1
M I M E
3 1 0
E N G I N E E R I N G
E C O N O M Y
SOLUTIONS TO PROBLEM EXERCISES – PRODUCTION AND COST ANALYSES
1.
According to the information given, both the revenue and cost functions associated with
snow removal activities are linear.
i)
The number of hours required to break even (Q
*
) is determined from the following relation-
ship:
Q
*
= FC / (f - vc)
in which FC represents the daily fixed cost, f the hourly fee, and vc the constant average variable
cost.
Q
*
= 70 / (30.00 - 12.50) = 4 hours
ii)
The additional number of hours required to produce a before-tax profit of $60 is deter-
mined by dividing the profit requirement by the contribution margin, i.e. (f - vc):
60 / (30.00 - 12.50) = 3.4
Thus, the total number of hours required is 7.4.
2.
At the annual sales volume of 80 000 units, and in the absence of depreciation allowances,
the taxable income (TI) is:
TI = 80 000 p - (FC + 80 000 vc)
= 80 000 p - [100 000 + 80 000 (5)] = 80 000 p - 500 000
in which p is the selling price, FC the fixed costs, and vc the average variable cost at a produc-
tion rate of 80 000 units per year
.
Therefore, the after-tax profit (TP) is:
TP = 80 000 p - 500 000 - t (80 000 p - 500 000) = (80 000 p - 500 000) (1 - t)
in which t is the tax rate.
For an after-tax profit of $20 000,
(80 000 p - 500 000) (1 - 0.45) = 20 000
and
p = 6.705
A selling price of $6.70 per unit
is required.

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*