Chapter 5, Problem 18P

Summary Introduction

To determine: How to select the best decision based on Expected Monetary Value (EMV) criterion.

Introduction: Expected Monetary Value (EMV) is a system for calculating expected returns for certain decision made by a company.

Answer to Problem 18P

The low-technology approach can be selected with a cost of $145,000.

Explanation of Solution

Given information:

$\text{Market}\text{<x-custom-btb-me data-me-id="1449" class="microExplainerHighlight">forecast</x-custom-btb-me>}=\text{200,000}\text{units}$

Strategies used:

Low-tech
Fixed cost	Probability	Variable cost
$45,000.00	0.3	$0.55
	0.4	$0.50
	0.3	$0.45

Sub-contract
Fixed cost	Probability	Variable cost
$65,000.00	0.7	$0.45
	0.2	$0.40
	0.1	$0.35

High-tech
Fixed cost	Probability	Variable cost
$75,000.00	0.9	$0.40
	0.1	$0.35
	0	$0.00

Market forecast		200,000	Total
Low-tech
Fixed cost	Probability	Variable cost
$45,000.00	0.3	$0.55	$155,000.00
	0.4	$0.50	$145,000.00
	0.3	$0.45	$135,000.00
Sub-contract			Total
Fixed cost	Probability	Variable cost
$65,000.00	0.7	$0.45	$155,000.00
	0.2	$0.40	$145,000.00
	0.1	$0.35	$135,000.00
High-tech			Total
Fixed cost	Probability	Variable cost
$75,000.00	0.9	$0.40	$155,000.00
	0.1	$0.35	$145,000.00
	0	$0.00	$0.00

Calculation of total cost:

Low technology:

• Probability 0.3

$\begin{array}{c}\text{Totalcost}=\text{Fixed}\text{cost}+\text{Variable}\text{cost}\\ =\$\text{45,000}+\left(200,000\times \$0.55\right)\\ =\$155,000\end{array}$

With a probability of 0.3, the variable cost is calculated by multiplying the total market forecast of 200,000 with the variable cost $0.55. The product is added with the fixed cost, which is $45,000. The resultant total cost is $155,000.

• Probability 0.4

$\begin{array}{c}\text{Totalcost}=\text{Fixed}\text{cost}+\text{Variable}\text{cost}\\ =\$\text{45,000}+\left(200,000\times \$0.50\right)\\ =\$145,000\end{array}$

With a probability of 0.4, the variable cost is calculated by multiplying the total market forecast of 200,000 with the variable cost $0.50. The product is added with the fixed cost, which is $45,000. The resultant total cost is $145,000.

• Probability 0.3

$\begin{array}{c}\text{Totalcost}=\text{Fixed}\text{cost}+\text{Variable}\text{cost}\\ =\$\text{45,000}+\left(200,000\times \$0.45\right)\\ =\$135,000\end{array}$

With a probability of 0.3, the variable cost is calculated by multiplying the total market forecast of 200,000 with the variable cost $0.45. The product is added with the fixed cost, which is $45,000. The resultant total cost is $135,000.

Sub-contract:

• Probability 0.7

$\begin{array}{c}\text{Totalcost}=\text{Fixed}\text{cost}+\text{Variable}\text{cost}\\ =\$6\text{5,000}+\left(200,000\times \$0.45\right)\\ =\$155,000\end{array}$

With a probability of 0.7, the variable cost is calculated by multiplying the total market forecast of 200,000 with the variable cost $0.45. The product is added with the fixed cost, which is $65,000. The resultant total cost is $155,000.

• Probability 0.2

$\begin{array}{c}\text{Totalcost}=\text{Fixed}\text{cost}+\text{Variable}\text{cost}\\ =\$6\text{5,000}+\left(200,000\times \$0.40\right)\\ =\$145,000\end{array}$

With a probability of 0.2, the variable cost is calculated by multiplying the total market forecast of 200,000 with the variable cost $0.40. The product is added with the fixed cost which is $65,000. The resultant total cost is $145,000.

• Probability 0.1

$\begin{array}{c}\text{Totalcost}=\text{Fixed}\text{cost}+\text{Variable}\text{cost}\\ =\$6\text{5,000}+\left(200,000\times \$0.35\right)\\ =\$135,000\end{array}$

With a probability of 0.1, the variable cost is calculated by multiplying the total market forecast of 200,000 with the variable cost $0.35. The product is added with the fixed cost which is $65,000. The resultant total cost is $135,000.

High-tech:

• Probability 0.9

$\begin{array}{c}\text{Totalcost}=\text{Fixed}\text{cost}+\text{Variable}\text{cost}\\ =\$7\text{5,000}+\left(200,000\times \$0.40\right)\\ =\$155,000\end{array}$

With a probability of 0.9, the variable cost is calculated by multiplying the total market forecast of 200,000 with the variable cost $0.40. The product is added with the fixed cost which is $75,000. The resultant total cost is $155,000.

• Probability 0.1

$\begin{array}{c}\text{Totalcost}=\text{Fixed}\text{cost}+\text{Variable}\text{cost}\\ =\$7\text{5,000}+\left(200,000\times \$0.35\right)\\ =\$145,000\end{array}$

With a probability of 0.1, the variable cost is calculated by multiplying the total market forecast of 200,000 with the variable cost $0.35. The product is added with the fixed cost which is $75,000. The resultant total cost is $145,000.

Hence, from the above calculations, it can be inferred that market forecast for low-technology (which consists of hiring several new junior engineers)at the cost of $145,000 can be selected.