Question

Risk and probability Micro-Pub, Inc., is considering the purchase of one of two microfilm cameras, R and S. Both should provide benefits over a 10-year period, and each requires an initial investment of $5,000. Management has constructed the following table of estimates of rates of return and probabilities for pessimistic, most likely, and optimistic results: a. Determine the range for the rate of return for each of the two cameras. b. Determine the value of the expected return for each camera. c. Which camera purchase is riskier? Why? a. The range for the rate of return for camera R is 17 %. (Round to the nearest whole number.) Data Table The range for the rate of return for camera S is 11 %. (Round to the nearest whole number.) b. The value of the expected return for camera R is%. (Round to two decimal places.) (Click on the icon located on the top-right corner of the data table below in order to copy its contents into a spreadsheet.) Camera R Probability Amount $5,000 Camera S Probability 1.00 Amount Initial investment Annual rate of return 1.00 $5,000 Pessimistic 18% 29% 35% 0.21 0.48 0.31 20% 28% 31% 0.21 0.57 0.22 Most likely Optimistic Print Done

Answer 1

Calculation of asset A are below:

State	Probability	Asset A	Probability weighted	(Xa-Averatge Xa)2
Pessimistic	0.21	18.00%	0.21 x 18 = 3.78%	0.21(18-28.55)^2 = 0.0023373525
Most Likely	0.48	29.00%	0.48 x 29 = 13.92%	0.48(29-28.55)^2 = 0.0000097200
Optimistic	0.31	35.00%	0.31 x 35 = 10.85%	0.31(35-28.55)^2 = 0.0012896775
Expected return			3.78+13.92+10.85 = 28.55%
Variance = sum of (Xa-Averatge Xa)2				0.3636750%
Standard deviation = square root of variance				6.03055%

Calculation of asset B are below:

State	Probability	Asset B	Probability weighted	(Xb-Averatge Xb)2
Pessimistic	0.21	20.00%	0.21 x 20 = 4.20%	0.21(20-27.25)^2 = 0.0011038125
Most Likely	0.57	28.00%	0.57 x 28 = 13.44%	0.57(28-27.25)^2 = 0.0000270000
Optimistic	0.22	31.00%	0.22 x 31 = 9.61%	0.22(31-27.25)^2 = 0.0004359375
Expected return			4.20+13.44+9.61 = 27.25%
Variance = sum of (Xb-Averatge Xb)2				0.1566750%
Standard deviation = square root of variance				3.95822%

So expected return of A is 28.55% and B is 27.25% and as the standard deviation of Asset A is higher, it is riskier