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Chapter 7: Problem 4

Financial Breakeven L.J.'s Toys Inc. just purchased a \(\mathbf{\$ 2 5 0 , 0 0 0}\) machine to produce toy cars. The machine will be fully depreciated by the straight-line method over its five-year economic life. Each toy sells for \(\$ 25\). The variable cost per toy is \(\$ 6\), and the firm incurs fixed costs of \(\$ 360,000\) each year. The corporate tax rate for the company is 34 percent. The appropriate discount rate is 12 percent. What is the financial break-even point for the project?

Short Answer

Expert verified
The financial break-even point for L.J.'s Toys Inc. is calculated in several steps: determining the depreciation of the machine, calculating total costs, total income before tax, taxable income and tax, net income after tax, and present value of the net income after tax. The equation for the financial break-even point is: \(\sum^{5}_{t=1}\dfrac{[(19Q - \$410,000) - 0.34(19Q - \$410,000)]}{(1+0.12)^t}=0\) Solving for Q will provide the financial break-even point for the project in terms of the number of toys produced.

Step by step solution

01

Calculate Depreciation

First, we need to find the annual depreciation of the machine. Depreciation is calculated as: \(Depreciation = \dfrac{Cost\:of\:Machine}{Economic\:Life}\) \(Depreciation = \dfrac{\$250,000}{5}\) Depreciation is $50,000 per year.
02

Calculate Total Costs

Let's now calculate the yearly total costs, which consist of fixed costs, variable costs, and depreciation. Total Costs = Fixed Costs + Variable Costs + Depreciation Variable Costs for each toy are \(6, so we will multiply \)6 by the number of toys produced, denoted as 'Q'. Total Costs = \(360,000 + 6Q + \)50,000 Total Costs = $410,000 + 6Q
03

Calculate Total Income Before Tax

We'll now calculate the total income before tax. Each toy is sold for $25, so the total income before tax will be: Total Income Before Tax = 25Q
04

Calculate Taxable Income and Tax

In this step, we will calculate the taxable income and the corporate tax. The taxable income is the difference between the total income before tax and the total costs: Taxable Income = Total Income Before Tax 鈥� Total Costs Taxable Income = 25Q - ($410,000 + 6Q) Taxable Income = 19Q 鈥� $410,000 The corporate tax rate is 34%, so the tax will be: Tax = 0.34 x (Taxable Income) = 0.34 x (19Q - $410,000)
05

Calculate Net Income After Tax

Next, we will calculate the net income after tax as follows: Net Income After Tax = Taxable Income - Tax Net Income After Tax = (19Q - \(410,000) - 0.34(19Q - \)410,000)
06

Calculate Present Value of Net Income After Tax

Using the discount rate of 12%, calculate the present value of net income after tax for each year: Present Value of Net Income After Tax = \(\dfrac{\text{Net Income After Tax}}{(1 + Discount\:Rate)^{t}}\) (where t is the year)
07

Find the Financial Break-even Point

The financial break-even point is the number of toys, Q, which will result in a present value of net income after tax equal to zero: \(\sum^{5}_{t=1}\dfrac{[(19Q - \$410,000) - 0.34(19Q - \$410,000)]}{(1+0.12)^t}=0\) Now, we must solve for Q to find the financial break-even point for the project. This may require a numerical method, like the Newton-Raphson method or using a financial calculator or spreadsheet software. After finding the value of Q, we will have the financial break-even point for L.J.'s Toys Inc.

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Key Concepts

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

Depreciation Calculation
Understanding depreciation is crucial when considering the costs of a long-term asset. Depreciation represents the allocation of the cost of an asset over its useful life. For L.J.'s Toys Inc., the new machine worth \(250,000 is depreciated using the straight-line method, which means the same amount is expensed annually.

The formula for straight-line depreciation is:
Depreciation = \(\dfrac{Cost\:of\:Machine}{Economic\:Life}\)
So, for the toy company, the annual depreciation would be \)50,000 per year over its five-year life span. This yearly deduction affects the taxable income, which in turn influences the company's net income after taxes.
Fixed and Variable Costs
The financial health of a company depends on how well it manages its costs. Fixed costs, such as the yearly \(360,000 L.J.'s Toys Inc. commits to, do not fluctuate with production levels. In contrast, variable costs (\)6 per toy) scale directly with the quantity of output.

Understanding fixed versus variable costs is vital for calculating break-even points and making strategic business decisions. It's the combination of these costs, plus the depreciation, that forms the total expense of the company, which is then set against revenue to determine profitability.
Taxable Income Computation
Taxable income is a critical figure, as it dictates the tax liability of a business. It's calculated by subtracting all allowable expenses from the revenue. In the provided exercise, the formula for taxable income of L.J.'s Toys Inc. is:
Taxable Income = Total Income Before Tax 鈥� Total Costs
Given that the total costs include fixed costs, variable costs, and depreciation, and the total income before tax is generated from sales revenue ($25 per toy), the difference represents the amount on which the company must pay taxes. This calculation directly impacts the net income after tax.
Net Income After Tax
Net income after tax is the amount of money a company retains after paying all its taxes. It's a decisive measure of profitability. For L.J.'s Toys Inc., one needs to apply the corporate tax rate which stands at 34% to the taxable income, to derive the taxes owed. The subsequent deduction from the taxable income results in the net income after tax:
Net Income After Tax = Taxable Income - Tax
This figure is particularly crucial for stakeholders as it affects reinvestment, dividend distribution, and it also serves as an indicator of financial performance.
Present Value of Net Income
Evaluating the present value of future net income allows a company like L.J.'s Toys Inc. to understand the value of money over time, considering a specific rate of return or discount rate. The discount rate used by L.J.'s Toys Inc. is 12%, which reflects the company's cost of capital and inflation expectations.
The present value is calculated by discounting the net income after tax for each year by the discount rate. This calculation assists in identifying the break-even point, which is the quantity of product output required to achieve a present value of net income after tax of zero - a critical metric for long-term financial planning.

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Most popular questions from this chapter

Sensitivity Analysis Consider a four-year project with the following information: Initial fixed asset investment \(=\mathbf{\$ 3 8 0 , 0 0 0}\); straight-line depreciation to zero over the four-year life; zero salvage value; price \(=\$ 54\); variable costs \(=\$ 42 ;\) fixed costs \(=\$ 185,000\); quantity sold \(=90,000\) units; tax rate \(=34\) percent. How sensitive is OCF to changes in quantity sold?

Financial Break-Even Analysis You are considering investing in a company that cultivates abalone for sale to local restaurants. Use the following information: The discount rate for the company is 15 percent, the initial investment in equipment is \(\$ 360,000\), and the project's economic life is seven years. Assume the equipment is depreciated on a straight-line basis over the project's life. 1\. What is the accounting break-even level for the project? 2\. What is the financial break-even level for the project?

Abandonment Decisions Consider the following project for Hand Clapper, Inc. The company is considering a four-year project to manufacture clap-command garage door openers. This project requires an initial investment of \(\$ 10\) million that will be depreciated straight-line to zero over the project's life. An initial investment in net working capital of \(\$ 1.3\) million is required to support spare parts inventory; this cost is fully recoverable whenever the project ends. The company believes it can generate \(\$ 7.35\) million in pretax revenues with \(\$ 2.4\) million in total pretax operating costs. The tax rate is 38 percent, and the discount rate is 16 percent. The market value of the equipment over the life of the project is as follows: 1\. Assuming Hand Clapper operates this project for four years, what is the NPV? 2\. Now compute the project NPVs assuming the project is abandoned after only one year, after two years, and after three years. What economic life for this project maximizes its value to the firm? What does this problem tell you about not considering abandonment possibilities when evaluating projects?

Financial Breakeven The Cornchopper Company is considering the purchase of a new harvester. Cornchopper has hired you to determine the break-even purchase price in terms of present value of the harvester. This break-even purchase price is the price at which the project's NPV is zero. Base your analysis on the following facts: \- The new harvester is not expected to affect revenues, but pretax operating expenses will be reduced by \(\$ 12,000\) per year for 10 years. \- The old harvester is now 5 years old, with 10 years of its scheduled life remaining. It was originally purchased for \(\$ 50,000\) and has been depreciated by the straight-line method. \- The old harvester can be sold for \(\$ 18,000\) today. \- The new harvester will be depreciated by the straight-line method over its 10-year life. \- The corporate tax rate is 34 percent. \- The firm's required rate of return is 15 percent. \- The initial investment, the proceeds from selling the old harvester, and any resulting tax effects occur immediately. \- All other cash flows occur at year-end. \- The market value of each harvester at the end of its economic life is zero.

Option to Wait Hickock Mining is evaluating when to open a gold mine. The mine has 60,000 ounces of gold left that can be mined, and mining operations will produce 7,500 ounces per year. The required return on the gold mine is 12 percent, and it will cost \(\$ 14\) million to open the mine. When the mine is opened, the company will sign a contract that will guarantee the price of gold for the remaining life of the mine. If the mine is opened today, each ounce of gold will generate an aftertax cash flow of \(\$ \mathbf{4 5 0}\) per ounce. If the company waits one year, there is a 60 percent probability that the contract price will generate an aftertax cash flow of \(\$ 500\) per ounce and a 40 percent probability that the aftertax cash flow will be \(\$ 410\) per ounce. What is the value of the option to wait?
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