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

The graph is straight line except for the September month over head cost

Month	overhead cost	nursing hours	over head Cost per nursing hour	patient Days	over head cost per Patient day
July	$950000	50000	19	7900	120.25
Aug	$1070000	52000	20.58	8900	120.22
Sep	$825000	40000	20.63	8700	94.83
Oct	$922500	43500	21.21	6900	133.70
Nov	$1150000	64000	17.97	11900	96.64
Dec	$890000	41500	21.45	6700	131.85

(8700,825000)is away from the straight line . At 6900 patient days the over head cost is 922500 which more than at 8700 patient days the over head cost 825000

difference in overhead cost vanable cost per Nursing hour = difference In Nursing his 1150000 - 825000 64000 – 40000 325Doo - 13.54/Nursingh 20000

regression analysis using nursing hours as the cost driver produces accurate cost data because

fined over head cost Total over head cost = 825000 @40000 Nursinghrs les cost 9541600 rariable over head - 40000 X 13.54 fined over head cost 283400 equation for over head cost 13.5ux Nursing hours +283400 per month a overhead cost @49000 wrhis = 13.5ux 49000+ 283400 = 946860 Regression analysis equation for overhead cost = (2.81796x Nursinghrs +346245 @ 49000 Noor ar = 12.81796x49000+346245 over head - sing costs has 4 628080 +346245 = 974325 Regression analysis wring Number of patient days equation for over head cost = 47.970926x No. of patient + 559764 days over head costs ( 8500 - 47.970926x -850o +559764 patient days - 967517

RSQ for nursing hours 0.909311

RSQ for patient days 0.563496482

The rsq 1 represents better correlation among the data

So rsq 0.909311 is more better than rsq 0.563496482