Question

Hooper Chemical Company, a major chemical firm that uses such raw materials as carbon and petroleum as part of its production process, is examining a plastics firm to add to its operations. Before the acquisition, the normal expected outcomes for the firm were as follows:
  

	Outcomes ($ millions)			Probability
Recession	$	40			0.2
Normal economy		60			0.1
Strong economy		80			0.7

Compute the expected value, standard deviation, and coefficient of variation prior to the acquisition. (Do not round intermediate calculations. Enter your dollar answers in millions rounded to 2 decimal places (e.g., $12,300,000 should be entered as "12.30"). Round the coefficient of variation to 3 decimal places.)
  Expected value=

Standard deviation =

Coefficient of variance=

Answer 1

Expected outcome E(r) =  $\sum_{}^{}$ p(s)*r(s),

where p(s) is the probability of each scenario,

and r(s) is the expected outcome of each scenario.

Variance of portfolio $\sigma$ ²  = $\sum_{}^{}$ p(s)*[r(s) - E(r)]²

where [r(s) - E(r)]² is the squared deviation from the expected outcome.

Standard deviation =  $\sqrt{}$variance

Expected Value = $70,000,000

Standard deviation = $36,271,201

Coefficient of variance =  Standard deviation / Expected Value

Coefficient of variance = $36,271,201 / $70,000,000 = 0.5182, or 51.82%

2 A B C D 1 Status 2 Recession 3 Normal 4 Strong 5 Expected Value 6 Variance 7 Standard deviation Outcome r(s) $40,000,000 $60,000,000 $80,000,000 Probability (s) 0.2 0.1 0.7 p(s) *r(s) $8,000,000 $6,000,000 $56,000,000 $ 70,000,000 Squared deviation from E(r.) $3,844,000,000,000,000 $4,096,000,000,000,000 $196,000,000,000,000 $8,136,000,000,000,000 $ 1,315,600,000,000,000 36,271,201

А в с 1 Status 2 Recession 3 Normal 4 Strong 5 Expected Value 6 Variance 7 Standard deviation Outcome r(s) Probability p(s) p(s) *r(s) Squared deviation from E(r.) 40000000 =B2*C2 =(D2-$D$5)^2 60000000 0.1 =B3*C3 =(D3-$D$5)^2 80000000 0.7 =B4*C4 =(D4-$D$5)^2 =SUM(D2:04) =SUM(E2:E4) =SUMPRODUCT(C2:04,E2:E4)