Question

Suppose that a businessman is contemplating the purchase of a \(\$ 35,000\) machine, and that he estimates that the machine will provide a return (net of operating costs) of \(\$ 10,000\) per year for 4 years. Assume that the going rate of interest is a) 8 percent, b) 2 percent Should he buy it?

Short answer

In conclusion, the businessman should not purchase the machine at an 8% interest rate, as the present value of future cash flows ($33,120.51) is less than the initial investment cost ($35,000). However, he should purchase the machine at a 2% interest rate since the present value of future cash flows is higher ($38,074.21), indicating a profitable decision.

Step-by-step solution

Identify the cash flows

We can see that the investment cost of purchasing the machine is \(35,000 and the future cash flows are \)10,000 per annum for 4 years. The cash flows can be represented as: Year 0: Invest $35,000 (represented as a negative cash flow) Year 1: Receive $10,000 Year 2: Receive $10,000 Year 3: Receive $10,000 Year 4: Receive $10,000

Calculate the present value of the cash flows at 8% interest rate

Using the PV formula, we will now calculate the present value of each cash flow at an interest rate of 8%: PV = CF/(1+r)^n where PV is the present value, CF is the cash flow, r is the interest rate, and n is the year. PV(Year 1) = \(10,000 / (1+0.08)^1 = \)10,000 / 1.08 ≈ $9,259.26 PV(Year 2) = \(10,000 / (1+0.08)^2 = \)10,000 / 1.1664 ≈ $8,573.55 PV(Year 3) = \(10,000 / (1+0.08)^3 = \)10,000 / 1.2597 ≈ $7,938.60 PV(Year 4) = \(10,000 / (1+0.08)^4 = \)10,000 / 1.3605 ≈ $7,349.10 The total present value of future cash flows at 8% interest rate is: PV_total = PV(Year 1) + PV(Year 2) + PV(Year 3) + PV(Year 4) PV_total = \(9,259.26 + \)8,573.55 + \(7,938.60 + \)7,349.10 ≈ $33,120.51

Calculate the present value of the cash flows at 2% interest rate

We will now calculate the present value of each cash flow at an interest rate of 2%: PV(Year 1) = \(10,000 / (1+0.02)^1 = \)10,000 / 1.02 ≈ $9,803.92 PV(Year 2) = \(10,000 / (1+0.02)^2 = \)10,000 / 1.0404 ≈ $9,611.75 PV(Year 3) = \(10,000 / (1+0.02)^3 = \)10,000 / 1.0612 ≈ $9,422.47 PV(Year 4) = \(10,000 / (1+0.02)^4 = \)10,000 / 1.0824 ≈ $9,236.07 The total present value of future cash flows at 2% interest rate is: PV_total = PV(Year 1) + PV(Year 2) + PV(Year 3) + PV(Year 4) PV_total = \(9,803.92 + \)9,611.75 + \(9,422.47 + \)9,236.07 ≈ $38,074.21

Compare the present value of cash flows with the initial investment cost

Now that we have calculated the present value of the cash flows at both interest rates, we can compare them with the initial investment cost of $35,000. For the 8% interest rate: PV_total (8%) = $33,120.51 Investment cost = $35,000 The businessman should not buy the machine at an 8% interest rate since the present value of the cash flows is less than the investment cost. For the 2% interest rate: PV_total (2%) = $38,074.21 Investment cost = $35,000 The businessman should buy the machine at a 2% interest rate since the present value of the cash flows is greater than the investment cost. In conclusion, the businessman should purchase the machine at a 2% interest rate, as the present value of future cash flows is higher than the initial investment cost, indicating a profitable decision.

Key concepts

Investment Decision Making

Making an investment decision involves evaluating potential projects or assets to determine their feasibility and profitability. You must consider both the costs and benefits over time when deciding whether to pursue a particular investment.
When faced with options like purchasing a machine, you should:

• Identify all relevant cash flows, including the initial investment and any future revenues or savings.
• Calculate the net present value (NPV) of these cash flows, which is critical in understanding the value of the investment in today’s terms.
• Compare the NPV with the initial investment to see if the investment will yield a net gain or loss.

This evaluation process ensures that you're making decisions that not only recover the initial investment but also contribute to the profitability of your business in the long run.

Interest Rates

Interest rates play a vital role in investment decision making by affecting the present value of future cash flows. They represent the cost of borrowing money or the opportunity cost of using funds for investment.
A higher interest rate decreases the present value of future cash flows, making an investment less attractive. Conversely, a lower interest rate increases the present value, making the investment more appealing.

• For instance, in the given exercise, the investment was evaluated at two different interest rates, 8% and 2%.
• At an 8% interest rate, the present value of the machine's cash flows was less than the initial cost, suggesting a non-profitable investment.
• However, at a 2% interest rate, the present value exceeded the investment cost, indicating a favorable investment opportunity.

Proper understanding and application of interest rates can greatly impact investment decisions.

Cash Flow Analysis

Cash flow analysis involves assessing a stream of cash flows over time to evaluate an investment's viability. It’s about looking at when and how much money comes in and goes out and then using this information to make investment decisions.
In the machine scenario, the cash flows included an initial negative cash flow (the purchase cost) and positive annual cash flows from returns. Each year's return is discounted to reflect its value today using the interest rate.

• This helps in knowing how much those future cash flows are worth at present, allowing for a clearer investment decision.
• By calculating the net present value (NPV) using discounted cash flows, businesses can objectively decide whether the projected returns justify the initial outlay.

Effective cash flow analysis helps in avoiding investments that may look profitable on the surface but aren't in reality, due to future returns being insufficient to cover the present costs.

Business Economics

Business economics involves applying economic theory and quantitative methods to analyze business enterprises and the factors contributing to their diversity of organizational structures and relationships.
In the context of investment decisions:

• Business economics provides the tools needed to make informed decisions on resource allocation and capital budgeting to ensure maximum returns.
• It helps in understanding market conditions, dynamic pricing, and cost structures, all of which influence key business strategies.
• The principles of business economics, such as opportunity cost and marginal analysis, are integral to evaluating the profitability of investments, understanding supply and demand dynamics, and making sound financial decisions.

This comprehensive understanding aids business managers in optimizing their strategies and achieving competitive advantage.