91Ó°ÊÓ

Calculating Project NPV J. Smythe, Inc., manufactures fine furniture. The company is deciding whether to introduce a new mahogany dining room table set. The set will sell for \(\$ 5,600\), including a set of eight chairs. The company feels that sales will be 1,800, 1,950, 2,500, 2,350, and 2,100 sets per year for the next five years, respectively. Variable costs will amount to 45 percent of sales, and fixed costs are \(\$ 1.9\) million per year. The new tables will require inventory amounting to 10 percent of sales, produced and stockpiled in the year prior to sales. It is believed that the addition of the new table will cause a loss of 250 tables per year of the oak tables the company produces. These tables sell for \(\$ 4,500\) and have variable costs of 40 percent of sales. The inventory for this oak table is also 10 percent of sales. J. Smythe currently has excess production capacity. If the company buys the necessary equipment today, it will cost \(\$ 16\) million. However, the excess production capacity means the company can produce the new table without buying the new equipment. The company controller has said that the current excess capacity will end in two years with current production. This means that if the company uses the current excess capacity for the new table, it will be forced to spend the \(\$ 16\) million in two years to accommodate the increased sales of its current products. In five years, the new equipment will have a market value of \(\$ 3.1\) million if purchased today, and \(\$ 7.4\) million if purchased in two years. The equipment is depreciated on a seven-year MACRS schedule. The company has a tax rate of 40 percent, and the required return for the project is 14 percent. 1\. Should J. Smythe undertake the new project? 2\. Can you perform an IRR analysis on this project? How many IRRs would you expect to find? 3\. How would you interpret the profitability index?

Step by step solution

01

Calculate Operating Cash Flows (OCF)

The operating cash flows will include revenues, variable costs, fixed costs, and tax savings from depreciation. Yearly Revenue from Mahogany Table: Revenue per table (5600) * Number of tables sold Variable Cost of Mahogany Table: Variable cost percent (45%) * Revenue Fixed Costs: 1.9 million Loss of Oak Table Revenue: Loss of Oak sales (250) * Oak table selling price (4500) Increased Oak Table Costs: Loss of Oak sales (250) * Oak table cost percentage (40%) * Oak table selling price (4500) Depreciation : We are given depreciation is on 7-year MACRS schedule. We can look up MACRS depreciation ratios for 7-year property and multiply by the equipment cost. Tax Savings from Depreciation: Depreciation * Tax rate (40%) Operating Cash Flows (OCF) each year = (Revenue from Mahogany Table - Loss of Oak Table Revenue - Variable Cost of Mahogany Table + Increased Oak Table Costs - Fixed Costs + Tax Savings from Depreciation) * (1 - Tax Rate)

02

Calculate working capital changes

Calculate the working capital changes for both the mahogany and oak tables. Mahogany Table Inventory change = 10% of mahogany table sales Oak Table Inventory change: -10% of 250 oak table loss Net working capital change = Mahogany table inventory change + Oak table inventory change

03

Calculate initial investments and terminal cash flows

If the equipment is purchased today, its initial investment cost is $16 million, and its terminal cash flow is the after-tax salvage value in year 5. Alternatively, if the equipment is purchased in two years, the initial investment is delayed, and its terminal cash flow has a higher after-tax salvage value. Calculate the terminal cash flows for both cases.

04

Calculate NPV, IRR, and profitability index

Calculate the Net Present Value (NPV) as the sum of the present values of operating cash flows, changes in working capital, and initial investments at the given required return (14%). Perform the IRR analysis by finding the discount rate(s) that makes the NPV zero. Note any expected multiple internal rates of return. Calculate the profitability index as the ratio of the present value of future cash flows and the initial investment. Interpret the results.

05

Conclusion

Based on the NPV and IRR analyses, determine if J. Smythe should undertake the new project. Answer the remaining questions related to IRR and profitability index interpretation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Internal Rate of Return (IRR)

The Internal Rate of Return (IRR) is a critical metric in capital budgeting that indicates the profitability of potential investments. It is the interest rate at which the net present value (NPV) of all the cash flows (both positive and negative) from a project or investment equals zero. The IRR can be thought of as the break-even interest rate, beyond which an investment makes a profit, and below which it encounters a loss.

When we perform an IRR analysis, we are essentially searching for the rates that balance the initial investment with the present value of future cash flows. This is accomplished by iterating different discount rates until the NPV is zero. Often, there could be multiple IRRs when the cash flow stream of a project changes direction more than once, that is, from positive to negative and vice versa. This is quite common in projects with alternating investment phases and cost savings over time.

A project with multiple IRRs can be a challenging scenario for decision-making. This is because it's unclear which IRR should be used as the benchmark. In such cases, a modified internal rate of return (MIRR) can provide a clearer picture as it assumes reinvestment at the project's cost of capital rather than the IRR. It is crucial to compare the IRR to the company's required rate of return or hurdle rate. If the IRR exceeds this hurdle rate, the project may be considered viable assuming all other factors are favorable.

Profitability Index

The Profitability Index (PI) is another tool used in capital budgeting to evaluate the desirability of an investment or project. It is calculated by dividing the present value of future cash flows generated by the project by the initial investment required for the project. Essentially, it is a ratio that tells an investor how much bang for their buck they are getting from an investment.

The formula for the Profitability Index is represented as:\[ \text{Profitability Index (PI)} = \frac{\text{Present Value of Future Cash Flows}}{\text{Initial Investment}} \]

A profitability index of 1 indicates a break-even point. Any value lower than 1 suggests that the project's NPV is negative, and it's not financially viable. On the other hand, a value greater than 1 implies that the project is expected to generate value, making it a potential investment to consider. Investors and management often use the PI to rank projects, especially when capital is limited, focusing on projects with the highest PI as those are perceived to yield the most value per unit of investment.

Capital Budgeting

Capital budgeting is the process that companies use to evaluate which long-term investments or projects they should undertake, based on their potential to generate positive returns over time. It involves estimating future cash flows from the investment, analyzing the risks involved, and considering the funding sources and the cost of capital.

In our given scenario, J. Smythe, Inc. is involved in capital budgeting as they decide whether to invest in a new mahogany dining room table set. The decision process includes detailed analysis using various methods like NPV, IRR, and the Profitability Index. It's crucial, especially in capital-intensive industries, to accurately forecast cash flows and assess equipment purchases, as these decisions can have significant long-term financial effects.

Other factors such as market trends, the competitive landscape, and the strategic fit of the project within the company's broader goals are also considered. Since capital budgeting decisions have long-term implications and are often irreversible or costly to undo, they require careful and thorough evaluation.