Question

A company is considering a 5-year project that opens a new product line and requires an initial outlay of $81,000. The assumed selling price is $96 per unit, and the variable cost is $62 per unit. Fixed costs not including depreciation are $22,000 per year. Assume depreciation is calculated using stright-line down to zero salvage value. If the required rate of return is 13% per year, what is the financial break-even point? (Answer to the nearest whole unit.)

Detailed explanation please

Answer 1

Financial breakeven point is the point at which NPV of a project is zero. NPV is calculated using the following formula:

NPV = Present value of cash inflows - Initial investment

Here, initial investment is given as $81,000.

Calculation of cash inflows

Step 1: Calculate Depreciation

Depreciation= (Cost - Salvage value)/ life

= ($81,000 - $0)/5

=$16,200

Thus, annual depreciation is $16,200.

STEP 2: Calculate annual cash flows

Now, let the breakeven level of units be X. Calculate the annual cash flows as follows:

Annual cash flows= Sales- Variable cost- Fixed cost - Depreciation

= (X*$96) - (X*$62) - $22,000 - $16,200

Now, to calculate the present value of cash flows, discount the cash flows with the present value annuity factor of 13% for 5 years as follows:

PVAF = P*[1-(1+r)^-n]/r

Substituting the value of rate and number of years, PVAF is 3.51723126.

STEP 3: Calculate NPV

NPV = PV of cash inflows- Initial investment

0 = (Annual cash flows* PVAF) - Initial investment

0 = [(X*$96) - (X*$62) - $22,000 - $16,200]* 3.51723126 - $81,000

Solving the above equation, the value of X is 1,800.86701.

Thus, rounding to nearest whole unit the financial breakeven point is 1,801 units.