ANALYSIS

Include your Expected Value Analysis and Decision Tree Analysis that was completed in the M$4\mathrm{.}2\mathrm{.}4$ Practice Scenario: $$Expected Value and Decision Tree.$$

Expected Value $($EV$)$ analysis helps in evaluating the potential outcomes of different decisions by considering the probabilities and payoffs of each outcome. For the Smart Farm Pro System, we can analyze different pricing strategies and market scenarios to determine the expected value for each strategy.

Scenario Assumptions:

High Market Acceptance: $40\%$ probability

Revenue: $$25$ millionCosts: $$10$ millionProfit: $$15$ million

Moderate Market Acceptance: $50\%$ probability

Revenue: $$15$ millionCosts: $$8$ millionProfit: $$7$ million

Low Market Acceptance: $10\%$ probability

Revenue: $$5$ millionCosts: $$6$ millionProfit: $-$$$1$ million $($Loss$)$

Expected Value Calculation: $[\backslash$text$\{$EV$\}=(\backslash$text$\{$Probability of High Acceptance$\}\backslash$times $\backslash$text$\{$Profit in High Acceptance$\})+(\backslash$text$\{$Probability of Moderate Acceptance$\}\backslash$times $\backslash$text$\{$Profit in Moderate Acceptance$\})+(\backslash$text$\{$Probability of Low Acceptance$\}\backslash$times $\backslash$text$\{$Profit$/$Loss in Low Acceptance$\})]$

$[\backslash$text$\{$EV$\}=(0\mathrm{.}40\backslash$times $15$M$)+(0\mathrm{.}50\backslash$times $7$M$)+(0\mathrm{.}10\backslash$times $-1$M$)]$

$[\backslash$text$\{$EV$\}=6$M $+3\mathrm{.}5$M $-0\mathrm{.}1$M $]$

$[\backslash$text$\{$EV$\}=9\mathrm{.}4$M $]$

The expected value of the pricing strategy for the Smart Farm Pro System is $$9\mathrm{.}4$ million.

Decision Tree Analysis

A decision tree helps visualize the different decisions and their potential outcomes, incorporating probabilities and payoffs. Below is a simplified decision tree for the Smart Farm Pro System pricing strategy:

Decision Node: Pricing Strategy

Option $1$: Base Price $$15,000$ with Subscription TiersOption $2$: Lower Base Price $$12,000($Assume lower costs attract more customers but reduce per$-$unit profit$)$

Option $1$: Base Price $$15,000$ with Subscription Tiers

High Market Acceptance $(40\%)$

Revenue: $$25$ millionCosts: $$10$ millionProfit: $$15$ million

Moderate Market Acceptance $(50\%)$

Revenue: $$15$ millionCosts: $$8$ millionProfit: $$7$ million

Low Market Acceptance $(10\%)$

Revenue: $$5$ millionCosts: $$6$ millionProfit: $-$$$1$ million

Expected Value for Option $1$: $$9\mathrm{.}4$ million $($as calculated above$)$

Option $2$: Lower Base Price $$12,000$ with Subscription Tiers

High Market Acceptance $(50\%)$

Revenue: $$22$ millionCosts: $$9$ millionProfit: $$13$ million

Moderate Market Acceptance $(40\%)$

Revenue: $$13$ millionCosts: $$7$ millionProfit: $$6$ million

Low Market Acceptance $(10\%)$

Revenue: $$4$ millionCosts: $$5$ millionProfit: $-$$$1$ million

Expected Value for Option $2$:

$[\backslash$text$\{$EV$\}=(0\mathrm{.}50\backslash$times $13$M$)+(0\mathrm{.}40\backslash$times $6$M$)+(0\mathrm{.}10\backslash$times $-1$M$)]$

$[\backslash$text$\{$EV$\}=6\mathrm{.}5$M $+2\mathrm{.}4$M $-0\mathrm{.}1$M $]$

$[\backslash$text$\{$EV$\}=8\mathrm{.}8$M $]$

Decision Tree Visualization

Pricing Strategy $/\backslash$ Base Price $$15,000$ Lower Base Price $$12,000/|\backslash /|\backslash$ High Mod Low High Mod Low $(40\%)(50\%)(10\%)(50\%)(40\%)(10\%)$ Profit: $$15$M $$7$M $-$$$1$M $$13$M $$6$M $-$$$1$M