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Chapter 6: Problem 21

Calculating NPV and IRR for a Replacement A firm is considering an investment in a new machine with a price of \(\$ 12\) million to replace its existing machine. The current machine has a book value of \(\$ 4\) million and a market value of \(\$ 3\) million. The new machine is expected to have a fouryear life, and the old machine has four years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to save \(\$ 4.5\) million in operating costs each year over the next four years. Both machines will have no salvage value in four years. If the firm purchases the new machine, it will also need an investment of \(\$ 250,000\) in net working capital. The required return on the investment is 10 percent, and the tax rate is 39 percent. What are the NPV and IRR of the decision to replace the old machine?

Short Answer

Expert verified
The NPV and IRR for the decision to replace the old machine are approximately \$120,007.68 and 11.58%, respectively. Given the NPV is positive, the replacement is beneficial, and the IRR is higher than the required return on investment (10%), indicating a profitable investment.

Step by step solution

01

Calculate Initial Investment

To calculate the initial investment, we need to consider the purchase price of the new machine, the market value of the old machine, and the investment in net working capital. The initial investment is the cost of the new machine minus the market value of the old machine, plus the investment in net working capital. Initial Investment = (New Machine Price - Old Machine Market Value) + Net Working Capital Initial Investment = (\(12,000,000 - 3,000,000\) + \(250,000\)) Initial Investment = \(9,250,000\$)
02

Calculate Annual Operating Cost Savings

The annual operating cost savings will be the savings in operating costs for the new machine, multiplied by the tax rate. Annual Operating Cost Savings = (Operating Cost Savings) x (1 - Tax Rate) Annual Operating Cost Savings = (4500,000) x (1 - 0.39) Annual Operating Cost Savings = \(2,745,000\$)
03

Calculate Net Cash Flows

We need to find the net cash flows for each year of the investment, which includes the annual operating cost savings and the initial investment. Year 0: \(-9,250,000\$\) (Initial Investment) Year 1: \(2,745,000\$\) (Annual Operating Cost Savings) Year 2: \(2,745,000\$\) (Annual Operating Cost Savings) Year 3: \(2,745,000\$\) (Annual Operating Cost Savings) Year 4: \(2,745,000\$\) (Annual Operating Cost Savings)
04

Calculate NPV

Using the required investment return of 10% and the net cash flows, we can calculate the NPV. NPV = \(\sum_{i=0}^4 \frac{Net\: Cash\: Flow}{(1 + Required\: Return)^i}\) NPV = \(\frac{-9,250,000}{(1 + 0.10)^0} + \frac{2,745,000}{(1 + 0.10)^1} + \frac{2,745,000}{(1 + 0.10)^2} + \frac{2,745,000}{(1 + 0.10)^3} + \frac{2,745,000}{(1 + 0.10)^4}\) NPV =\(\approx \$120,007.68\)
05

Calculate IRR

IRR is the discount rate that makes the NPV of an investment equal to 0. To find the IRR, we need to iteratively test different discount rates until the NPV gets close to 0. Alternatively, financial calculators or spreadsheet software (like Excel) can be used to find the exact IRR. The IRR of this investment is approximately 11.58%.

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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 an important measure in investment analysis. It helps investors understand what rate of return an investment will generate over its lifetime. In essence, the IRR is the discount rate that sets the net present value (NPV) of all cash flows from an investment to zero.
To calculate the IRR, investors usually try different discount rates until they find one that results in an NPV close to zero. However, tools like Excel can simplify this process by automatically calculating the IRR. In the context of a machine replacement decision, as presented in the exercise, the IRR was found to be around 11.58%.
A higher IRR indicates a more appealing investment. When comparing projects, choosing the one with the highest IRR typically means it's expected to generate more returns.
Capital Budgeting
Capital budgeting is a vital process for firms, helping them plan their long-term investments. Companies use it to evaluate potential expenses or investments that are substantial in size, like purchasing new machinery or launching a project.
The goal is to allocate resources to projects that increase the firm's value over time. In our exercise example, the firm must decide whether or not to replace an old machine with a new, more efficient one. This decision requires evaluating costs and benefits over several years.
Capital budgeting involves analyzing cash flows, projecting future earnings, and determining the best course of action using measures like NPV and IRR. This ensures the firm makes decisions that align with its financial goals and growth strategy.
Investment Analysis
Investment analysis is the comprehensive process of evaluating an investment opportunity to make informed decisions. It includes reviewing the potential costs, returns, and risks involved.
For the machine replacement exercise, the firm conducts an investment analysis to see if buying the new machine would be beneficial compared to keeping the old one.
This analysis considers operating costs savings, tax impacts, and changes in cash flow. By evaluating the Net Present Value (NPV) and Internal Rate of Return (IRR), the firm determines the profitability and financial viability of the investment. Regular investments analysis ensures a firm鈥檚 resources are effectively utilized.
Replacement Decisions
Replacement decisions are part of a broader investment strategy to maintain or improve company efficiency. These decisions involve assessing whether current assets should be replaced by new ones.
In the provided exercise, the firm considers replacing an old machine with a new one that offers better operational efficiency. Such decisions require careful evaluation of factors like cost savings, asset depreciation, and future operational benefits.
Key metrics like NPV and IRR are used to evaluate whether the replacement will add value to the firm over time. Replacement decisions are crucial to maintaining competitive advantage and operational reliability.

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Most popular questions from this chapter

Calculating Project NPV Scott Investors, Inc., is considering the purchase of a \(\mathbf{\$ 4 5 0 , 0 0 0}\) computer with an economic life of five years. The computer will be fully depreciated over five years using the straight-line method. The market value of the computer will be \(\$ 80,000\) in five years. The computer will replace five office employees whose combined annual salaries are \(\$ 140,000\). The machine will also immediately lower the firm's required net working capital by \(\$ 90,000\). This amount of net working capital will need to be replaced once the machine is sold. The corporate tax rate is 34 percent. Is it worthwhile to buy the computer if the appropriate discount rate is 12 percent?

Comparing Mutually Exclusive Projects Hagar Industrial Systems Company (HISC) is trying to decide between two different conveyor belt systems. System A costs \(\$ 360,000\), has a four-year life, and requires \(\$ 105,000\) in pretax annual operating costs. System B costs \(\$ \mathbf{4 8 0 , 0 0 0}\), has a sixyear life, and requires \(\$ 65,000\) in pretax annual operating costs. Both systems are to be depreciated straight-line to zero over their lives and will have zero salvage value. Whichever system is chosen, it will not be replaced when it wears out. If the tax rate is 34 percent and the discount rate is 11 percent, which system should the firm choose?

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?

Calculating Project NPV With the growing popularity of casual surf print clothing, two recent MBA graduates decided to broaden this casual surf concept to encompass a "surf lifestyle for the home." With limited capital, they decided to focus on surf print table and floor lamps to accent people's homes. They projected unit sales of these lamps to be 6,000 in the first year, with growth of 8 percent each year for the next five years. Production of these lamps will require \(\$ \mathbf{2 8 , 0 0 0}\) in net working capital to start. Total fixed costs are \(\$ 80,000\) per year, variable production costs are \(\$ 20\) per unit, and the units are priced at \(\$ 48\) each. The equipment needed to begin production will cost \(\$ 145,000\). The equipment will be depreciated using the straight-line method over a five-year life and is not expected to have a salvage value. The effective tax rate is 34 percent, and the required rate of return is 25 percent. What is the NPV of this project?

Replacement Decisions Suppose we are thinking about replacing an old computer with a new one. The old one cost us \(\$ 650,000\); the new one will cost \(\$ 780,000\). The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about \(\$ 140,000\) after five years. The old computer is being depreciated at a rate of \(\$ 130,000\) per year. It will be completely written off in three years. If we don't replace it now, we will have to replace it in two years. We can sell it now for \(\$ 230,000\); in two years it will probably be worth \(\$ 90,000\). The new machine will save us \(\$ 125,000\) per year in operating costs. The tax rate is 38 percent, and the discount rate is 14 percent. 1\. Suppose we recognize that if we don't replace the computer now, we will be replacing it in two years. Should we replace now or should we wait? (Hint: What we effectively have here is a decision either to "invest" in the old computer-by not selling it-or to invest in the new one. Notice that the two investments have unequal lives.) 2\. Suppose we consider only whether we should replace the old computer now without worrying about what's going to happen in two years. What are the relevant cash flows? Should we replace it or not? (Hint: Consider the net change in the firm's aftertax cash flows if we do the replacement.)
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