y = ax Insert Page Layout Review Home Formulas Data A Cumulative Cumulative Cumulative Avg DLH (y) 21 Output (x) DLH Month LN (y) LN (x) 0.716 6.528 22 January 23 February 24 March 25 April 26 May 27 June 28 July 29 August 30 September 31 October 32 November 33 December 684 1,400 2.047 2,220 1.888 0.635 7.070 1,176 1,836 3,095 3,765 1.686 0.522 7.515 2,340 2,952 1.609 0.476 7.758 4,525 1.533 0.427 7.990 3,588 5,290 1.474 0.388 8.185 1.422 4,236 6,025 0.352 8.351 4,836 6,685 1.382 0.324 8.484 5,484 6,180 7,380 1.346 0.297 8.610 8,090 1.309 0.269 8.729 6,852 7,527 8,780 9,480 1.281 0.248 8.832 0.231 8.926 1.259 Required 1. Estimate the relationship between the cumulative average direct labor-hours per unit and cumulative output (both in logarithms). Verify that the following is the result obtained by Inbee and Jim: Regression 1: Ln (Cumulative avg DLH per unit) = a + [b x Ln (Cumulative Output)] Variable Coefficient Standard Error t-Value Constant 2.087 0.024 85.44 Independent variable: Ln (Cum Output) -0.208 0.003 -69.046 p2 = 0.998; Durbin-Watson statistic = 2.66 2. Plot the data and regression line for the above estimation. Evaluate the regression using the criteria of economic plausibility, goodness of fit, and slope of the regression line. 3. Verify that the estimated slope coefficient corresponds to an 86.6% cumulative average-time learning curve. 4. Based on this new estimation, how will Inbee revise her budget for Hankuk's variable cost for the ex- pected output of 650 units in January 2018? How confident is she of this new cost estimate?

FINANCIAL ACCOUNTING
10th Edition
ISBN:9781259964947
Author:Libby
Publisher:Libby
Chapter1: Financial Statements And Business Decisions
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Cost estimation, learning curves (continuation of 10-44). Inbee is concerned that she still does not understand the relationship between output and labor consumption. She consults with Jim Park, the head of engineering, and shares the results of her regression estimation. Jim indicates that the production of new smartphone models exhibits significant learning effects—as Hankuk gains experience with production, it can produce additional units using less time. He suggests that it is more appropriate to specify the following relationship:

where x is cumulative production in units, y is the cumulative average direct labor-hours per unit (i.e., cumulative DLH divided by cumulative production), and a and b are parameters of the learning effect. To estimate this, Inbee and Jim use the original data to calculate the cumulative output and cumulative average labor-hours per unit for each month. They then take natural logarithms of these variables in order to be able to estimate a regression equation. Here is the transformed data:

y = ax
Transcribed Image Text:y = ax
Insert
Page Layout
Review
Home
Formulas
Data
A
Cumulative
Cumulative
Cumulative Avg DLH
(y)
21
Output
(x)
DLH
Month
LN (y)
LN (x)
0.716 6.528
22 January
23 February
24 March
25 April
26 May
27 June
28 July
29 August
30 September
31 October
32 November
33 December
684
1,400
2.047
2,220
1.888
0.635 7.070
1,176
1,836
3,095
3,765
1.686
0.522 7.515
2,340
2,952
1.609
0.476 7.758
4,525
1.533
0.427
7.990
3,588
5,290
1.474
0.388 8.185
1.422
4,236
6,025
0.352
8.351
4,836
6,685
1.382
0.324 8.484
5,484
6,180
7,380
1.346
0.297 8.610
8,090
1.309
0.269
8.729
6,852
7,527
8,780
9,480
1.281
0.248 8.832
0.231 8.926
1.259
Required
1. Estimate the relationship between the cumulative average direct labor-hours per unit and cumulative
output (both in logarithms). Verify that the following is the result obtained by Inbee and Jim:
Regression 1: Ln (Cumulative avg DLH per unit) = a + [b x Ln (Cumulative Output)]
Variable
Coefficient
Standard Error
t-Value
Constant
2.087
0.024
85.44
Independent variable: Ln (Cum Output)
-0.208
0.003
-69.046
p2 = 0.998; Durbin-Watson statistic = 2.66
2. Plot the data and regression line for the above estimation. Evaluate the regression using the criteria of
economic plausibility, goodness of fit, and slope of the regression line.
3. Verify that the estimated slope coefficient corresponds to an 86.6% cumulative average-time learning
curve.
4. Based on this new estimation, how will Inbee revise her budget for Hankuk's variable cost for the ex-
pected output of 650 units in January 2018? How confident is she of this new cost estimate?
Transcribed Image Text:Insert Page Layout Review Home Formulas Data A Cumulative Cumulative Cumulative Avg DLH (y) 21 Output (x) DLH Month LN (y) LN (x) 0.716 6.528 22 January 23 February 24 March 25 April 26 May 27 June 28 July 29 August 30 September 31 October 32 November 33 December 684 1,400 2.047 2,220 1.888 0.635 7.070 1,176 1,836 3,095 3,765 1.686 0.522 7.515 2,340 2,952 1.609 0.476 7.758 4,525 1.533 0.427 7.990 3,588 5,290 1.474 0.388 8.185 1.422 4,236 6,025 0.352 8.351 4,836 6,685 1.382 0.324 8.484 5,484 6,180 7,380 1.346 0.297 8.610 8,090 1.309 0.269 8.729 6,852 7,527 8,780 9,480 1.281 0.248 8.832 0.231 8.926 1.259 Required 1. Estimate the relationship between the cumulative average direct labor-hours per unit and cumulative output (both in logarithms). Verify that the following is the result obtained by Inbee and Jim: Regression 1: Ln (Cumulative avg DLH per unit) = a + [b x Ln (Cumulative Output)] Variable Coefficient Standard Error t-Value Constant 2.087 0.024 85.44 Independent variable: Ln (Cum Output) -0.208 0.003 -69.046 p2 = 0.998; Durbin-Watson statistic = 2.66 2. Plot the data and regression line for the above estimation. Evaluate the regression using the criteria of economic plausibility, goodness of fit, and slope of the regression line. 3. Verify that the estimated slope coefficient corresponds to an 86.6% cumulative average-time learning curve. 4. Based on this new estimation, how will Inbee revise her budget for Hankuk's variable cost for the ex- pected output of 650 units in January 2018? How confident is she of this new cost estimate?
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