Affan Limited (AL) is evaluating a new product proposal. The proposed selling price is Rs. 36,000 per unit and the carriable costs are Rs. 12,000 per unit. The incremental cash fixed costs for the product will be Rs. 32,000,000 per annum. The discounted cash flow calculation results in appositive NPV. Year Particulars Cash Flow Disc. rate PV 0 Initial cash flow (200,000,000) 1.000 (200,000,000) 1 to 5 Annual cash flow 64,000,000 3.791 242,624,000 5 Working cap. released 10,000,000 0.621 6,210,000 What is the percentage change in selling price that would result in the project having net present value of zero?

Step-by-step explanation:To find the percentage change in the selling price that would result in the project having a net present value (NPV) of zero, we need to perform sensitivity analysis.

Let's denote:

�

P as the original selling price

�

′

P

′

as the new selling price (after the change)

�

DCF as the discounted cash flow

�

NPV as the net present value

Given:

Initial cash flow = -Rs. 200,000,000

Annual cash flow = Rs. 64,000,000 for 5 years

Working capital released = Rs. 10,000,000

Discount rate = 3.791 for annual cash flows and 0.621 for working capital released

The formula for NPV is:

�

=

Initial cash flow

+

Annual cash flow (discounted)

+

Working capital released (discounted)

NPV=Initial cash flow+Annual cash flow (discounted)+Working capital released (discounted)

Let's calculate the NPV using the original selling price:

�

=

−

200

,

000

,

000

+

(

64

,

000

,

000

×

3.791

×

5

)

+

(

10

,

000

,

000

×

0.621

)

NPV=−200,000,000+(64,000,000×3.791×5)+(10,000,000×0.621)

�

=

−

200

,

000

,

000

+

1

,

216

,

640

,

000

+

6

,

210

,

000

NPV=−200,000,000+1,216,640,000+6,210,000

�

=

1

,

022

,

850

,

000

NPV=1,022,850,000

Now, we want to find the new selling price (

�

′

P

′

) that would result in NPV = 0.

For the new NPV equation, we replace the original selling price with

�

′

P

′

:

�

=

−

200

,

000

,

000

+

(

�

′

−

12

,

000

)

×

64

,

000

,

000

×

3.791

×

5

)

+

(

10

,

000

,

000

×

0.621

)

NPV=−200,000,000+((P

′

−12,000)×64,000,000×3.791×5)+(10,000,000×0.621)

Now, we solve for

�

′

P

′

such that NPV = 0:

0

=

−

200

,

000

,

000

+

(

�

′

−

12

,

000

)

×

64

,

000

,

000

×

3.791

×

5

)

+

(

10

,

000

,

000

×

0.621

)

0=−200,000,000+((P

′

−12,000)×64,000,000×3.791×5)+(10,000,000×0.621)

Solving for

�

′

P

′

, we find:

�

′

=

200

,

000

,

000

−

(

10

,

000

,

000

×

0.621

)

64

,

000

,

000

×

3.791

×

5

+

12

,

000

P

′

=

64,000,000×3.791×5

200,000,000−(10,000,000×0.621)

+12,000

�

′

=

200

,

000

,

000

−

6

,

210

,

000

1

,

216

,

640

,

000

+

12

,

000

P

′

=

1,216,640,000

200,000,000−6,210,000

+12,000

�

′

=

193

,

790

,

000

1

,

216

,

640

,

000

+

12

,

000

P

′

=

1,216,640,000

193,790,000

+12,000

�

′

≈

0.159

+

12

,

000

P

′

≈0.159+12,000

�

′

≈

12

,

000

×

1.159

P

′

≈12,000×1.159

�

′

≈

13

,

908

P

′

≈13,908

So, the new selling price (

�

′

P

′

) that would result in NPV = 0 is approximately Rs. 13,908.

Now, to find the percentage change in selling price, we use the formula:

Percentage change

=

�

′

−

�

×

100

%

Percentage change=

P

′

−P

×100%

Substituting the values:

Percentage change

=

13

,

908

−

36

,

000

36

,

000

×

100

%

Percentage change=

36,000

13,908−36,000

×100%

Percentage change

=

−

22

,

092

36

,

000

×

100

%

Percentage change=

36,000

−22,092

×100%

Percentage change

≈

−

61.367

%

Percentage change≈−61.367%

So, a percentage change of approximately -61.367% in the selling price would result in the project having a net present value of zero.