P8.10 Cost-Volume-Profit Analysis. Untouchable Package Service (UPS) offers overnight pack- age delivery to Canadian business customers. UPS has recently decided to expand its facilities to better satisfy current and projected demand. Current volume totals 2 million packages per week at a price of $12 each, and average variable costs are constant at all output levels. Fixed
costs are $3 million per week, and profit contribution averages one-third of revenues on each delivery. After completion of the expansion project, fixed costs will double, but variable costs will decline by 25%.
A. Calculate the change in UPS’s weekly breakeven output level that is due to expansion.
B. Assuming that volume remains at 2 million packages per week, calculate the change in the degree of operating leverage that is due to expansion.
C. Again assuming that volume remains at 2 million packages per week, what is the effect of expansion on weekly profit?
Cost estimation and cost containment are an important concern for a wide range of for-profit and not-for-profit organizations offering health care services. For such organizations, the accurate measurement of nursing costs per patient day (a measure of output) is necessary for effective management. Similarly, such cost estimates are of significant interest to public officials at the fed- eral, state, and local government levels. For example, many state Medicaid reimbursement pro- grams base their payment rates on historical accounting measures of average costs per unit of service. However, these historical average costs may or may not be relevant for hospital man- agement decisions. During periods of substantial excess capacity, the overhead component of average costs may become irrelevant. When the facilities of providers are fully used and facility expansion becomes necessary to increase services, then all costs, including overhead, are rele- vant. As a result, historical average costs provide a useful basis for planning purposes only if appropriate assumptions can be made about the relative length of periods of peak versus off- peak facility usage. From a public-policy perspective, a further potential problem arises when hospital expense reimbursement programs are based on historical average costs per day, because the care needs and nursing costs of various patient groups can vary widely. For example, if the care received by the average publicly supported Medicaid patient actually costs more than that received by non-Medicaid patients, Medicaid reimbursement based on average costs for the entire facility would be inequitable to providers and could create access barriers for some Medicaid patients.
As an alternative to traditional cost estimation methods, one might consider using the engi- neering technique to estimate nursing costs. For example, the labor cost of each type of service could be estimated as the product of an estimate of the time required to perform each service times the estimated wage rate per unit of time. Multiplying this figure by an estimate of the frequency of service provides an estimate of the aggregate cost of the service. A possible limitation to the accuracy of this engineering cost-estimation method is that treatment of a variety of illnesses often requires a combination of nursing services. To the extent that multiple services can be provided simultaneously, the engineering technique will tend to overstate actual costs unless the effect on costs of service “packaging” is allowed for.
Nursing cost estimation is also possible by means of a carefully designed regression-based approach using variable cost and service data collected at the ward, unit, or facility level. Weekly labor costs for registered nurses (RNs), licensed practical nurses (LPNs), and nursing aides might be related to a variety of patient services performed during a given measurement period. With suf- ficient variability in cost and service levels over time, useful estimates of variable labor costs become possible for each type of service and for each patient category (e.g., Medicaid, non-Medicaid). An important advantage of a regression-based approach is that it explicitly allows for the effect of serv- ice packaging on variable costs. For example, if shots and wound-dressing services are typically provided together, this will be reflected in the regression-based estimates of variable costs per unit.
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