Final answer:
The director should make a capital budget since this is used for long-term investments like purchasing playground equipment for an existing child care center.
Step-by-step explanation:
A director looking to purchase new playground equipment for an existing child care center should prepare a capital budget. This type of budget is designed for long-term investments or for the purchase of fixed assets that will be used over an extended period of time. Playground equipment is a substantial, long-term asset that falls under capital expenditures, which are typically for the acquisition, improvement, or maintenance of long-term assets such as property, buildings, or equipment.
An operational budget would cover the day-to-day running costs of the child care center, while an emergency budget is reserved for unforeseen circumstances, and a contingency budget is allocated for unexpected events or costs during a project. Therefore, the correct answer here is b. Capital budget.