Question

Your company is deciding whether to invest in a new machine. The new machine will increase cash flow by $425,000 per ear. You believe the technology used in the machine has a ten year lift; in other words; no matter when you purchase the machine, it will be obsolete ten years from today. The machine is currently priced at $2,600,000. The cost of the machine will decline by $230,000 per year until it reaches $1,450,000, where it will remain. If you required return is 12%, should you purchase the machine? If so, when should you purchase it?

Answer 1

To determine whether to purchase the machine, calculate the present value of the cash flows using the required return. The present value is higher than the cost, so the machine should be purchased. Calculate the present value of the declining cost to find the best purchase time.

Step-by-step explanation:

In order to determine whether to purchase the machine, we need to calculate the present value of the cash flows. The cash flow of $425,000 per year for ten years can be discounted to their present value using the required return of 12%. Using the formula for the present value of an annuity, the present value of the cash flows is:

PV = CF × [(1 - (1 + r)^-n)/r]

Plugging in the values, we get:

PV = $425,000 × [(1 - (1 + 0.12)^-10)/0.12] = $2,653,402.79

Since the present value of the cash flows is higher than the cost of the machine ($2,600,000), the machine should be purchased. As for when to purchase it, we should consider the declining cost of the machine. The cost declines by $230,000 per year until it reaches $1,450,000. We can calculate the present value of the declining cost to find the most optimal purchase time:

PV of declining cost = Cost × [(1 - (1 + r)^-n)/r]

Using the formula, we can calculate the present value for each year and compare it to the present value of the cash flows to determine the best purchase time.