Question

Company "A" is investment project that will last 10 years. The initial investment is $25 million for equipment, which will be depreciated for tax purposes at the beginning of the project, when the equipment is purchased (Year 0). The equipment is expected to have no value at the end of the project.

Estimates for year 1 - 10 are sales price of $10 per unit and variable costs $5 per unit. Sales quantity is expected to grow by 5% per year. Fixed costs are estimated to be $1.0 million in Year 1, which will also grow at 5%. The discount rate is 10% and tax rate 25%

Based on the estimations above, calculate the number of units that Company "A" needs to sell in the first year (Year 1) to achieve a financial break-even for the project (Net Present Value basis).

Answer 1

Let Q= the number of units to be sold in first year.

Cash flow = [(1 − T) × (revenue − expenses)] + (T × depreciation)

= [(1-.25) × (10Q− 5Q− 10,00.000)] + (0.25 × 25,00,000)]

= 0.75 * (5Q - 1000000) +(6,25,000)

= 3.75Q - 750000 +625000

=3.75Q - 125000

10%, 1year annuity factor =0.909

Therefore, for NPV to equal zero:

0 = (3.75Q - 125000) * 0.909

0 = 3.40875Q - 113625

Q = 113625/3.40875

Q = 33333.33 units

Hence to reach breakeven in first year 33333.33 units to be sold.