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Project A involves buying expensive machinery which produces a better product at a lower cost. The reason for this is that D6 refers to the depreciation applied to the profits of the period. What does IRR mean? Suppose you are trying to decide between two projects A and B.. Applying the Gordon cost of equity formula—Courier Corporation Courier Corporation stock symbol CRRC is a book manufacturer that has experienced rapid growth of sales and profits.
In his opinion. The "Less Is More" company manufactures swimsuits. The company is considering expanding to the bath robes market. Use a 2-dimensional data table to determine the sensitivity of the profitability to the price and quantity.
Depreciation and terminal value: The machine will be depreciated over 10 years to zero salvage value. The machine can produce up to one million ice cream bars annually. What is the minimum price that the company should charge for each bar if the project is to be profitable?
Assume that the price of the bar does not affect sales. The proposed investment plan includes: The company is considering buying a new machine. The terminal value of the machine is 0.
The life span of the machine is 6 years and the machine has no disposal value. The "Car Clean" company operates a car wash business. The new machine is faster then the old one. What is the NPV of replacing the old machine? The Coka company is a soft drink company. The Coka company is considering whether to start manufacturing cans in its plant. Which photocopy machine should the firm buy? A company is considering whether to buy a regular or color photocopier for the office.
The company has two alternatives to choose from: During the five months of the summer May- September demand is 2. The machines are being depreciated on a straight-line basis to zero salvage value.
If the company manufactures 1. The company has two machines. The Easy Sight company manufactures sunglasses. Plot a graph showing the profitability of investment in each machine type depending on the annual production. Demand for sunglasses is seasonal. The ZZZ Company is considering investing in a new machine for one of its factories. The annual costs of the shipping line are estimated at 60 gold coins annually.
Use data tables in order to show the profitability of the project as dependent on the annual earnings and the tax rate. Assume that due to insurance and storage costs it is uneconomical to store sunglasses at the factory.
Poseidon is considering opening a shipping line from Athens to Rhodes. In order to open the shipping line Poseidon will have to purchase two ships that cost 1. The life span of each ship is 10 years.
What is the maximum tax rate at which the project will be profitable? At the board meeting on Olympus. The Manufacturing project: The loan will have to be paid back in 6 equal annual payments. What is the minimum loan that the IOC should give in order that the project will be profitable?
Kane Running Shoes is considering the manufacturing of a special shoe for race walking which will indicate if an athlete is running i. Assume that at the end of project that is. The project went ahead. The company is about to launch a new line of products. What is the minimum number of shoes Nike has to sell annually for the project to be profitable in each of the following two cases: The marketing department has to decide whether to use an aggressive or regular campaign.
Aggressive campaign Initial cost. As a result Kane is expecting a large drop in sales of the SWS shoes. The Aphrodite company is a manufacture of perfume.
In order to mass-produce the new drug the company needs to purchase new machines. The expected life span of each machine is 5 years. The demand for the new drug is given by the following equation: Monthly growth in profits month Calculate the NPV of each campaign and decide which campaign should the company undertake. Use data table in order to show the differential NPV as a function of first month payment and growth rate of the aggressive campaign.
The Long-Life company has a 10 year monopoly for selling a new vaccine that is capable of curing all known cancers. How many vaccines will the company produce annually? The Gordon dividend model: Weighted average cost of capital page Applying the Gordon cost of equity formula—Courier Corporation The basic principle is that the discount rate for a stream of cash flows should be appropriate to the riskiness of the cash flows May Two uses of the WACC This is a preliminary draft of a chapter of Principles of Finance by Simon Benninga benninga wharton Make sure the material is updated before distributing it Chapter A real estate investment.
Here are two examples: During the rafting season. To complete the NPV analysis. Since the riskiness of the cash flows PFE. The White Water financial analyst has derived the set of anticipated cash flows for the new raft. By being the first rafting company on the river to have the self-sealing rafts.
Chapter 6. Weighted average cost of capital page 2. The raft is more expensive than the existing rafts operated by the company because it is self- sealing—holes in the raft are automatically and permanently fixed by a new technology. In this chapter we discuss the weighted average cost of capital WACC. The WACC is the average rate of return the firm has to pay its shareholders and its lenders.
Weighted average cost of capital page 3. GF has to decide on an appropriate discount rate for the anticipated DC cash flows. The income of a corporation is taxed at the corporate income tax rate. In order to value DC. The shareholders own stock in the firm. The company is considering buying Dazzling Cascade Water Company. When the firm is profitable. Weighted average cost of capital page 4. The debtholders may be banks. The shareholders in the firm have limited liability. Debtholders are promised a fixed return interest on their lending to the firm.
The cost of equity. They all represent the market-adjusted rate that investors get or demand on various investments or securities. Weighted average cost of capital page 5. United Transport Inc. Another way of putting this is that the WACC is the average return shareholders and debtholders expect to receive from the company. The weighted average cost of capital WACC is the average return that the company has to pay to its equity and debt investors.
Weighted average cost of capital page 6.
So be patient! Of the five parameters in the WACC calculation. A model for calculating rE is given in Section 6. This is the question in the computation of the WACC.
Most often we calculate TC by computing the average tax rate of the firm. We will usually take E to equal the number of shares of the firm times the market price per share. Weighted average cost of capital page 7. We will call the formula the Gordon dividend model. An actual example of a calculation for D is given below in Section 6.
A detailed example of the calculation of rD for an actual firm is given in Section 6. Here are some facts about the company and its stock: Weighted average cost of capital page 8. This dividend was paid on March 1. You want value XYZ shares by discounting the stream of future anticipated dividends. Then the future anticipated dividends per share are: Here is an example which presents most of the logic of our model: It is March 2. In predicting the future dividends of XYZ Corp. Div1 Div2 Div3 fair share value today..
Using rE to discount the future anticipated dividends. E PFE. Weighted average cost of capital page 9. According to the Gordon dividend model of the previous subsection. Using the Gordon dividend model to calculate the cost of equity rE In the previous subsection we derived the value of a share P0 based on the current dividend per share Div0. Turning this formula around to solve for the cost of equity rE gives: P0 This is the Gordon dividend model cost of equity formula.
In this section we turn this formula around: We derive the cost of equity rE based on the current value of a share P0. In the Gordon dividend model the cost of equity rE —the discount rate to be applied to equity cash flows—is the sum of two terms: D0 10 3 Dividend growth rate.
Suppose you buy the P0 stock today. The term is the P0 anticipated next period dividend return. Div0 3. Applying the Gordon cost of equity formula—Courier Corporation Courier Corporation stock symbol CRRC is a book manufacturer that has experienced rapid growth of sales and profits. This is the anticipated dividend yield of the stock. P0 This the growth rate of all future dividends paid on the stock. Gordon dividend model cost of equity We derive this below from the dividend series in cells B3: In this case the P0 is the stock price on the date of the calculation 30 September In the example above.
Here are two alternative ways to D compute the growth rate g: Use a different time period. Div 0. In choosing as the base year. If—as in the current example—we use as the base year instead of You might want to use this model to project the dividend growth rate. This gives a cost of equity of You might decide that the past history of Courier dividends is not indicative of its future dividend payouts. Using a different base year Year ended Dividend 2 30 Sept per share 3 0. In this case. Ignore historical dividends altogether.
Look at the data below: Courier purchased stock from its shareholders in open- market repurchase transactions. Making up a future growth rate of dividends 2 g. Using the total equity payout instead of per-share data In some of the years — In the examples for Courier Corporation which follow. Using the figures from column D and using the total market value of the equity on 30 September Column D gives the total equity payout: Most dividend-paying firms think their shareholders want to see a steady pattern of dividend growth.
So if they have extra cash. When some of the shares of the firm are repurchased. If you let your stock be repurchased. Firms repurchase stock instead of paying extra dividends for several reasons: So all parties gain.
Why do firms repurchase stock? In recent years share buybacks have exceeded dividends as a form of distribution to shareholders. When a dividend is paid. Courier had 2.
As you can see from the previous spreadsheet. On 30 September Before we can do this. You can see that the debt has been borrowed at various interest rates. In Figure 6. The debt items are marked. In theory rD ought to be the marginal cost of debt— the borrowing rate of the company for additional debt. A plausible alternative is use information about the current borrowing rate of the company. Figure 6. We use the borrowing rate of 7.
We use From Courier Corp. Number of shares times current share price 6 Sept. Computed from total equity payouts 3 Cost of debt. B6 8 9 Percentage of equity. TC We presume that this rate of return reflects the average risk of shareholder and debtholder future cash flows.
There are two important cases where this is often true: The value of the Courier is the discounted value of its future anticipated FCFs. Thus the WACC represents a weighted average of the riskiness of shareholder and debtholder cash flows. Below we define the concept of free cash flow FCF. When a company is considering investing in a project whose risk is comparable to the riskiness of the company as a whole.
This is plausible. When the riskiness of a stream of cash flows is similar to the riskiness of the cash flows received by shareholders and debtholders. The cash flows. This could be something as simple as another printing press to print more books or a warehouse to house them. Suppose the company is thinking of investing in a project whose riskiness is like the riskiness of its current business. Recall that Courier is in the book printing business. In all of these cases.
For our purposes in this chapter. The second major use of the WACC is to value companies. If the following table gives you problems. To accurately define the FCF. For purposes of calculating the FCF. The FCF includes all current liability items related to operations. Capital expenditures CAPEX An increase in fixed assets the long-term productive assets of the company is a use of cash.
The sum of the next two items is the change in net working capital. This increase in current liabilities—when related to sales—provides cash to the firm.
We do this by: The FCF definition takes changes in working capital and purchases of new fixed assets into account separately. Since there are 2. This compares favorably with the current share price of Courier.
The idea was that because most cash flows occur throughout the year—the appropriate discounting process should discount them as if they occur in mid-year. In terms of the computation just done for Courier. The WACC is defined as: Both of these uses have been illustrated in this chapter. If we implement mid-year discounting for Courier. For Courier. In many cases professionals do extensive sensitivity analysis on the WACC and the FCF growth to establish a price range—the range of valuations which appears to be reasonable.
Another estimate of its tax rates might thus be A final warning Cost of capital calculations are critical for valuations and controversial. In the table below we summarize how we derived each of the elements of this formula: They involve a mixture of theory and judgment. Almost every number in the WACC calculation above can be determined in several ways. State taxes are another 2.
In practice we usually use either: The most important modification you might want to make to the WACC calculation above involves the cost of equity rE.
In Chapter 14 we will show you how to use this model to calculate the cost of equity. Calculate the cost of equity rE for a company having: Compute the weighted average cost of capital WACC for a company having: Complete the??? Consider the following data regarding Cinema Company. January 4. Find the cost of equity rE of Cinema using the Gordon dividend model for the total equity payout. You know that tomorrow the company will pay its annual dividend in the amount of 1. After a quick research you have come up with the following data: After a quick search you have found the following data: It is 1 January Using the Gordon model for the total equity payout.
As an experienced investor. You are considering a new project to your firm. What is the company cost of capital? To your judgment. After this time.
You just bought a share of ABC Corp. The company does not repurchase any of its shares. You are considering purchasing a stock of ABC Corp. Repeat the question by using mid-year discounting as well. What is your implied cost of equity for ABC? XYZ Corp. Should you take this project? You are given the following information for Twin Inc.
Assume that business risk is unchanged. Long-Term Debt Outstanding: Starting a firm Stop and think! This is a preliminary draft of a chapter of Principles of Finance by Simon Benninga benninga wharton..
The next half year October Chapter 7: Accounting principles page Computing the free cash flow for the second half year Three basic accounting statements Using the FCF in a valuation exercise Computing the free cash flow FCF All the material is copyright and the rights belong to the author and to MIT Press The consolidated statement of cash flows This is an accounting chapter for finance students: We write all of our accounts and information directly onto the balance sheet.
This chapter will help you understand three basic accounting statements: The balance sheet. One of the things you will notice is that—with the exception of this sentence—we never refer to debits and credits. In addition we will explain in detail the concept of free cash flow. Accounting principles page 2. In this section we summarize these statements. It includes items such as: Accounting principles page 3.
Excel functions used This chapter uses only the most basic Excel functions.
The balance sheet The balance sheet is a double-columned statement. It also includes items such as the billings the company has sent out for which it has not received payment accounts receivable. This column includes items like: Accounting principles page 4. Money paid by shareholders to the company for shares in the company Accrued retained earnings: Bills that the Inventories company must pay Accounts receivable: Customer Taxes payable: Taxes that the company billings that are not yet paid knows it will have to pay in the short term Fixed assets—assets with a longer life Land Long-term liabilities—debt financing that has Plant.
These two aims are not equivalent. What the company owns Liabilities and equity: Who put up the money for the assets Short-term assets—assets with a short life Short-term liabilities—financing which the generally less than one year.
This period is most often a year. But these issues are for later! In section 7. Accounting principles page 5. Gramps gave no credit and paid all his bills in cash. But when writing down the profit at the end of the day. A basic misunderstanding—the corner grocery store versus IBM or: By economic logic. Here are some examples which even Gramps would agree with: Gramps will pay him a day later.
But most business use the accrual accounting method discussed in this chapter. This was his profit for the day. You can do your accounting using the cash accounting method—whatever remains in the till or in your bank account is your profit over a given period. In this method.
Accounting principles page 6. By the logic of cash accounting. These examples can be multiplied. Accounting principles page 7. Add back sales of equipment. Because the profit and loss statement does not necessarily reflect the realities of how cash flows into and out of the firm as a result of its activies. At this point their balance sheet looks like this: They pay for the car in cash. Starting a firm Brother and Sister live in Anytown. Along with the taxi sign on top of the car.
Brother and sister: Accounting principles page 8. H38 40 Salaries This is probably the worst transgression you can make in an accounting framework! Accounting principles page 9. This profit is added to the initial equity of the firm as retained earnings meaning: Because the loan has to be paid back in the short-term. Like the first. ATS underwent a dramatic expansion: Brother and Sister bought another taxi. A Note on Terminology Almost every accounting item in our example has another equally valid name.
On the last day of February. As you will see below. The bonus as yet unpaid is listed as a Current PFE. An account receivable is an asset of the firm some firms sell their accounts receivable—if you can sell it. Accountants and the tax authorities define a capital asset as an asset that: On the one hand. By doing this WorldCom over-reported its income. The cash account on the balance sheet is obviously a current asset.
This would be similar to ATS listing the salaries of their taxi drivers as the purchase of a fixed asset. Similarly— see next bullet—any reasonably anticipated expense should be recorded in the profit and loss statement as a cost. Any reasonably anticipated receipt should be put in the profit and loss statement as a sale. Capital assets are not immediately listed on the profit and loss as expenses.
The gas station has agreed to extend credit to ATS—the company can now pay its gasoline bills on the 10th of the month following. At the end of June. This company always pays one month in arrears. June The following events occurred during this three-month period: At the end of the period. They paid this whole amount in May The mortgage conditions are: Here are the new balance sheet and profit and loss statement: The building an old gas station includes a garage.
Here are some examples: When the building starts to be depreciated. The signing bonus was an expense in the April accounting period. H94 96 Fuel An outlay is recorded as an expense only if it is required in the current period to produce income. There are several different interpretations of depreciation: The second taxi is 4 months old it was PFE. They bought the first taxi on 1 January. Since we have not thus far included the costs of fixed assets the taxis. The main difference between the profit and loss statements shown thus far and the statement that the accountant prepares is depreciation.
The accountant explains that: Preparing a profit and loss statement for January. To take care of this. H Repayment of car loan principal Jan-June financial statements including depreciation and taxes Assets Liabilities and equity Profit and loss for the period Current assets Current liabilities Sales For purposes of computing the Federal tax.
The taxes PFE. This is the sum of the end-June account receivable from the flour mill plus the pre-paid insurance PFE. Cash flow from operating activities Cash flow from operating activities includes the profit after taxes for the period minus increases in operating current assets plus increases in operating current liabilities: A B Consolidated statement of cash flows Cash flow from operating activities Profit after taxes The purpose of the consolidated statement of cash flows is to explain the growth over the period of the cash balances on the balance sheet.
Therefore we add it back. Why only debt repayments? Cash flow from investing activities Cash flow from investing activities includes acquisition of fixed assets land. Cash flow from financing activities This item includes money raised by the company from sale of stock.
A B Cash flow from investing activities Payments for fixed assets Taxis A B Cash flow from financing activities Proceeds from new debt For finance purposes recall. B Add increases in current liabilities Computing the free cash flow FCF The consolidated statement of cash flows gives the amount of cash generated by ATS during its first half year of existence. Added to the initial cash balance of the company over this period. The FCF is defined as: Our measure of this is the free cash flow FCF.
Add back after-tax interest expenses The FCF is an operating concept: The consolidated statement of cash flows does not give this information. Subtract increase in fixed assets at This represents the amount spent on new cost assets over the period.
Subtract increase in current assets For purposes of the FCF. Another way of looking at this is that the FCF is the amount of cash generated by the firm if everything were financed with equity. These financial items are not included in the FCF. Interest expenses are a financial non- operating item and should therefore be added back.
To compute the FCF it is handy to put the profit and loss and the balance sheet in two side-by-side columns. C18 -SUM B The taxi loan is financing and not 49 Add increase in operating current liabilities Changes in 48 Subtract increase in operating current assets If ATS had paid all its operating expenses in cash and collected all its operating payments in cash during the first 6 months of its existence.
During this period the company bought no more new assets. Did Brother-Sister do well this half year? Or should we be worried by their negative free cash flow? It paid its bills faithfully at the end of each month. During the period July — December. ATS was paying its gasoline bill at the end of the following month.
Month month Interest 39 Jul 4. This created: In order not to stress the business. Month month Interest 49 Jul Dec December 1 financial statements including depreciation and taxes 2 3 Assets Liabilities and equity Profit and loss 4 Current assets Current liabilities 5 Cash Taxi loan from bank 0 Sales June Fuel June Computing the free cash flow for the second half year In rows below we calculate the free cash flow for the company at the end of December December D18 -SUM C C18 50 Add increase in operating current liabilities Not bad for a new company!
In financial theory. Which depreciation do you add back in the cash flow? They make the following assumptions: Brother and Sister perform such a valuation.
The reason for this is that D6 refers to the depreciation applied to the profits of the period. At the end of At this date it will quietly expire. Brother-sister figure that in another few years. The net. Outstanding mortgage 17 Value of equity E9 Add back cash balances 14 on 31 December Valuing the business To value the business.
ATS need to compute the cash flows and discount them by an appropriate cost of capital. Had Brother and Sister valued their firm by using mid-year discounting. Mid-year discounting assumes that the annual cash flows occur in mid-year. Technical comment: In addition we showed how to construct a free cash flow statement and how to use this statement to value a business. Free cash flow FCF: Building a financial planning model Reconciling the cash balances—the consolidated statement of cash flows Initial accounting statements for a financial planning model Financial planning models look like accounting statements These models are called financial planning models or pro forma models Extending the model to years 2 and beyond Chapter 8: Financial planning models page For example—does an increase in the growth rate of sales create cash or use cash?
The answer is not always clear: More sales produce more profits and hence produce more cash. They can be used to predict the future free cash flows. A financial planning model can help us sort out these two opposing trends. Financial planning models have a variety of uses: Building a financial planning model helps you predict whether the firm will need financing in the future.
Financial planning models page 2. In the next chapter we will use a financial planning model to value the firm. When you make a business plan which you then take to investors to get financing or to a bank to explain why you need a loan and can pay it back. The model you build illustrates your assumptions about the financial and business environment in which your firm will operate in the future.
In this chapter we develop a simple model that illustrates the methodology of financial planning models. Chapter 9 shows how to use the pro forma prediction of future cash flows to value a firm. To illustrate the process by which financial planning models are constructed. Financial planning models page 3. While most of the terminology in this chapter follows the standard accounting nomenclature. Financial planning models page 4.
Financial planning models page 5. Inventories include both raw materials to be used for production and unsold finished products. For our financial planning model. These are payments due from customers and are generated by the operations of the firm.
An example might be rent paid by the firm for future periods: If the firm pays this rent in advance for example. Here are several typical items that would be included in the financial planning model definition of current assets. Inventories are part of the operating current assets of the financial planning model. Which accounting current assets are not included in the financial planning model definition of current assets?
There are two important examples: To emphasize this point. Prepaid expenses are costs which the firm pays before it actually receives the associated services. In most cases.
Financial planning models page 6. A taxi driver needs to keep some cash on hand in order to make change for his customers. The distinction between cash as an operating asset and cash as a store of value is usually obvious once you understand the business of the firm. This item on the balance sheet refers to other financial assets— such as stocks and bonds—bought by the firm. It is not an operating current asset. Financial planning models page 7.
Here are two typical items that would be included in the current liabilities of our financial planning model: These are unpaid bills the firm owes to its suppliers. Accountants include this item in current liabilities. Accountants include this item in PFE.
Accounting current liability items that are not included in the financial planning model definition of current liabilities are typically financial items. Since this item is related to the operations of the firm. These are borrowings by the firm that are due within one year. The financial statements of XYZ Corp. Current liabilities For purposes of the financial planning model. A typical financial planning model has three major components: Also called the value drivers. We will make assumptions about how the firm finances itself in the future.
Financial planning models page 8. Building a financial planning model Now that we have our terminology straight.
What is the mix between debt and new equity issued? Other model parameters are derived from the following financial statement relations. Over the five-year horizon of the financial planning model. The annual depreciation charge is 10 percent of the average value of the fixed assets on the books during the year.
In our example Whimsical Toenails current year 0 level of sales is 1. In Chapter 9 we will use the financial planning model to project the future free cash flows of the firm in order to value the firm. Financial planning models page 9. End-year net fixed assets are assumed to be 77 percent of annual sales. Company management does not intend to either issue new stock nor repurchases stock over the five-year model horizon.
Whimsical Toenails earns 8 percent on the average balances of cash. In our model this item is the plug: The cash item is defined so that the left-hand side of the balance sheet always equals the right-hand side of the balance sheet: Assumed to be 50 percent of sales.
In this initial financial planning model we make the following assumptions: Whimsical currently has debt of on its balance sheet. Every financial planning model has a plug. Once the debt is fully repaid. We assume that Whimsical Toenails pays out 40 percent of its profits after taxes as dividends to shareholders. Current assets. For the Whimsical Toenails financial model. Investor Relations Rieter maintains a regular and transparent communication with its shareholders, investors and other stakeholders.
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