10-1
CHAPTER 10
DETERMINING HOW COSTS BEHAVE
10-37
Cost estimation, incremental unit-time learning model.
1.
Cost to produce the 2nd through the 7th boats:
Direct materials, 6
×
$200,000
$1,200,000
Direct manufacturing labor (DML), 72,671
1
×
$40
2,906,840
Variable manufacturing overhead, 72,671
×
$25
1,816,775
Other manufacturing overhead, 20% of DML costs
581,368
Total costs
$6,504,983
1
The direct labor hours to produce the second through the seventh boats can be calculated via a table
format, given the assumption of an incremental unit-time learning curve of 90%:
90% Learning Curve
Cumulative
Number of
Units (
X
)
Individual Unit Time for
X
th
Unit (
y
)
*
: Labor Hours
Cumulative
Total Time:
Labor-Hours
(1)
(2)
(3)
1
15,000
15,000
2
13,500
= (15,000
×
0.90)
28,500
3
12,693
41,193
4
12,150
= (13,500
×
0.90)
53,343
5
11,745
65,088
6
11,424
76,512
7
11,159
87,671
*Calculated as
y
=
aX
b
where
a
= 15,000,
b
= – 0.152004, and
X
= 1, 2, 3,. . .7.
The direct manufacturing labor-hours to produce the second through the seventh boat is 87,671 –
15,000 = 72,671 hours.
2.
Difference in total costs to manufacture the second through the seventh boat under the
incremental unit-time learning model and the cumulative average-time learning model is
$6,504,983 (calculated in requirement 1 of this problem) – $5,807,249 (from requirement 1 of
Problem 10-36) = $697,734, i.e., the total costs are higher for the incremental unit-time model.
The incremental unit-time learning curve has a slower rate of decline in the time required
to produce successive units than does the cumulative average-time learning curve (see Problem
10-36, requirement 1). Assuming the same 90% factor is used for both curves:
Estimated Cumulative Direct Manufacturing Labor-Hours
Cumulative
Number of Units
Cumulative Average-
Time Learning Model
Incremental Unit-Time
Learning Model
1
2
4
7
15,000
27,000
48,600
78,113
15,000
28,500
53,343
87,671