Mr. Charles Lackey, an owner of a small bakery business, is worried about increa

Question

Mr. Charles Lackey, an owner of a small bakery business, is worried about increased costs-particularly energy. Last year's record can provide a fairly good estimate of the parameters for this year. Charles does not believe things have changed much, but he did invest an additional $3,(X)0 for modification to the bakery's ovens to make them more energy efficient. The modifications were supposed to make the ovens at least 15% more efficient. Charles has asked you to check the energy savings of the new ovens and also to look over other measures of the bakery's productivity to see if the modifications were beneficial. You have the following data to work with: Calculate all Single Factor Productivity Ratios for last year as well as current year using information given in Table 1. Calculate and briefly discuss Single Factor Productivity Index for each measure using last year as a base year. What would be your response to Mr. Lackey's request? Assume that demand is expected to increase by 10% in the coming year (2013). Because of the size of the store, no new ovens can be added. At a staff meeting, one employee suggested ways to load the ovens differently so that more loaves of bread can be cooked at one time. This new process is expected to increase production from 1550 dozen this year (2012) to 1600 dozen in the coming year (2013) without any increase in any input factors. Suppose labor rate is $8 per hour and energy costs is $0.60 per BTU, Calculate Total Factor Productivity ratio and respond to Mr. Lackey about any increase or decrease in TFP over the last year.

Explanation / Answer

a. Single Factor Productivity should be calculated as follows:

Energy Change:

Year 2011 : 1500*12/3000 = 6.0 loaves/BTU

Year 2012 : 1550*12/2750 = 6.76 loaves/BT

Percent Change: (6.76-6)/6*100= 12.66%

From the above results we infer that there is definitely an increase in the energy productivity which means that there is savings in energy.

Labor Change:

Year 2011 : 1500*12/350 = 51.43 loaves/labor hour

year 2012 : 1550*12/325 = 57.23 loaves/labor hour

Percent Change: (57.23-51.43)/51.43*100= 11.27%

Labor productivity has also increased over the year.

Investment Change:

Year 2011 : 1500*12/15000 = 1.2 loaves/$ investment

Year 2012 : 1550*12/18000 = 1.03 loaves/$ investment

Percent Change: (1.03-1.2)/1.2*100= -14.16%

From the above results we infer that Investment productivity has decreased. This could have happened due to an increase in energy and labor productivity.

b. We need to calculate multi-factor productivity and the calculation are as follows:

Year 2011 : 1500*12/(350*8+3000*0.6+15000) = 0.91

Year 2012 : 1550*12/(325*8+2750*0.6+18000) = 0.83

Year 2013 : 1600*12/(325*8+2750*0.6+18000) = 0.86

Percent Change from 2012 to 2011 : (0.83-0.91)/0.91*100 = -8079%

Percent Change from 2013 from 2012: (0.86-0.83)/0.83*100= 3.61%

So as can be seen the modification could only make the ovens 3.61% more efficient and not 15% more efficient.

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