Final answer:
To calculate the annual rate of return for the new machine, the initial investment cost and the net annual savings are required. Due to missing data and potential typos, an accurate calculation cannot be completed with the provided information.
Step-by-step explanation:
To calculate the annual rate of return for the new machine, we need to know the initial investment cost, the annual net income or savings that the machine will provide, and the estimated life of the machine. The question does not provide all this information directly. However, if we consider that the annual administrative expenses are lower with the new machine ($87) compared to the old machine ($78,000), there seems to be a significant annual saving. Still, without the actual costs and revenues associated, we cannot calculate an accurate annual rate of return. To perform the calculation, we should take the machine's net annual savings and divide it by the initial cost of the machine. This would provide the annual rate of return as a percentage.
It should be noted that the provided information appears to have some inconsistencies or missing data, such as the seemingly far lower administrative expenses with the new machine which could be a typo. Moreover, details like the cost of the new machine or the expected life of the machine are essential to calculating the annual rate of return correctly.