Question

Your inventory manager has asked you to approve the purchase of a new inventory control software package. The software will cost \(200,000\) and will last for four years, after which it will become obsolete. If you do not approve this purchase, your company will have to hire two new inventory clerks, paying each \(30,000\) per year. Answer the following questions: a. Should you approve the purchase of the inventory control software if the relevant annual interest rate is 7 percent? b. Would your answer to part (a) change if the annual interest rate is 9 percent? Explain. c. Would your answer to part (a) change if the software cost \(220,000\) ? Explain. d. Would your answer to part (a) change if the software would not become obsolete until the last day of its sixth year?

Short answer

The answer would depend on the results of the present value calculations. For parts (b), (c) and (d), a change in the interest rate, the software cost or the software's years of use may alter the decision if it makes the present value of one option less than the other.

Step-by-step solution

Calculate the present value (PV) of the software cost

The software is a one-time cost for 4 years. For the first part (a), the annual interest or discount rate is 7%. So we can calculate the PV of the software cost using the formula \[PV = FV / (1 + r)^n\] where: - FV is the future value, in this case the cost of the software: $200,000 - r is the discount rate: 7% (or 0.07) - n is the number of periods: 4

Calculate the present value (PV) of the clerks' salaries

Now calculate the cost of having two clerks for 4 years, which also the future value. Each clerk costs $30,000 per year and two would cost $60,000 per year. The present value of future clerk salaries can be calculated by treating the yearly salaries as an annuity, since an annuity represents a series of identical payments over a period of time. The formula for the present value of an annuity is \[PV = Pmt * ((1 - (1 + r)^(-n)) / r)\] where: - Pmt (payment) is the cost of the clerk’s salary each year: $60,000 - r is the discount rate: 7% (or 0.07) - n is the number of periods: 4

Compare the present values and make decision

Comparison of the present values of the two options will determine if it's more economical to invest in software or hire clerks. If the PV of the software cost is less than the PV of the clerks' salary, then it would be better to buy the software. Otherwise, it's more economical to hire the clerks. For parts (b), (c) and (d) of the exercise, repeat Steps 1, 2 and 3 while adjusting the respective variables as described in each part - the interest rate, the software cost, and the software's years of validity.

Key concepts

Cost-Benefit Analysis

When it comes to business decisions, cost-benefit analysis (CBA) is a systematic process to calculate the strengths and weaknesses of alternatives. It is used to determine options that provide the best approach to achieve benefits while preserving savings. For example, in deciding whether to purchase new software or to hire more staff, a company would estimate the costs associated with both options and the benefits they would generate over time.

A cost-benefit analysis involves enumerating and evaluating all the costs involved in a project and comparing them with the anticipated benefits, both expressed in monetary terms. When carrying out a CBA, you would typically:

• List all the project expenses and savings over a period.
• Estimate the benefits of each action.
• Compare the total expected costs against the total expected benefits.
• Decide which option offers the greatest net benefit at the least cost.

In the provided textbook exercise, the analysis begins by calculating the present value of both scenarios: investing in software against the hiring of two new employees. Presenting costs and benefits in present value terms is crucial because it accounts for the time value of money, ensuring that dollars are compared on a 'like for like' basis across different time periods.

Time Value of Money

The concept of the time value of money (TVM) is a fundamental principle in finance that asserts money available now is worth more than the same amount in the future due to its potential earning capacity. This core principle is the basis for investment analysis, decision-making and long-term financial planning. It reflects the opportunity cost of foregone alternatives, making it essential for understanding the benefits of investing.

To quantify the time value of money, various formulas can be used to calculate the present value (PV) or future value (FV) of cash flows occurring at different times. The present value indicates how much a future sum of money is worth today, given a certain interest rate, and involves discounting future cash flows to the present. This is crucial in our exercise when assessing the four-year impact of spending on software versus hiring personnel.

The formula \[PV = \frac{FV}{(1 + r)^n}\] is used to discount a future value, where \(r\) is the interest rate and \(n\) is the number of periods until payment. Higher rates or longer periods reduce the present value, showing that money in the future is less valuable than money today.

Investment Appraisal

Investment appraisal is the evaluation of the profitability and financial viability of a proposed investment. There are several techniques used to assess the value of an investment, such as net present value (NPV), internal rate of return (IRR), payback period, and profitability index. These methods help analysts and investors determine whether an investment will yield a satisfactory return, taking into account factors like the cost of capital and risk.

Present value analysis, an integral part of investment appraisal, was demonstrated in the exercise by comparing the present value of software costs against the present value of hiring additional staff. This assessment is made to decide which option is more financially beneficial over a given period. By considering the investment's cash flows, the cost of capital, and the expected lifespan of the investment, decision-makers can use investment appraisal techniques to make well-informed choices.

In scenarios like those presented in the exercise—where variables such as the interest rate and the time horizon change—it's crucial to reassess the investment using the appropriate appraisal techniques to ensure the decision remains economically sound with the new parameters. This vigilance ensures the optimal allocation of resources for the highest financial return.