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Chapter 6: Problem 18

Cash Flow Valuation Phillips Industries runs a small manufacturing operation. For this fiscal year, it expects real net cash flows of \(\$ 155,000\). Phillips is an ongoing operation, but it expects competitive pressures to erode its real net cash flows at 5 percent per year in perpetuity. The appropriate real discount rate for Phillips is 11 percent. All net cash flows are received at year-end. What is the present value of the net cash flows from Phillips's operations?

Short Answer

Expert verified
The present value of the net cash flows from Phillips's operations is \(\$968,750\) using the present value of perpetuity formula with growth, given a discount rate of 11% and a constant growth rate of -5%.

Step by step solution

01

Calculate the constant growth rate of cash flows

As the cash flows erode by 5% each year, the constant growth rate (g) is -5%.
02

Identify the discount rate

The exercise states that the real discount rate is 11%, so we will use this as the discount rate (r) in our calculations.
03

Calculate the present value of the perpetuity

We will now use the present value of perpetuity formula with growth to calculate the present value of Phillips's net cash flows: PV = \(\frac{CF_1}{r-g}\) Here, PV is the present value, CF_1 is the cash flow for the first year, r is the discount rate, and g is the constant growth rate. Plugging in the values, we get: PV = \(\frac{\$155,000}{0.11-(-0.05)}\)
04

Solve for PV

Now we can solve for PV: PV = \(\frac{\$155,000}{0.16}\) PV = \(\$ 968,750\) The present value of the net cash flows from Phillips's operations is \(\$968,750\).

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Key Concepts

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

Discount Rate
The discount rate is a pivotal component in cash flow valuation, influencing how future cash values are perceived today. It serves as a measure of the risk associated with future cash flows and the return required by investors. In our exercise, Phillips Industries uses a discount rate of 11%. This rate considers factors like inflation and investment risk, capturing the time value of money. A higher discount rate indicates greater uncertainty, whereas a lower one suggests a more secure investment. Understanding the discount rate is essential as it determines how cash flows are adjusted back to their present values.
Perpetuity
Perpetuity refers to a series of cash flows that continue indefinitely. In the context of Phillips Industries, their cash flows are expected to persist forever, despite decreasing by a certain percentage each year. Calculating the value of perpetuity involves assessing these endless cash flows and is useful in determining valuations for firms with predictable, ongoing operations. For Phillips, perpetuity means their cash flows will never cease, but they will diminish over time at a specified rate due to competitive pressures.
Growth Rate
The growth rate in this scenario is negative, indicating shrinking cash flows over time. For Phillips Industries, the growth rate is estimated at -5%, reflecting a decline due to market competition. This rate affects the present value calculation by reducing the future cash flow valuations. Understanding growth rates, whether positive or negative, helps in predicting how cash flows evolve, impacting the valuation and financial planning of businesses.
Present Value
Present value (PV) represents the current worth of future cash flows, considering the discount rate and growth rate. It allows businesses to assess the 'today's value' of expected finances. For Phillips Industries, the PV was calculated using the formula for a growing perpetuity: \[PV = \frac{CF_1}{r-g}\]In this case, with an expected cash flow of \(\\(155,000\), a discount rate of 11%, and a growth rate of -5%, the PV results in \(\\)968,750\). This computation is crucial for investment assessments, ensuring resources are allocated toward profitable ventures.
Net Cash Flows
Net cash flows are the actual funds available to a business after accounting for all operating expenses, taxes, and capital expenses. For Phillips Industries, the starting point for valuing cash flows was the projected net cash flow of \(\$155,000\). Estimating net cash flows accurately helps firms plan their finances, make investment decisions, and manage liquidity. In valuation terms, net cash flows represent the lifeblood of a company's operations, giving insight into its financial health and potential growth.

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Most popular questions from this chapter

Project Evaluation Dog Up! Franks is looking at a new sausage system with an installed cost of \(\$ 420,000\). This cost will be depreciated straight-line to zero over the project's five-year life, at the end of which the sausage system can be scrapped for \(\$ 60,000\). The sausage system will save the firm \(\$ 135,000\) per year in pretax operating costs, and the system requires an initial investment in net working capital of \(\$ 28,000\). If the tax rate is 34 percent and the discount rate is 10 percent, what is the NPV of this project?

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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?

Calculating a Bid Price Your company has been approached to bid on a contract to sell 9,000 voice recognition (VR) computer keyboards a year for four years. Due to technological improvements, beyond that time they will be outdated and no sales will be possible. The equipment necessary for the production will cost \(\$ 3.2\) million and will be depreciated on a straight-line basis to a zero salvage value. Production will require an investment in net working capital of \(\mathbf{\$ 7 5 , 0 0 0}\) to be returned at the end of the project, and the equipment can be sold for \(\$ 200,000\) at the end of production. Fixed costs are \(\$ 600,000\) per year, and variable costs are \(\$ 165\) per unit. In addition to the contract, you feel your company can sell \(4,000,12,000,14,000\), and 7,000 additional units to companies in other countries over the next four years, respectively, at a price of \(\$ 275\). This price is fixed. The tax rate is 40 percent, and the required return is 13 percent. Additionally, the president of the company will undertake the project only if it has an NPV of \(\$ 100,000\). What bid price should you set for the contract?

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?
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