Expected Value Exercise
Tom Wilson is the operations manager for BiCorp, a real
estate investment firm. Tom must decide
if BiCorp is to invest in a strip mall in a northeast metropolitan area.
If the shopping center is highly successful,
after tax profits will be $100,000 per year.
Moderate success would yield an annual profit of $50,000, while the
project will lose $10,000 per year if it is unsuccessful. Past experience suggests that there is a 40%
chance that the project will be highly successful, a 40% chance of moderate
success, and a 20% probability that the project will be unsuccessful.
a. Calculate
the expected value and standard deviation of profit.
b. The
project requires an $800,000 investment.
If BiCorp has an 8% opportunity cost on invested funds of similar riskiness,
should the project be undertaken?
a. EU = (0.4 x 100,000) + (0.4 x 50,000) + (0.2 x -10,000) = 40,000+20,000-2,000 = 58,000
ReplyDeleteDeviation = 0,4[(100,000 - 58,000)square + 0,4[(50,000 - 58,000)square + 0,2[(-10,000 - 58,000)square = 705,600,000 + 25,600,000 + 924,800,000 = 1,656,000,000
Standard Deviation = 40,693.98
b. 0.08 x 800,000 = 64,000
The opportunity cost is larger than the expected value, so the project should not be undertaken
a. Expected Value: $100,000(0.4) + $50,000(0.4)+ (-$10,000)(0.2)
ReplyDelete= $40,000 + $20,000 - $2,000
= $58,000
Standard deviation=
the root of :
=(0.4)($100,000-$58,000)^2 + (0.4)($50,000-$58,000)^2 +(0.2)($-10,000-$58,000)^2
= $1,656,000,000
the root of $1,656,000,000 is 40,693.98
b. Bio-Corpʹs opportunity cost is 8%. Thus, the opportunity cost is : 0.08 × 800,000 = 64,000.
The expected value of the project is smaller than the opportunity cost. In conclusion, Bi-Corp should not undertake the project.
a. E(X) = (Pr highly successful) (X highly successful) + (Pr moderate success) (X moderate success) + (Pr unsuccessful) (X unsuccessful)
ReplyDeleteE(x) = (0.4)(100000) + (0.4)(50000) +(0.2)(10000)
= 40000 + 20.000 + 2000
=62000
to find the standard deviation we take a root from variance
variance= 0.4[(x1)-E(x1) square + 0.4[(50000-62000)]square + 0.2[(10000-)]square
=577.600.000 + 57.600.000 + 540.800.000
=1.176.000.000
root of 1.176.000.000
=34.292,86
b. 800.000 x 8%
= 64.000
with the same standard deviation, they offer bigger opportunity cost. So we should not take the project because we can get more from the opportunity cost which is bigger that the expected value of the project itself
a) EU(X) = Pr (highly successful) (x highly successful) + Pr(moderate success) (x moderate success) + Pr (unsuccessful) (x unsuccessful)
ReplyDeleteEU = (0.4 x 100,000) + (0.4 x 50,000) + (0.2 x -10,000) = 40,000+20,000-2,000 = 58,000
standard Deviation = 0,4[(100,000 - 58,000)2 + 0,4[(50,000 - 58,000)2+ 0,2[(-10,000 - 58,000)2 = 705,600,000 + 25,600,000 + 924,800,000 = 1,656,000,000
Standard Deviation = 40,693.98----> rooted from 1,656,000,000
b)0.8x800,000=64,000
no, the project shouldnt be undertaken, if we see EU is smaller than opportunity cost which is faced by bicorp.
Known:
ReplyDeleteThese are the prices after tax :
High Success = $100,000 per year
Moderate Success = $50,000 per year
Unsuccessfull = lost $10,000 per year
With the Probability of:
High Success = 40 % = 0.4
Moderate Success = 40 % = 0.4
Unsuccessfull = 20 % = 0.2
Solutions:
a. Expected Value = (High Income) (High Income Probability) + (Moderate Income) (Moderate Income Probability) + ( Least Income ) (Least Income Probability)
Expected Value = ($100,000 x 0.4 ) + ($50,000 x 0.4 ) + (- $10,000 x 0.2)
= $ 40,000 + $ 20,000 + ( - $ 2,000)
= $ 58,000
Since Standard Deviation is root Deviation, first we have to find the Deviation.
High Success Deviation = $ 100,000 - $ 58,000 = $ 42,000
Moderate Success Deviation = $ 50,000 - $ 58,000 = - $ 8,000
Unsuccess Deviation = - $ 10,000 - $ 58,000 = - $ 68,000
Standard Deviation of Profit ={[(High Success Deviation )^2 ](Probability High Success Deviation)} +{[ (Moderate Success Deviation)^2] (Probability Moderate Success Deviation)} + {[(Unsuccess Deviation)^2 ](Probability Unsuccess Deviation)}
Standard Deviation of Profit
={[ ( $ 42,000 )^2] (0.4)} +{[ ( - $ 8,000)^2] (0.4)} +{[ (-68,000)^2] (0.2)}^1/2
= { $ 1,764,000,000 (0,4)} + { $ 64,000,000 (0.4)} + { $ 4,624,000,000 (0.2)}^1/2
= {$ 705,600,000 + $ 25,600,000 + $ 924,800,000}^1/2
= $ 1,656,000,000^1/2
= $ 40,693.97989875
b. If the project requires:
Investment $ 800,000
And if BiCorp has 8%(0.08) opportunity
Should the Project undertaken?
First, we have to compare the opportunity cost with the expected value. If the Opportunity Cost is smaller than the Expected Value, the project should be undertaken. But if If the Opportunity Cost is greater than the Expected Value, the project should NOT be undertaken.
Opportunity Cost = (probability of investment) (investment)
= 0.008 * $ 800,000
= 64,000
So the conclusion is the project should NOT be undertaken, because the Expected Value is smaller than the Opportunity Cost.
A.] E(V)= (P1 x X1) + ... + (Pn x Xn)
ReplyDelete= (P1 x X1) + (P2 x X2) + (P3 x X3)
= (0.4 x 100,000)+ 0.4 x 50,000)+(0.2 x -10,000)
= $ 58
SD = P1 (X1- E(v)) + ... + Pn (Xn-E(v))
=(0.4) (100,000-58,000)x2 +(0.4)(50,000-58,000)x2 + (0.2)(-10,000-58,000)x2
= $ 1,656
b.] 8% x 800 = 64
no, the project should not be undertaken by bicorp,because the opportunity cost is bogger than the expected value which smaller.
As we know the successful chance is 40 percent and the profit is 100,000 dollar, the chance of moderate successful is 40 percent too and the profit is 50,000 dollar, the probability of unsuccessful is 20 percent and the loss is 10.000 so expected value= (0.4x100,000)+(0.4x50,000)+(0,2x-10000)=40,000+20,000-2,000=58,000
ReplyDeleteStandard deviation is
a. Expected Value = (0.4 x 100,000) + (0.4 x 50,000) + (0.2 x -10,000) = 40,000+20,000-2,000 = 58,000
ReplyDeleteStandard Deviation = 0,4[(100,000 - 58,000)square + 0,4[(50,000 - 58,000)square + 0,2[(-10,000 - 58,000)square = 705,600,000 + 25,600,000 + 924,800,000 = 1,656,000,000
Standard Deviation = 40,693.98 (root of 1,656,00,000)
b. 0.08 x 800,000 = 64,000
Opportunity cost is higher, therefore don't take the project
ANSWER:
ReplyDeletea. Expected Value = 58,000
Standard Deviation = 40,693.98
b. Bio-Corp's opportunity cost is 8% of 800,000 or 0.08 × 800,000 = 64,000.
The expected value of the project is less than the opportunity cost.
Bi-Corp should not undertake the project.