Question

Please tell me the detailed

11. Digi Calculator proposes to invest $9 million in a new factory. Fixed costs are $2 million a year. A calculator costs $8 per unit to manufacture and can be sold for $24 per unit. The factory lasts for 4 years and the cost of capital is 20%. Assume no taxes, all cash flows arrive at the year-ends and the residual value of assets is zero after 4 years. What is the NPV break-even level of annual units of sales? A) 125,000 units. B) 217,500 units C) 342,288 units D) 437,500 units.

Answer 1

Solution:

The NPV break even level of annual units of sales is the point where its present value of cash inflows is equal to the Initial Investment in the Project / Factory

Thus it is that level of sales where the discounted cash inflows is equal to the Initial Investment in the project / factory.

Calculation of Annual cash Inflows :

The formula for calculating the annual cash Inflow is

= [ (Sales - Manufacturing Cost - Fixed Cost )

As per the information given in the question we have

Sales price per unit = $ 24   ; Let the units of sales be “x” units

Thus sales value = $ 24 * x = 24x

Manufacturing Cost per unit = $ 8   ; Let the units of sales be “x” units

Thus total Manufacturing costs = $ 8 * x = 8x

Fixed Cost = $ 2,000,000 ;

Applying the above information we have the annual after tax cash inflows

= ( 24x – 8x - $ 2,000,000 )

= ( 16x - $ 2,000,000 )

Thus the annual cash inflows = 16x - $ 2,000,000

Calculation of present value of cash Inflows :

As per the information given in the question

Discount rate for the project = 20 %    ; No. of years of the project = 4 Years

The present value factor at 20 % for four years is = PVIFA(20 %, 4) = 2.588735

Thus the present value of cash inflows of the project = Annual cash inflows * PVIFA(20 %, 4)

= ( 16x - $ 2,000,000 ) * 2.588735

= 41.419753x – $ 5,177,469.135802

The present value of after tax cash inflows of the project = 41.419753x – $ 5,177,469.135802

Calculation of NPV Break-even level of annual units of sales :

We know that at the NPV Break – even level of annual units of sales, the present value of cash inflows of the project = Initial Investment

Thus we have

41.419753x – $ 5,177,469.135802 = $ 9,000,000

41.419753x = $ 5,177,469.135802 + $ 9,000,000

41.419753x = $ 14,177,469.135802

x = $ 14,177,469.135802 / 41.419753

x = 342,287.630402

x = 342,288 units ( when rounded off to the nearest whole number )

Thus the NPV Break even level of annual units of sales = 342,288 units

The solution is Option C) 342,288 units