Question

A firm purchased some equipment at a very favorable price of $40,000. The equipment reduced costs by $1000 per year during 7 years of use. After 7 years, the equipment was sold for $50,000. Assuming interest at 9%, did the equipment purchase prove to be desirable?

Answer 1

To assess if the equipment purchase was desirable, we calculate its NPV by discounting the cost savings and sale price back to present value at a 9% discount rate. The investment was desirable if the NPV is positive, meaning the present value of cash inflows exceeded the initial cost.

Step-by-step explanation:

To determine if the equipment purchase was desirable, we need to calculate the net present value (NPV) of the investment. The NPV takes into account the initial cost of the equipment, the annual cost savings for 7 years, the sale price after 7 years, and the discount rate of 9%.

NPV Calculation:

• Initial cost: -$40,000 (negative because it is a cash outflow).
• Annual savings for 7 years: $1000 each year, which need to be discounted back to present value.
• Sale price after 7 years: $50,000, which also needs to be discounted back to present value.

Using the formula for NPV:

NPV = ∑ (Rt / (1+i)^t) - C

Where Rt = net cash inflows during the period t (savings or sale price), i = discount rate (9%), and C = initial investment cost.

If the NPV is positive, the investment was desirable because it means that the present value of cash inflows exceeded the initial cost, even after adjusting for the time value of money.