Question

A company has a profit-volume ratio of
20%. To maintain the same contribution,
by what percentage (%) must sales be
increased to offset 10% reduction in selling
price?​

Answer 1

100%

Explanation:

let y1 be old qty

y2 be new qty

Rs.1 S old s.p.p.u

Rs.0.9S New s.p.p.u (10% reduction)

Total Old contribution = y1 x (S-V)

Total New Contribution = y2 x (0.9S-V)

Both the contribution are same (Given)

∴ y1 x (S-V)= y2 x (0.9S-V)

Y1       0.9S- V

__ =  ________

Y2          S-V

Y1        (S-V) - (0.1S)

___=   _________

Y2        S-V

Y1        0.9S-V

___=   ______      =  1 - 0.1 (S/S-V)

Y2        S-V

Since C/S = PV Ratio = 20%(Given)

i.e S-V = P   Ratio 20%

     S       V

Y1 = 1 - 0.1 (1/20%)

Y2

Y1= 1 - 0.1 * 100/20

Y2  

Y1= 1 - 0.5

Y2  

Y1= 0.5

Y2  

Y1 = 0.5Y2

Y2 = Y1/0.5

Y2 = 2y1

∴New qty sold is double the old qty

Answer 2

Answer:

80% sales must be increased to offset 10% reduction in selling price.

Explanation:

The Profit-Volume Ratio is the measure of the rate of change of profit due to change in volume of sales, given by

$\dfrac{P}{V} =\dfrac{contribution}{sales} \times 100$

Given the company has a profit-volume ratio of 20%.

If we assume sales = 100

Then from the formula, contribution = 20

Also the existing variable cost = sales - contribution$=100-20=80$

Given there is a reduction in the selling price by 10%.

Then new selling price = $100-10\% \times 100=90$

Hence, the new contribution with the same variable cost

$= new~ selling ~price - variable~ cost =90-80=10$

Therefore, the new sales volume

= $\dfrac{20}{10} \times 90=180$

Therefore, the volume sales have to be increased from 100 to 180.  

Hence the 80% sales must be increased to offset 10% reduction in selling price.