Chapter 5, Problem 8P

A manager is trying to decide whether to purchase a certain part or to have it produced internally. Internal production could use either of two processes. One would entail a variable cost of $17 per unit and an annual fixed cost of $200,000; the other would entail a variable cost of $14 per unit and an annual fixed cost of $240,000. Three vendors are willing to provide the part. Vendor A has a price of $20 per unit for any volune up to 30,000 units. Vendor B has a price of $22 per unit for demand of 1,000 units or less, and $18 per unit for larger quantities. Vendor C offers a price of $21 per unit for the first 1,000 units, and $19 per unit for additional units.

Summary Introduction

To determine: The best alternative from a cost standpoint for an annual volume of 10,000 units and 20,000 units.

Introduction: Decision-making is the process that helps to make decision. It is the process of choosing a best alternative by evaluating many alternatives.

Answer to Problem 8P

The best alternative from a cost standpoint for an annual volume of 10,000 and 20,000 units are purchasing parts from Vendor B.

Explanation of Solution

Given information:

A manager has to decide whether to purchase a product or produce it internally. Internal production consists of two processes. Variable cost and fixed cost of the first process is $17 and $200,000 respectively. Variable cost and fixed cost of the second process is $14 and $240,000 respectively.

There are three vendors available to purchase a product. Vendor A has a price of $20 per unit up to 30,000 units. Vendor B has a price of $22 per unit if the demand is 1,000 units or less and $18 for larger volumes. Vendor C has a price of $21 per unit for first 1,000 units and $19 per unit for additional units.

Determine the best alternative from a cost standpoint for an annual volume of 10,000 units:

Calculate the total cost for the first internal process:

It is calculated by adding the fixed cost with the value attained by multiplying the variable cost and the annual volume. Annual volume is given as 10,000 units. Hence, the total cost for the first internal process is $370,000.

$\begin{array}{c}\text{Total cost}=\text{Fixed cost}+\left(\text{Variable cost}\times \text{Annual volume}\right)\\ =\$200,000+\left(\$17\times 10,000\right)\\ =\$200,000+170,000\\ =\$370,000\end{array}$

Calculate the total cost for the second internal process:

It is calculated by adding the fixed cost with the value attained by multiplying the variable cost and the annual volume. Annual volume is given as 10,000 units. Hence, the total cost for the first internal process is $380,000.

$\begin{array}{c}\text{Total cost}=\text{Fixed cost}+\left(\text{Variable cost}\times \text{Annual volume}\right)\\ =\$240,000+\left(\$14\times 10,000\right)\\ =\$240,000+140,000\\ =\$380,000\end{array}$

Calculate the total cost for the Vendor A:

It is calculated by multiplying the price and the annual volume. Hence, the total cost for Vendor A is $200,000.

$\begin{array}{c}\text{Total cost}=\text{Price}\times \text{Annual volume}\\ =\$20\times 10,000\\ =\$200,000\end{array}$

Calculate the total cost for the Vendor B:

It is calculated by multiplying the price and the annual volume. It is given that the price is $22 if the volume is less than 1,000 and $18 if the volume is larger. As the annual volume is more than 1,000, the price is $18. Hence, the total cost for Vendor B is $180,000.

$\begin{array}{c}\text{Total cost}=\text{Price}\times \text{Annual volume}\\ =\$18\times 10,000\\ =\$180,000\end{array}$

Calculate the total cost for the Vendor C:

It is calculated by multiplying the price and the annual volume. It is given that the price is $21 for the volume up to 1,000 and $19 for the additional volume. Thus, price is $21 for the 1,000 units and $19 for additional 9,000 units. Hence, the total cost for Vendor C is $192,000.

$\begin{array}{c}\text{Total cost}=\left(\text{Price}\times \text{Annual volume}\right)+\left(\text{Price}\times \text{Additional volume}\right)\\ =\left(\$21\times 1,000\right)+\left(\$19\times 9,000\right)\\ =\$21,000+\$171,000\\ =\$192,000\end{array}$

At the annual volume of 10,000 units, Vendor B has the lowest total cost of ($180,000). Hence, it should be chosen from a cost standpoint.

Determine the best alternative from a cost standpoint for an annual volume of 20,000 units:

Calculate the total cost for the first internal process:

It is calculated by adding the fixed cost with the value attained by multiplying the variable cost and the annual volume. Annual volume is given as 20,000 units. Hence, the total cost for the first internal process is $540,000.

$\begin{array}{c}\text{Total cost}=\text{Fixed cost}+\left(\text{Variable cost}\times \text{Annual volume}\right)\\ =\$200,000+\left(\$17\times 20,000\right)\\ =\$200,000+340,000\\ =\$540,000\end{array}$

Calculate the total cost for the second internal process:

It is calculated by adding the fixed cost with the value attained by multiplying the variable cost and the annual volume. Annual volume is given as 20,000 units. Hence, the total cost for the first internal process is $520,000.

$\begin{array}{c}\text{Total cost}=\text{Fixed cost}+\left(\text{Variable cost}\times \text{Annual volume}\right)\\ =\$240,000+\left(\$14\times 20,000\right)\\ =\$240,000+280,000\\ =\$520,000\end{array}$

Calculate the total cost for the Vendor A:

It is calculated by multiplying the price and the annual volume. Hence, the total cost for Vendor A is $400,000.

$\begin{array}{c}\text{Total cost}=\text{Price}\times \text{Annual volume}\\ =\$20\times 20,000\\ =\$400,000\end{array}$

Calculate the total cost for the Vendor B:

It is calculated by multiplying the price and the annual volume. It is given that the price is $22 if the volume is less than 1,000 and $18 if the volume is larger. As the annual volume is more than 1,000, the price is $18. Hence, the total cost for Vendor B is $360,000.

$\begin{array}{c}\text{Total cost}=\text{Price}\times \text{Annual volume}\\ =\$18\times 20,000\\ =\$360,000\end{array}$

Calculate the total cost for the Vendor C:

It is calculated by multiplying the price and the annual volume. It is given that the price is $21 for the volume up to 1,000 and $19 for the additional volume. Thus, price is $21 for the 1,000 units and $19 for additional 19,000 units. Hence, the total cost for Vendor C is $382,000.

$\begin{array}{c}\text{Total cost}=\left(\text{Price}\times \text{Annual volume}\right)+\left(\text{Price}\times \text{Additional volume}\right)\\ =\left(\$21\times 1,000\right)+\left(\$19\times 19,000\right)\\ =\$21,000+\$361,000\\ =\$382,000\end{array}$

At the annual volume of 20,000 units, Vendor B has the lowest total cost of ($360,000). Hence, it should be chosen from a cost standpoint.

Summary Introduction

To determine: The range of the best alternative.

Introduction:Decision-making is the process that helps to make decision. It is the process of choosing a best alternative by evaluating many alternatives.

Answer to Problem 8P

The ranges were determined and First internal process and Vendor C are never best.

Explanation of Solution

Given information:

A manager has to decide whether to purchase a product or produce it internally. Internal production consists of two processes. Variable cost and fixed cost of the first process is $17 and $200,000 respectively. Variable cost and fixed cost of the second process is $14 and $240,000 respectively.

There are three vendors available to purchase a product. Vendor A has a price of $20 per unit up to 30,000 units. Vendor B has a price of $22 per unit if the demand is 1,000 units or less and $18 for larger volumes. Vendor C has a price of $21 per unit for first 1,000 units and $19 per unit for additional units.

Cost function for each alternative if the annual volume is 1-1,000 units:

First internal process:

$\$200,000+\$17Q$

Second internal process:

$\$240,000+\$14Q$

Vendor A:

$\$20Q$

Vendor B:

$\$22Q$

Vendor C:

$\$21Q$

When considering the cost functions, Vendor A would exhibit less cost when compare to Vendor B and Vendor C. Vendor A should be preferred over other alternatives. The graph is as follows:

Cost function for each alternative if the annual volume is more than 1,000 units:

First internal process:

$\$200,000+\$17Q$

Second internal process:

$\$240,000+\$14Q$

Vendor A:

$\$20Q$

Vendor B:

$\$18Q$

Vendor C:

$\$21Q+\$19\left(Q-1,000\right)$

When considering the cost functions, Vendor B would dominate Vendor A and Vendor C. Hence, Vendor A and Vendor C should be eliminated. The graph considering two internal processes and Vendor B is as follows:

Determine the value of Q by equaling two cost equations:

Equal the cost function of second internal process and Vendor B to determine the value of Q.

$\begin{array}{c}\$18Q=\$240,000+\$14Q\\ \$18Q-\$14Q=\$240,000\\ \$4Q=\$240,000\end{array}$

$\begin{array}{c}Q=\frac{\$240,000}{\$4}\\ =60,000\text{ units}\end{array}$

Calculate the total cost of first internal process:

Substitute the value Q in the cost equation of first internal process. Hence, the total cost is $1,220,000.

$\begin{array}{c}\text{Total cost}=\$200,000+\$17Q\\ =\$200,000+\left(\$17\times 60,000\right)\\ =\$200,000+1,020,000\\ =1,220,000\end{array}$

Calculate the total cost of second internal process:

Substitute the value Q in the cost equation of second internal process. Hence, the total cost is $1,080,000.

$\begin{array}{c}\text{Total cost}=\$240,000+\$14Q\\ =\$240,000+\left(\$14\times 60,000\right)\\ =\$240,000+840,000\\ =1,080,000\end{array}$

Calculate the total cost of Vendor A:

Substitute the value Q in the cost equation of Vendor A. Hence, the total cost is $1,200,000.

$\begin{array}{c}\text{Total cost}=\$20Q\\ =\$20\times 60,000\\ =1,200,000\end{array}$

Calculate the total cost of Vendor B:

Substitute the value Q in the cost equation of Vendor B. Hence, the total cost is $1,080,000.

$\begin{array}{c}\text{Total cost}=\$18Q\\ =\$18\times 60,000\\ =1,080,000\end{array}$

Calculate the total cost of Vendor C:

Substitute the value Q in the cost equation of Vendor C. Hence, the total cost is $1,142,000.

$\begin{array}{c}\text{Total cost}=\$21Q+\$19\left(Q-1,000\right)\\ =\$21,000+\left(\$19\times 59,000\right)\\ =\$21,000+\$1,121,000\\ =\$1,142,000\end{array}$

Inference:

• Vendor A should be preferred when the purchasing quantity ranges from 1 to 1,000 units.
• Vendor B should be preferred when the purchasing quantity ranges from 1,001 to 59,999 units.
• There would indifferent between Vendor B and second internal process if the quantity is 60,000 units.
• Second internal process should be preferred if the quantity is more than 60,000 units.

First internal process and Vendor C are never best.