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Chapter 6: Problem 26

EAC and Inflation Office Automation, Inc., must choose between two copiers, the XX40 or the RH45. The XX40 costs \(\$ 1,500\) and will last for three years. The copier will require a real aftertax cost of \(\$ 120\) per year after all relevant expenses. The RH45 costs \(\$ 2,300\) and will last five years. The real aftertax cost for the RH45 will be \(\$ 150\) per year. All cash flows occur at the end of the year. The inflation rate is expected to be 5 percent per year, and the nominal discount rate is 14 percent. Which copier should the company choose?

Short Answer

Expert verified
The company should choose the XX40 copier model, as its present value of costs (\(-\$1396.17\)) is less than the RH45 copier's present value of costs (\(-\$2188.31\)).

Step by step solution

01

Find the real discount rate.

To calculate the real discount rate, use the formula \( (1 + r) = (1 + i) \cdot (1 + \rho) \), with i = 0.14 (14% nominal discount rate) and 蟻 = 0.05 (5% inflation rate). \( (1 + r) = (1 + 0.14) \cdot (1 + 0.05) \) \( 1 + r = 1.14 \cdot 1.05 \) \( 1 + r = 1.197 \) \( r = 0.197 \) The real discount rate is 19.7%.
02

Calculate the present value of the costs of each copier.

We'll use the formula: \( PV = \sum_{t=1}^n \frac{CF_t}{(1+r)^t} \), where PV is the present value, CF_t is the cash flow at time t, and n is the number of years. For the XX40 copier: Cash flows: \(-\$1500, -\$120,-\$120,-\$120\) PV = \(\frac{-1500}{(1+0.197)^1} + \frac{-120}{(1+0.197)^2} + \frac{-120}{(1+0.197)^3}\) PV = \(-\frac{1500}{1.197} - \frac{120}{1.197^2} - \frac{120}{1.197^3}\) PV = \(-\$1253.13 - \$84.10 - \$58.94\) PV = \(-\$1396.17\) For the RH45 copier: Cash flows: \(-\$2300, -\$150,-\$150,-\$150,-\$150,-\$150\) PV = \(\frac{-2300}{(1+0.197)^1} + \frac{-150}{(1+0.197)^2} + \frac{-150}{(1+0.197)^3} + \frac{-150}{(1+0.197)^4} + \frac{-150}{(1+0.197)^5}\) PV = \(-\frac{2300}{1.197} - \frac{150}{1.197^2} - \frac{150}{1.197^3} - \frac{150}{1.197^4} - \frac{150}{1.197^5}\) PV = \(-\$1922.22 - \$105.08 - \$73.48 - \$51.46 - \$36.07\) PV = \(-\$2188.31\)
03

Compare the present values and decide.

Now that we have the present values of the costs for both copiers: XX40: \(-\$1396.17\) RH45: \(-\$2188.31\) Since the present value of the costs for the XX40 copier is less than the present value of the costs for the RH45 copier, the company should choose the XX40 model.

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Key Concepts

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

Real Discount Rate
The real discount rate is an essential concept in evaluating future cash flows, as it adjusts the nominal discount rate for inflation. This allows us to understand the true cost of borrowing when inflation is considered. While the nominal discount rate might look impressive at first glance, including inflation gives a more accurate picture of profitability. The formula to calculate the real discount rate is:
  • \[ (1 + r) = (1 + i) \cdot (1 + \rho) \]
Here:
  • \( r \) is the real discount rate,
  • \( i \) is the nominal discount rate,
  • \( \rho \) is the inflation rate.
In the example given, with a nominal discount rate of 14% and an inflation rate of 5%, the real discount rate calculates to 19.7%.
This rate reflects the actual purchasing power and cost of funds for the company, informing better financial decision-making.
Cash Flows
In financial analysis, cash flows are the money transfer predicted over a certain period received or spent. They are crucial because they represent the incremental cash impact of one choice over another. For our copier decision, cash flows include the initial purchase costs and ongoing maintenance expenses. Both copiers have different cash flow profiles. The XX40 incurs lower annual aftertax costs and fewer years of expenses compared to the RH45.
This breaks down as follows:
  • XX40: Initial cost of \(-\\(1500\) and annual costs of \(-\\)120\) for three years.
  • RH45: Initial cost of \(-\\(2300\) and annual costs of \(-\\)150\) for five years.
These cash flows are then discounted using the real discount rate, making the present value comparison straightforward. In this case, it helps the company determine which option is cheaper in today's terms.
Nominal Discount Rate
The nominal discount rate represents the overall cost of funds without adjusting for inflation. It's critical in valuing future cash flows in today's terms, but it doesn't account for the diminishing purchasing power due to inflation. Often, it鈥檚 used initially to gauge the feasibility of a project.
  • This is the rate of return required before considering inflation effects, listed as 14% in the example.
Using this rate, we can calculate the undiscounted future cash flows. However, only after adjusting this rate for inflation, we get the real discount rate, providing more meaningful insights into cash-flow analysis and investment decisions.
Thus, while it鈥檚 a necessary starting point, full analysis needs the real discount rate to obtain accurate results.
Inflation Rate
Inflation rate measures the rate at which general level of prices for goods and services rises over time, eroding purchasing power. It鈥檚 a critical factor in investment decisions as it affects the value of future cash flows. In the copier exercise, a 5% inflation rate was considered.
  • As inflation increases, the nominal dollar amount of cash flows doesn't alter, but its real value decreases.
  • Thus, normalizing cash flows via inflation adjusted discount rates ensures comparisons are in the same purchasing power terms.
By factoring the inflation rate into the discount rate calculation, we adjust the nominal rate to reflect true economic costs and benefits. Without this adjustment, we risk over- or underestimating the value of future cash flows that inflation can erode.

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Most popular questions from this chapter

Project Analysis and Inflation Dickinson Brothers, Inc., is considering investing in a machine to produce computer keyboards. The price of the machine will be \(\$ 530,000\), and its economic life is five years. The machine will be fully depreciated by the straight-line method. The machine will produce 15,000 keyboards each year. The price of each keyboard will be \(\$ 40\) in the first year and will increase by 5 percent per year. The production cost per keyboard will be \(\$ 20\) in the first year and will increase by 6 percent per year. The project will have an annual fixed cost of \(\$ 75,000\) and require an immediate investment of \(\$ \mathbf{2 5 , 0 0 0}\) in net working capital. The corporate tax rate for the company is 34 percent. If the appropriate discount rate is 15 percent, what is the NPV of the investment?

Calculating NPV Howell Petroleum is considering a new project that complements its existing business. The machine required for the project costs \(\$ 1.8\) million. The marketing department predicts that sales related to the project will be \(\$ 1.1\) million per year for the next four years, after which the market will cease to exist. The machine will be depreciated down to zero over its fouryear economic life using the straight-line method. Cost of goods sold and operating expenses related to the project are predicted to be 25 percent of sales. Howell also needs to add net working capital of \(\$ 150,000\) immediately. The additional net working capital will be recovered in full at the end of the project's life. The corporate tax rate is 35 percent. The required rate of return for Howell is 16 percent. Should Howell proceed with the project?

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 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?

Project Analysis Benson Enterprises is evaluating alternative uses for a three-story manufacturing and warehousing building that it has purchased for \(\$ 850,000\). The company can continue to rent the building to the present occupants for \(\$ 36,000\) per year. The present occupants have indicated an interest in staying in the building for at least another 15 years. Alternatively, the company could modify the existing structure to use for its own manufacturing and warehousing needs. Benson's production engineer feels the building could be adapted to handle one of two new product lines. The cost and revenue data for the two product alternatives are as follows: The building will be used for only 15 years for either product \(A\) or product \(B\). After 15 years the building will be too small for efficient production of either product line. At that time, Benson plans to rent the building to firms similar to the current occupants. To rent the building again, Benson will need to restore the building to its present layout. The estimated cash cost of restoring the building if product \(A\) has been undertaken is \(\$ \mathbf{2 9}, 000\). If product \(B\) has been manufactured, the cash cost will be \(\$ 35,000\). These cash costs can be deducted for tax purposes in the year the expenditures occur. Benson will depreciate the original building shell (purchased for \(\$ \mathbf{8 5 0 , 0 0 0}\) ) over a 30 -year life to zero, regardless of which alternative it chooses. The building modifications and equipment purchases for either product are estimated to have a 15-year life. They will be depreciated by the straight-line method. The firm's tax rate is 34 percent, and its required rate of return on such investments is 12 percent. For simplicity, assume all cash flows occur at the end of the year. The initial outlays for modifications and equipment will occur today (year 0 ), and the restoration outlays will occur at the end of year 15. Benson has other profitable ongoing operations that are sufficient to cover any losses. Which use of the building would you recommend to management?
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