1. Quantitative analysis in budgeting
By 黄郡漪 吴思佳 杨秋霞

2. Topic list
1. Analysing fixed and variable costs: high-low method 2. Learning curves 3. Applying expected values

3. High-low method highest activity level lowest activity level
Total cost at high activity level-total cost at low activity level
Total units at high activity level-total units at low activity level
= variable cost per unit (v)

4. The usefulness of the high-low method
a.Ignores cost information apart from cost of highest and lowest volumes. Not be representative
b.Inaccurate cost estimates
c.Historical information.changed

5. Learning curves
Learning curve theory applies to situations where the work force as a whole improves in efficiency with experience.
Learning rate is expressed as a percentage value,eg:80% learning curve
Learning effect is that as the work force learns from experience how to make the new product,there is a big reduction in the time to make additional units

6. The graphical approach

7. The third and fourth units together take: 90% * 100 = 90 hours
Every time that the cumulative output of the priduct doubles.
Eg: 90% learning curve,the labour time to make the first unit is 100 hours.
The first two units
Average time :
Total time:
The second unit take:
The first four units
Average time:
The third and fourth units together take:
90% * 100 = 90 hours
90 * 2 = 180 hours
180 – 100 = 80 hours
90% * 90 = 81 hours
81 * 4 = 324 hours
324 – 180 = 144 hours

8. The two approaches to learning curve problems
Method 1. The tabular approach
 Method 2. The algebraic approach

9. where output is doubling
Method 1 – The tabular approach: cumulative average time and the learning rate
where output is doubling
The cumulative average time per unit produced is assumed to decrease by a constant percentage every time total output of the product doubles.

10. The algebraic approach
Formula
Y=the cumulative average time per unit to produce X units
X=cumulative numbers of units
a=time taken for thr first unit of output
b=logLR/log2
LR=learning rate

11. conditions for the learning effect to apply
1.The activity is labour intensive
2.A repetitive process for each unit
3.Low turnover of labour force
4.Early stage of production
5.No prolonged breaks in production

12. Notes for formula X Y b

13. Calculating the time for specific unit
calculate the incremental time for unit
特殊数字规律法
X 翻倍

14. Question P252 720*r*r=405 r=0.75 cumulative production
cumulative average cost 1
720 2
720*r 4
720*r*r

15. Using the formula
log y=log a +b log X

16. Learning curves and steady production
When a steady state is reached,a standard time
and standard labour cost for the product can be
established.

17. Limitations of learning curve theory
1.The stable conditions necessary for the learning curve to take place may not be present.
2.The employees need to be motivated,agree to the plan and keep to the learning schedule-this assumption may not hold.
3.Accurate and appropriate learning curve data may be difficult to estimate.
4.It assumes a constant rate learning factor.
5.Steady state time rate is inaccuracy.

18. TRANSITIONAL PAGE

19. Expected values in budgeting
To determine the best combination of expected profit and risk.

20. Probabilistic budgeting 概率预算
It assigns probabilities to different conditions to derive an EV of budgeted profit.

21. Best possible
Most possible

22. Example Probability Profit Expected value Worst possible 0.3 (220)
(66)
Most likely
0.6
300
180
Best possible
0.1
770 77
Expected value of profit
191

23. Problems Time-consuming
May not reflect an outcome that is actually expected to happen.
Little practical value (cost>benefit)

24. 预算方法 特点
使用项目举例
固定预算
以固定业务量编制
销售、研发、业务部门预算
弹性预算
按照可能发生的业务量编制预算
生产成本预算
零基预算
以零为基数编制预算，不考虑过去费用
进入新领域
滚动预算
始终以12个月作为预算期
多种预算
概率预算
针对不确定性项目，估计发生的概率测算
新产品、新业务

25. Thank you