Question

1. What is the approximate variance of returns if over the past 3 years an investment returned 8.0%, -12.0%, and 15.0%?
A. 31
B. 131
C. 182
D. 961

2. What is the approximate standard deviation of returns if over the past 4 years an investment returned 8.0%, -12.0%, -12.0%, and 15.0%?
A. 9.26%
B. 10.26%
C. 11.26%
D. 12.01%

3.  A proposed capital project will cost $20 million and generate $4 million annually in after-tax cash flows for 10 years. The cost of capital for a project of this risk level is 12.2%. Should the project be accepted? Why or why not?

Answer 1

!) Mean = ( 8-12+15)/3 = 11/3 %

Variance =1/3* [ (8-11/3)^2 + (-12-11/3)^2 + (15-11/3)^2 ] = 392.667/3 = 130.88

ans is 131

2) mean = (8-12-12+15)/4 = -1/4 %

Variance = 1/4* [ (8+1/4)^2 + (-12+1/4)^2 + (-12+1/4)^2 + (15+1/4)^2) = 144.1875

Standard deviation = sqrt(variance) = 12 %

3) NPV = -20 + 4/1.122 + 4/1.22^2 + ......+4/1.122^10

NPV = $2.417 million

NPV > 0

so accept the project

Answer 2

1.mean = (8.0% -12.0%+ 15.0%)/3 = 3.67%

approximate variance of returns = ((8.0%-3.67%)^2 +(-12.0%-3.67%)^2+ (15.0%-3.67%)^2)/3= 131

B. 131

2.Mean =( 8.0% -12.0% -12.0%+ 15.0%)/4 =-0.25%

standard deviation = ( (8.0%+0.25%)^2+( -12.0%+0.25%)^2+( -12.0%+0.25%)^2+ (15.0%+0.25%)^2)/4 = 12.01%

D. 12.01%

3. NPV = -20 + 4/1.122 +4/1.122^2 + 4/1.122^3.....4/1.122^10 = $2.42

the project shuld be accepted as it has positive NPV