Q6BP Possible outcomes for three inve... [FREE SOLUTION]

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Foundations Of Financial Management

Stanley B. Block, Geoffrey A. Hirt, Bartley Danielsen

Business Studies

16th Edition 路 768 pages

ISBN: 9781259277160

Chapter 4: Q6BP (page 439)

Possible outcomes for three investment alternatives and their probabilities of occurrence are given next.
Alternative 1 Alternative 2 Alternative 3
Outcomes Probability Outcomes Probability Outcomes Probability
Failure ................... 50 0.2 90 0.3 95 0.2
Acceptable ........... 90 0.4 190 0.3 215 0.6
Successful ............ 135 0.4 225 0.4 380 0.2
Rank the three alternatives in terms of risk from lowest to highest (compute the coefficient of variation).

Short Answer

Expert verified

Table showing the Ranks
	Coefficient of variation	Rank
Alternative 1	0.3209	Rank 1
Alternative 2	0.5687	Rank 2
Alternative 3	0.9954	Rank 3

Step by step solution

Compute expected value

$\begin{matrix} Expected value Alternative 1 = Respective sales 脳 Respective probability \\ = (50 脳 0.20) + (90 脳 0.40) + (135 脳 0.40) \\ = 10 + 36 + 54 \\ = 100 units \end{matrix}$

$\begin{matrix} Expected value Alternative 2 = Respective sales 脳 Respective probability \\ = (90 脳 0.30) + (190 脳 0.30) + (225 脳 0.40) \\ = 27 + 57 + 90 \\ = 174 units \end{matrix}$

$\begin{matrix} Expected value Alternative 3 = Respective sales 脳 Respective probability \\ = (95 脳 0.20) + (215 脳 0.60) + (380 脳 0.20) \\ = 19 + 129 + 76 \\ = 224 units \end{matrix}$

Computation of total probability

Alternative 1

Probability	Sales	Probability*(sales-Expected sales)²	Total
0.20	50	0.20*(50-100)²	500
0.40	90	0.40*(90-100)²	40
0.40	135	0.40*(135-100)²	490
			1030

Alternative 2

Probability	Sales	Probability*(sales-Expected sales)²	Total
0.30	90	0.30*(90-174)²	2116.8
0.30	190	0.30*(190-174)²	76.8
0.40	225	0.40*(225-174)²	1040.4
			3234

Alternative 3

Probability	Sales	Probability*(sales-Expected sales)²	Total
0.20	95	0.20*(95-224)²	4992.3
0.60	215	0.60*(215-224)²	48.6
0.20	380	0.20*(380-224)²	4867.2
			9908.1

Computation of Standard deviation ( approx )

$\begin{matrix} Standard deviation Alternative 1 = \sqrt{\begin{array}{l} Probability 脳 {(sales - Expectedsales)}^{2} \end{array}} \\ = \sqrt{1030} \\ = 32.09 units \end{matrix}$

$\begin{matrix} Standard deviation Alternative 2 = \sqrt{\begin{array}{l} Probability 脳 {(sales - Expected sales)}^{2} \end{array}} \\ = \sqrt{3234} \\ = 56.87 units \end{matrix}$

$\begin{matrix} Standard deviation Alternative 3 = \sqrt{\begin{array}{l} Probability 脳 {(sales - Expected sales)}^{2} \end{array}} \\ = \sqrt{9908.1} \\ = 99.54 units \end{matrix}$

Computation of co-efficient of variation ( approx.)

$\begin{matrix} Coefficient of variation Alternative 1 = \frac{Standard deviation}{Expected sales} \\ = \frac{32.09}{100} \\ = 0.3209 \end{matrix}$

$\begin{matrix} Coefficient of variation Alternative 2 = \frac{Standard deviation}{Expected sales} \\ = \frac{56.87}{100} \\ = 0.5687 \end{matrix}$

$\begin{matrix} Coefficient of variation Alternative 3 = \frac{Standard deviation}{Expected sales} \\ = \frac{99.54}{100} \\ = 0.9954 \end{matrix}$

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Short Answer

Step by step solution

Compute expected value

Computation of total probability

Computation of Standard deviation ( approx )

Computation of co-efficient of variation ( approx.)

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