Question

A hospital is analyzing its overhead costs. It is not clear whether the number of patient days or nursing hours would be the best cost driver to use in predicting the hospital’s overhead. The latest information on the hospital is as follows:

Month              Hospital           Nursing                        No. of              Overhead         Overhead Cost

                        Overhead         Hours               Patient              Cost Per           Per Patient

                        Costs                                        Days                Nursing Hr.      Day

July                  $950,000         50,000             7,900               $19.00             $120.25

August            $1,070,000       52,000             8,900               $20.58             $120.22

September         $825,000        40,000             8,700               $20.63             $ 94.83

October                        $922,500         43,500             6,900               $21.21             $133.70

November      $1,150,000       64,000            11,900              $17.97             $ 96.64

December        $890,000         41,500           6,750               $21.45             $131.85

                                                                                                                                               

Required:

• Graph the hospital’s overhead costs against the number of patient days. Note: This is for your benefit so that you can answer Question 3; you do not need to submit this graph as part of the assignment.

• Graph the hospital’s overhead costs against nursing hours. Note: This is for your benefit so that you can answer Question 3; you do not need to submit this graph as part of the assignment.

• Based on the graphs that you drew, do the data appear to be straight forward or do you see any potential problems with the data (i.e, do the data points form straight lines)? Please explain.

• Using the high-low method, determine the hospital’s variable cost per nursing hour, rounded to two decimal places.

• Now that you have calculated both the variable and fixed portions hospital overhead costs, write out the equation for hospital overhead costs using the high-low method.

• Using the cost equation that you just wrote, predict hospital overhead costs if 49,000 nursing hours are expended in a month.

• The hospital ran a regression analysis using nursing hours as the cost driver to predict total hospital overhead costs. The regression analysis produced the following data:

Intercept	346245
Slope	12.81796
RSQ	0.909311

Round the variable portion of the regression equation formula to two decimal places. Based on the regression equation formula, what will the predicted total hospital overhead costs be if 49,000 nursing hours are expended during a month?

• The hospital then ran a regression analysis using number of patient days as cost driver. The regression analysis produced the following data:

Intercept	559764
Slope	47.970926
RSQ	0.563496482

Again, round the variable portion of the regression equation to two decimal places. If 8,500 patient days are predicted for a month, what is the total predicted hospital overhead costs using the regression equation?

• Which regression equation, the one using nursing hours as the cost driver or the one using patient days as the cost driver, produces the most accurate correlation (best explanation of) the predicted hospital overhead costs. How do you know that your answer is correct? In other words, justify your answer.

Answer 1

1) The hospital's overhead costs appear to be a Mixed cost. If it were afixed cost, it would remain constant in total each month. If it were a variable cost, it would remain constant on a per unit(of activity) basis. Both of the hospital's overhead cost per nursing hour and overhead cost per patient day vary with volume
2. Graph the​ hospital's overhead costs against nursing hours.
Hospital
Nursing Hours	Hospital Overhead Costs
50,000	$950,000
52,000	$1,070,000
40,000	$825,000
43,500	$922,500
64,000	$1,150,000
41,500	$890,000
3. Graph the​ hospital's overhead costs against the number of patient days.
Number of Patient Days	Hospital Overhead Costs
7,900	$950,000
8,900	$1,070,000
8,700	$825,000
6,900	$922,500
11,900	$1,150,000
6,750	$890,000
4. Do the data appear to be sound or do you see any potential data​ problems? Explain.
The data does  appear to contain  outlier in the graph depicting overhead costs against nursing hours in th month of August  . In the graph of overhead costs vs. patient days, there does appear to be an outlier. The September  and August data points appear out of line with the other data points. If any of the data points are out of line, management should check into this data before continuing with the analysis.
5. Use the​ high-low method to determine the​ hospital's cost equation using nursing hours as the cost driver. Predict total overhead costs if 49,000 nursing hours are predicted for the month.
	Nursing Hours	Hospital Overhead Costs
High	64,000	$1,150,000
Low	40,000	$825,000
Difference	24,000	325,000
Variable cost per unit = $325,000/24000	$             13.54
Fixed Cost = $825,000 - $13.54 x 40000	$    283,333.33
Cost Eq. = $283,333.33  + $13.54X
Total overhead cost = $283,333.33  + $13.54 x 49000	$    615,104.17
6) If 49000 nursing hours are predicted for the​ month, what is the total predicted hospital​overhead?
Intercept = fixed cost	346,245.00
X Variable 1 = Variable cost per unit	12.81796
If  49000 nursing hours are predicted for the​ month, what is the total predicted hospital​overhead?
Total overhead cost = $346,245 + $12.82 x 49000	$    974,325.04
7) If 8,500  patient days are predicted for the​ month, what is the total predicted hospital​overhead?
	Coefficients
Intercept	$    559,764.00
X Variable 1	$             47.97
If 8500  patient days are predicted for the​ month, what is the total predicted hospital​overhead?
Total overhead cost = 559,764 + (47.97 x 8500)	$    967,516.87
8) Which regression equation, the one using nursing hours as the cost driver or the one using patient days as the cost driver, produces the most accurate correlation (best explanation of) the predicted hospital overhead costs. How do you know that your answer is correct? In other words, justify your answer
We have the most confidence in the cost equation using nursing hours. The R-square value for that equation was the highest.

Hospital Overhead Costs $1,400,000 $1,200,000 $1,000,000 Plot Area $800,000 $600,000 $400,000 $200,000 Nursing Hours $0 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000

Hospital Overhead Costs $1,400,000 $1,200,000 1,000,000 $800,000 $600,000 $400,000 $200,000 Number of Patient Days- s0 10,000 0 2,000 4,000 6,000 8,000 12,000 14,000