Chapter 13, Problem 25BEA

During the week of May 10, Hyrum Manufacturing produced and shipped 16,000 units of its aluminum wheels: 4,000 units of Model A and 12,000 units of Model B. The cycle time for Model A is 1.09 hours and for Model B is 0.47 hour. The following costs and production hours were incurred:

Required:

1. 1. Assume that the value-stream costs and total units shipped apply only to one model (a single-product value stream). Calculate the unit cost, and comment on its accuracy.
2. 2. Assume that Model A is responsible for 40% of the materials cost. Calculate the unit cost for Models A and B, and comment on its accuracy. Explain the rationale for using units shipped instead of units produced in the calculation.
3. 3. Calculate the unit cost for the two models, using DBC. Explain when and why this cost is more accurate than the unit cost calculated in Requirement 2.

To determine

Compute unit cost assuming that the value-stream cost and total units shipped apply to a single model.

Answer to Problem 25BEA

Unit cost is $56.25

Explanation of Solution

Value Stream:

Value stream consists of the processes through which a product goes; that is from procurement to delivery. In value stream, all processes are covered whether or not they add value to the product.

Computation of unit cost:

Unit cost can be computed by using formula:

$\text{Unit}\text{cost}=\frac{\text{Total}\text{value}\text{stream}\text{cost}}{\text{Total}\text{units}}$

Substitute $900,000 for total value stream cost and 16,000 for total units in the above formula.

$\begin{array}{c}\text{Unit}\text{cost}=\frac{\$900,000}{16,000}\\ =\$56.25\end{array}$

In case, there is only one product and all the costs are directly attributable to that product, then unit cost computed would provide accurate result.

Therefore, assuming that the value-stream cost and total units shipped apply to a single model, unit cost is $56.25

To determine

Compute unit cost of both the models in case, Model A is responsible for 40% of the material cost. Comment on accuracy of the results and provide the rationale behind using units shipped instead of units produced.

Answer to Problem 25BEA

Unit cost of model A and B is $72.825 and $50.725 respectively.

Explanation of Solution

Computation of unit cost:

Particulars	Model A ($)	Model B ($)
Units shipped	4,000	12,000
Material cost	$\left(442,000\times 40\%\right)$ 176,800	$\left(442,000\times 60\%\right)$ 265,200
Material cost per unit (A)	$\left(\frac{176,800}{4,000}\right)$ 44.20	$\left(\frac{265,200}{12,000}\right)$ 22.10
Conversion cost per unit1 (B)	28.625	28.625
Unit cost $\left(\text{A}+\text{B}\right)$	72.825	50.725

Table (1)

Units shipped are used to compute per unit cost rather than units produced. This is done to encourage the reduction of goods produced, in excess of units to be shipped.

This would happen because value stream cost includes goods that are produced and unit cost would increase if goods shipped are lesser than goods produced.

Therefore, unit cost of model A and B is $72.825 and $50.725 respectively.

Working Notes:

1. Computation of conversion cost per unit:

$\begin{array}{c}\text{Conversion}\text{cost}\text{per}\text{unit}=\frac{\text{Total}\text{cost}-\text{Material}\text{cost}}{\text{Units}\text{shipped}}\\ =\frac{\$900,000-\$442,000}{16,000}\\ =\frac{\$458,000}{16,000}\\ =\$28.625\end{array}$

To determine

Compute unit cost for each model using duration based costing.

Answer to Problem 25BEA

Unit cost of model A and B would be $94.122 and $43.626 respectively.

Explanation of Solution

Duration Based Costing:

In duration based costing, value stream conversion cost is distributed amongst products in proportion of the cycle time.

Computation of unit cost:

Particulars	Model A ($)	Model B ($)
Units shipped	4,000	12,000
Material cost	$\left(442,000\times 40\%\right)$ 176,800	$\left(442,000\times 60\%\right)$ 265,200
Material cost per unit (A)	$\left(\frac{176,800}{4,000}\right)$ 44.20	$\left(\frac{265,200}{12,000}\right)$ 22.10
Conversion cost rate per hour1	45.8	45.8
Cycle time per unit (hours)	1.09	0.47
Conversion cost per unit (B)	$\left(45.8\times 1.09\right)$ 49.922	$\left(45.8\times 0.47\right)$ 21.526
Unit cost $\left(\text{A}+\text{B}\right)$	94.122	43.626

Table (2)

Duration bond costing would provide better results when products are not homogeneous and time taken by each type of product varies.

Therefore, unit cost of model A and B would be $94.122 and $43.626 respectively.

Working Notes:

1. Computation of conversion cost rate:

$\begin{array}{c}\text{Conversion}\text{cost}\text{rate}=\frac{\text{Total}\text{cost}-\text{Material}\text{cost}}{\text{Total}\text{production}\text{hours}}\\ =\frac{\$900,000-\$442,000}{10,000}\\ =\frac{\$458,000}{10,000}\\ =\$45.8\end{array}$