Omaro Ltd. would like to clear their warehouse and yard of damaged equipment and metal scrap. If the company purchases an industrial recycling bin for $1800, a contractor will pick up the materials and pay by the kilogram for the scrap. Omaro adjusts all cash flows for time value and uses a 10% discount rate. What dollar value of scrap do they have to generate each year to be able to break even on their investment in three years?

Question

Quizplus · Accepted Answer

To calculate the annual dollar value of scrap required to break even in three years, we need to use the Net Present Value (NPV) formula.

First, we need to calculate the present value of the initial investment of $1800, which is simply $1800.

Next, we need to calculate the present value of the revenue generated by selling the scrap. Let's say the contractor pays $0.20 per kilogram of scrap, and the company expects to generate 3000 kilograms of scrap each year. This means the annual revenue from scrap would be:

Annual revenue = $0.20/kg * 3000 kg = $600

However, we need to adjust this for the time value of money. To calculate the present value of this revenue stream over three years, we use the following formula:

Present value = Annual revenue * (1 - (1 + r)^-n) / r

Where r is the discount rate and n is the number of years. Plugging in the numbers, we get:

Present value = $600 * (1 - (1 + 0.10)^-3) / 0.10 = $1544.26

Adding the present value of the initial investment, we get the total present value:

Total present value = $1800 + $1544.26 = $3344.26

Now, we need to solve for the annual revenue required to break even. We can rearrange the formula above to solve for the annual revenue:

Annual revenue = (Total present value - Present value of initial investment) * r / (1 - (1 + r)^-n)

Plugging in the numbers, we get:

Annual revenue = ($3344.26 - $1800) * 0.10 / (1 - (1 + 0.10)^-3) = $724.22

So the answer is (C), $724.

Omaro Ltd Would Like to Clear Their Warehouse and Yard of of Damaged