Question

Suppose you were considering purchasing a $5000 machine today that would generate additional net profit of $2000 booked at the end of each year. Assuming you need a 15 percent return to justify the investment, would the investment be worth doing if you had only three years of payouts? Would your answer change if you had four years of $2000 payouts? Why or why not?

Answer 1

The investment in a $5000 machine generating a net profit of $2000 per year must be evaluated based on the present value of the future payouts using a 15% discount rate. If the present value over three years is less than the cost of the machine, the investment is not justified. An additional year of payouts could potentially make the investment worth it by increasing the present value.

Step-by-step explanation:

The scenario described is considering purchasing a $5000 machine today in hopes that it would yield an additional net profit of $2000 at the end of each year. To determine whether this investment is worthwhile, we need to consider the present value (PV) of the future payouts using a discount rate that represents the investor's required rate of return—which in this case is 15%. For an investment period of three years, the present value of payouts would be calculated as follows:

PV = $2000 / (1 + 0.15) + $2000 / (1 + 0.15)^2 + $2000 / (1 + 0.15)^3

After calculating, if this present value is less than $5000, the investment isn't justified. If we extend the investment period to four years, we add another discounted payout:

PV = $2000 / (1 + 0.15) + $2000 / (1 + 0.15)^2 + $2000 / (1 + 0.15)^3 + $2000 / (1 + 0.15)^4

Comparing this new present value to the initial investment will show whether the additional year of payouts makes the investment worth doing. Generally, the longer the period of receiving payouts, the higher the present value of the investment, which would potentially justify the initial cost of the machine.