The differential cost from accepting the offer is $97,500.
To calculate the differential cost from the acceptance of the offer, we need to understand that the differential cost is the difference in the company's costs between two alternatives. In this case, the alternatives are accepting or not accepting the offer to sell additional units at a given price.
From the information provided:
- The offer is to sell 15,000 units at $17.50 per unit.
- The unit manufacturing costs consist of variable costs of $11 and fixed costs of $1.
Since the acceptance of the offer will not affect normal production or domestic sales prices, the fixed costs are likely to remain unchanged (sunk cost) and do not affect the differential cost. Therefore, we only need to consider the variable costs for the additional units.
Here are the steps to calculate the differential cost:
1. Calculate the total variable cost for the additional units if the offer is accepted:
![\[ \text{Total Variable Cost} = \text{Variable Cost per Unit} * \text{Number of Units} \]](https://img.qammunity.org/2024/formulas/business/high-school/pktcmoiz8m5966tmyl0wh9vd0lfhg3m2qo.png)
![\[ \text{Total Variable Cost} = $11 * 15,000 \]](https://img.qammunity.org/2024/formulas/business/high-school/zcgn5dm71fu3y5f0xgsuykypubcd0kjcua.png)
2. Calculate the total revenue from the offer:
![\[ \text{Total Revenue} = \text{Offer Price per Unit} * \text{Number of Units} \]](https://img.qammunity.org/2024/formulas/business/high-school/yaibn4tsa5oivjek3sv6zuginbqzqum5pi.png)
![\[ \text{Total Revenue} = $17.50 * 15,000 \]](https://img.qammunity.org/2024/formulas/business/high-school/w0cuhf4s2c4soffxvsddnbb4wst9ixsp5h.png)
3. The differential cost is the total variable cost subtracted from the total revenue:
![\[ \text{Differential Cost} = \text{Total Revenue} - \text{Total Variable Cost} \]](https://img.qammunity.org/2024/formulas/business/high-school/54a64h6nt0jhnnszhu5kkvoyaafw7ph0zr.png)
Let's perform these calculations.
Here's the step-by-step calculation for the differential cost:
Step 1: Calculate the total variable cost for the additional units.
![\[ \text{Total Variable Cost} = \text{Variable Cost per Unit} * \text{Number of Units} \]](https://img.qammunity.org/2024/formulas/business/high-school/pktcmoiz8m5966tmyl0wh9vd0lfhg3m2qo.png)
![\[ \text{Total Variable Cost} = \$11 * 15,000 \]](https://img.qammunity.org/2024/formulas/business/high-school/xwjgpbecgyjh27c4cg2w6lftyg3lnkb8fl.png)
![\[ \text{Total Variable Cost} = \$165,000 \]](https://img.qammunity.org/2024/formulas/business/high-school/fv655l6xwbmh5a9puhablxojx2kw3weacj.png)
Step 2: Calculate the total revenue from the offer.**
![\[ \text{Total Revenue} = \text{Offer Price per Unit} * \text{Number of Units} \]](https://img.qammunity.org/2024/formulas/business/high-school/yaibn4tsa5oivjek3sv6zuginbqzqum5pi.png)
![\[ \text{Total Revenue} = \$17.50 * 15,000 \]](https://img.qammunity.org/2024/formulas/business/high-school/rl9pdelj3lyksbg0m7d14c0jasascr8ufl.png)
![\[ \text{Total Revenue} = \$262,500 \]](https://img.qammunity.org/2024/formulas/business/high-school/yzhivc9ibqlpykjbvuiftmkvhppd36gfv1.png)
Step 3: Calculate the differential cost, which is the difference between the total revenue and the total variable cost.
![\[ \text{Differential Cost} = \text{Total Revenue} - \text{Total Variable Cost} \]](https://img.qammunity.org/2024/formulas/business/high-school/54a64h6nt0jhnnszhu5kkvoyaafw7ph0zr.png)
![\[ \text{Differential Cost} = \$262,500 - \$165,000 \]](https://img.qammunity.org/2024/formulas/business/high-school/1kxi359pjoykd95muezykpu2zi9onxjqho.png)
![\[ \text{Differential Cost} = \$97,500 \]](https://img.qammunity.org/2024/formulas/business/high-school/f8918su5hg4cubthyoyzchnibkid9i1y97.png)
The differential cost from accepting the offer is $97,500.