Cortez Company is planning to introduce a new product that will sell for $108 per unit. The following manufacturing cost estimates have been made on 20,000 units to be produced the first year: Direct materials $ 800,000 Direct labor 800,000 (= $16 per hour × 50,000 hours) Manufacturing overhead costs have not yet been estimated for the new product, but monthly data on total production and overhead costs for the past 24 months have been analyzed using simple linear regression. The following results were derived from the simple regression and provide the basis for overhead cost estimates for the new product. Simple Regression Analysis Results Dependent variable—Factory overhead costs Independent variable—Direct labor-hours Computed values Intercept $ 120,000 Coefficient on independent variable $ 5.00 Coefficient of correlation .917 R2 .841 Required: a. What percentage of the variation in overhead costs is explained by the independent variable? a. 84.10% b. 92.50% c. 100.90% d. 75.70% e. None of the above b. What is the total overhead cost for an estimated activity level of 70,000 direct labor-hours? a. $470,000 b. $480,000 c. $460,000 d. $490,000 e. None of the above c. How much is the variable manufacturing cost per unit, using the variable overhead estimated by the regression (assuming that direct materials and direct labor are variable costs)? a. $93.00 b. $102.00 c. $112.00 d. $84.00 e. None of the above
Cortez Company is planning to introduce a new product that will sell for $108 per unit. The following manufacturing cost estimates have been made on 20,000 units to be produced the first year:
| Direct materials | $ | 800,000 | |
| Direct labor | 800,000 | (= $16 per hour × 50,000 hours) | |
Manufacturing
| Simple Regression Analysis Results | |||
| Dependent variable— |
|||
| Independent variable—Direct labor-hours | |||
| Computed values | |||
| Intercept | $ | 120,000 | |
| Coefficient on independent variable | $ | 5.00 | |
| Coefficient of correlation | .917 | ||
| R2 | .841 | ||
Required:
a. What percentage of the variation in overhead costs is explained by the independent variable?
b. What is the total overhead cost for an estimated activity level of 70,000 direct labor-hours?
c. How much is the variable manufacturing cost per unit, using the variable overhead estimated by the regression (assuming that direct materials and direct labor are variable costs)?
d. What is the expected contribution margin per unit to be earned during the first year on 20,000 units of the new product? (Assume that all marketing and administrative costs are fixed.)
e. What is the manufacturing cost equation implied by these results?
a. Total cost = $800,000 + ($5.00 × Number of units)
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