $2,000,000 ; $125,000) = (-1.05) = 0.1469

so firm 1 has less probability of return being less than $1750000 then firm 2, so we firm 1 must be choosen.

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