Finance

Assignment 2 Resources
he following resources may be useful in learning about time value of money (TVM) and how to calculate TVM in Excel:
• Alexander, M., & Kusleika, D. (2016). Excel 2016 formulas. John Wiley & Sons, Inc.
• You will find explanations on using Excel to calculate financials in these chapters:
 Chapter 11, “Borrowing and Investing Formulas.”
 Chapter 12, “Discounting and Depreciation Formulas.”
 Chapter 13, “Financial Schedules.”
• Ross, S. A., Westerfield, R. W., Jaffe, J. F., & Jordan, B. D. (2021). Corporate finance: Core principles and applications (6th ed.). McGraw-Hill. Available in the
o Chapter 4, “Discounted Cash Flow Valuation,” pages 82-128.
• Schmidt, C. E. (2016). A journey through time: From the present value to the future value and back or: Retirement planning: A comprehensible application of the time value of money concept. American Journal of Business Education, 9(3), 137-143.
• Time Value of Money |
• Time Value of Money
• ________________________________________
•

• Speaker
The time value of money is likely the most significant issue, with regard to finance. It circumnavigates the entire area, future value, present value, and annuity. Some kind of a payment either being paid or received, trying to determine a rate, trying to determine the length of time. All of these components meld together, and will find themselves in various aspects of the firm; cost of capital, a representation of risk free rate, etcetera. In this section, you will want to get comfortable in determining the various components that make up the time value of money, both for any work that you undertake that involves that area, and in particular, for amassing your own individual personal wealth.
• Timelines are an excellent way to visually represent the time value of money, however, I would hastily add, it is in your best interest to get comfortable using either a calculator or a Spreadsheet Excel. Using that as an example, as a method of determining one or several of the components of the time value of money. The charts that you may have seen in the past, the time value charts that have imbedded values, are already precast within a calculator. This makes the process certainly more efficient, much easier, but it also increases the accuracy factor. That’s something that are you are going to want to have a high confidence in, when you are evaluating the time value of money. In particular, when solving for either rate and a period, it is much easier to get comfortable, get familiar, and get proficient, using a calculator or spreadsheet, because the interpolation, the trial and error, is not as necessary.
• In working with financial calculators, you will note that sometimes you need to enter a negative number. Sometimes, the calculator that you own will have what it is called negative polarity, which will require (usually) the present value to be entered as a negative number. You want to check the owner’s manual–sometimes you can get an extend version of an owner’s manual–go online, perhaps do a Google search, to find out other vendors that offer extended versions of the owner’s manual. I cannot stress enough that you are going to want to get comfortable, really be slick, be proficient, in utilizing your calculator, in order to make the best use of it.
• In this example we are seeing the process for calculating a present value. Here, the slide is using exponents. You will note that if you take that same $100 and divide it by 1.10 three times, you will get the same result. The exponent is really just a much faster way of providing that answer, providing that solution. As I had mentioned earlier, calculators already have the various time value tables built within them, so steps are saved. Of course, as I mentioned in earlier discussions, accuracy goes way up, because you are computing it in one step.
• The single biggest difference between an ordinary annuity and an annuity due (also known as an immediate annuity) is when the first payment is received, and then subsequent payments. One is the beginning of the year, beginning of the period. Boom, immediately hence, the annuity due is an immediate annuity. The ordinary annuity, the first payment either received or paid, whichever way the flow is going, happens at the end of that first period, and then subsequent periods.
• Most calculators or spreadsheet formations (Excel, etcetera) will have a selection for begin or end. You would want to get very comfortable utilizing the various keys, the various aspects of your calculator or spreadsheet, so that you set the solution that you are seeking up in the right mode. Is the payment coming at the beginning of the period or at the end of the period? Be sure and check for that, prior to the ensuing of your calculation.
• Albert Einstein was quoted as saying that the eighth wonder of the world is compound interest. You can best handle your own personal fortune, the amassing thereof, by taking advantage of time. Start early, save judiciously, put as much in as you are comfortable putting in. A comment I use to students is “give to yourself till it hurts.” You want to make sure that you are not overdoing it, but you certainly want to make sure that you are standing on you toes, as it were, when it comes to investing for yourself, for your future. So, take advantage of the time value of money, as it comes to your own personal wealth.
• Net present value is an excellent example of where you want to use either a calculator or an Excel type spreadsheet, especially with uneven cash flows. You will want to make sure that you are comfortable. The processes with most calculators is slightly different than the steps (the key strokes, the key steps) that you will take in inputting for present value, future value, the time value sequences. So, again, make sure that you have addressed this issue through the owner’s manual, the user’s manual, that you have with your calculator.
• When inputting the rate that you are going to be using for calculations, you are going to want to make sure that it is syncopatic with period. If it is an annual rate and it is 12 percent, as an example, obviously I would be 12. If it is the semiannual compounding, I would be 6. Keep in mind that if we are doing it for just one rotation, one period, then N would be 2. So, it is important that this is inputted appropriately.
• Just to carry the example one step further, if you had monthly compounding I, using 12 as an annual rate would be 1 percent, and then N would be 12. So, anyway, make sure that that is matched up when you are inputting this data in your calculator.
• This long end calculation demonstrates where you are using the exponents to quantify the periods. You will note that with a calculator this step is done for you, when you properly match the periods and the rate, as I discussed earlier.
• This is a good slide to demonstrate why you want to have proper inputs, as the verbiage stage, you are going to want to have future value as zero. So, when you conclude the process as a story problem, as “In at the end I want to have zero, I do not want to owe anything,” the future value being zero makes complete intuitive sense.
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o This presentation discusses the components that make up time value of money. The presenter also provides examples to compute and read the computations.
• Mayes, T. R. (n.d.). Microsoft Excel as a financial calculator part I. http://www.tvmcalcs.com/index.php/calculators/excel_tvm_functions/excel_tvm_functions_page1/
• Skillsoft. (n.d.). Financial statement analysis for non-financial professionals.
Go to the Analyzing the Financial Statement section in the Table of Contents menu, and select The Time Value of Money. Course Transcript
Financial Statement Analysis for Non-financial Professionals
Course Overview
Read the Course Overview.
Analyzing the Financial Statement
1. The Time Value of Money
2. Present Value and Future Value Calculations
3. Using Profitability Ratios for Analysis
4. Analyzing Efficiency Ratios
5. Liquidity Ratio Analysis
6. Analyzing Solvency Ratios
7. Horizontal Analysis
8. Vertical Analysis
Course Overview
[Course title: Financial Statement Analysis for Non-financial Professionals] Financial analysis helps you understand your organization’s financial standing, how it got there, and its strengths and weaknesses. In this course, you’ll learn about the concept of the Time Value of Money as well as the methods for analyzing financial statements from a non-financial professional’s perspective. These methods include using profitability ratios for analysis; analyzing Efficiency Ratios; Liquidity Ratio analysis; analyzing Solvency Ratios; and Vertical and Horizontal analysis.
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The Time Value of Money
Learning Objective
After completing this topic, you should be able to
• match key terms relating to the time value of money to their descriptions
1.
[Topic title: The Time Value of Money] Imagine you’ve been given a choice: you can either receive $25,000 in lottery winnings now or four years from now. Most people would probably say, “I want it now.” It’s almost always better to have money now instead of later because prices can increase and money can lose its value and purchasing power over time.
Right, now you have the money to spend. But…what if you want to save it instead? You can’t keep it under your mattress. But if you know about the time value of money, you can figure out the best way, from several options, to make your money grow.
One of these options is investment, which is using money or capital to purchase financial assets in order to gain profitable returns. You may have been in a situation where you had to decide which possible investment option was the best. However, because the value of money changes over time it’s impossible to compare, for example, cash flows that occur at different times.
To account for money changing value over time, the value that two or more amounts would have at the same point in time is calculated. You can either calculate the future value of an investment or calculate the present value of an amount to be received in the future.
The return on your investment is subject to factors such as the principal (p), which is the amount invested. Then consider the interest, or the cost a person or institution pays to use someone else’s money. It’s generally added to the amount invested at regular intervals. The interest rate (i) is expressed as an annual percentage of the principal. A final consideration is the period of time(n), which is the number of years your money is invested for.
As a consumer, you’ve probably heard about inflation. Inflation is the rate at which the lender is compensated for the possible loss of an investment’s value, or purchasing power, over time. Take the example of a company considering an investment that offers a 4% return. They must account for the current estimated inflation rate of 6% per year. The minimum rate of return on the investment must be high enough to make it worthwhile. In this case, inflation may end up costing the company money.
An annuity is another savings option. Annuities are a series of fixed payments at a specified frequency over the course of a fixed period of time. Annuities are calculated in a similar way to single amount future and present values. In the case of future value, an annuity is the sum of all the payments plus the accumulated compound interest on them. When you calculate an annuity’s future value, you need to know the interest rate, the number of compounding periods, and the amount of the periodic payments.
Now that you’re familiar with the time value of money, you can choose the best way to make your money grow.
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Present Value and Future Value Calculations
Learning Objective
After completing this topic, you should be able to
• recognize how to calculate the present and future values of a single amount
1.
[Topic title: Present Value and Future Value Calculations] At some point, you, like most people, will need to predict how the outcome of a particular financial decision will affect you. Interest, future value, present value – all play a key role in determining where your money should go. But, before any interest or future value calculations can be done, the values for principal (p), interest rate (i), and time (n) are required.
Forecasting is essential for making informed investment decisions. To get started with forecasting investment opportunities, you need to know two things. First, the present value – the value right now of an investment that is to be received at a future date. For example, the present value of $1,000 is $1,000. Investing it will make it grow depending upon the amount of time and the interest rate. The second is the future value – the value of a single amount at a specific future date after it has been invested, with compound interest added.
When calculating future and present values, notice the relationship between them. Looking closely, you’ll notice that for the future value of a single amount, the present value is one of the key components of the formula. Future value is equal to the present value – the principal invested – multiplied by the sum of 1 plus i, which is then raised to the power of n. “i” is the interest rate for the period, and “n” represents the number of periods for which the interest will be added.
Let’s try this. If you have $25,000 invested at an interest rate of 4%, or percentage fraction 0.04, for three years – you will end up with a value of 1.125. This value is called the Future Value Interest Factor (FVIF). [A Future Value Interest Factor (FVIF) table is displayed. It shows how projected future values of an amount over a period of 8 years with increasing interest rates.] When you multiply $25,000 by 1.125, you get a future value of $28,125.
Forecasting means looking forward to predict the future. But suppose you already know what your goal is and you want to know how much to invest now to reach that future goal. In a sense you’ll calculate backwards to get the present value. Present value is equal to the future value multiplied by the result of the following equation: one, divided by the sum of one plus i to the power of n.
The Present Value Interest Factor (PVIF) and the FVIF are available from a PVIF table that is freely downloadable off the Internet. [A sample Present Value Interest Factor (PVIF) table is displayed.] Let’s say you need $12,000 in two years. The interest rate is 5% and you want to find out the present value, or simply, how much to invest now. You begin by checking these numbers against the PVIF table to obtain the PVIF rate. In this case, it’s 0.907. To get the present value you multiply $12,000 by 0.907. This gives you $10,884. So if you need $12,000 in two years and the interest rate is 5%, you’d need to invest $10,884 today.
So understanding present and future value calculations will help you to make the investment choice that best suits your needs.
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Using Profitability Ratios for Analysis
Learning Objective
After completing this topic, you should be able to
• recognize how to calculate the value of key profitability ratios
1.
[Topic title: Using Profitability Ratios for Analysis] It’s safe to say that without profitability, a business wouldn’t survive in the long run. Profitability ratios help you determine if a company has the ability to earn a profit in the future. It includes Net Profit Margin, Return on Assets, and Return on Equity and uses elements of both Income Statements and Balance Sheets.
The Net Profit Margin ratio – also known as Profit Margin on Sales or Return on Sales (ROS) – measures how well a company can turn sales into net income. It measures management’s success in controlling costs and pricing and tells you the net profit per sales dollar after all expenses are deducted from the total sales amount.
To calculate the Net Profit Margin you divide Net Income by net Sales. Although a high profit margin is generally better than a low profit margin, this value shouldn’t be analyzed in isolation. It needs to be compared to ratios from previous years, to ratios of other companies in the same industry, or to an accepted reference value. Sometimes a low profit margin is just a part of doing business in a specific industry sector.
Take a company with a net income of $1.45 million and sales of $23.4 million. If you divide $1.45 million by $23.4 million and multiply by 100, the result is a 6.2% Net Profit Margin. This means that the company earns a profit of $6.20 for each $100.00 of sales revenue.
However any company can show a profit. So for more clarity let’s use another profitability ratio: the Return on Assets (ROA). ROA measures how well a company uses its assets to generate net income. So it indicates which businesses can make good profits with little assets.
It’s calculated as Net Income divided by Total Assets. This formula measures how much profit, after taxes, was earned on the total capital contributed by creditors and owners. So like Net Profit Margin, the higher the ROA, the better. So if a business has earned $375,000 in net income on $2,500,000 in assets. The ROA would be $375,000 divided by $2,500,000, which is 0.015. As a percentage the ROA is 15%.
The next ratio is Return on Equity (ROE), which measures the return shareholders are receiving on their investment in the company. It lets shareholders gauge management’s ability to return money for each dollar they’ve invested. You can use this ratio to compare the profitability of different companies in the same industry.
The formula is Net Income divided by Shareholders’ Equity. As with the other profitability ratios, the general rule for ROE is that higher is better. Shareholders’ Equity includes both capital stock and retained earnings. So a Net Income of $2,189,833 divided by a shareholders’ equity of $7,670,217 would result in 0.28549, or 28.55 %.
Profitability ratios help you to determine if a business is able to generate profits from assets, equity, and sales to ensure its long term survival.
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Analyzing Efficiency Ratios
Learning Objective
After completing this topic, you should be able to
• recognize how to calculate the value of key efficiency ratios
1.
[Topic title: Analyzing Efficiency Ratios] When investing in a business, you’re definitely hoping it’s profitable and a return will be coming your way. But in your analysis of a company’s financial status, give efficiency ratios some room at the table as well. They’re used for measuring management’s effectiveness in managing assets and liabilities to generate revenues and profits. To calculate efficiency ratios, you use information from Income Statements, Cash Flow Statements, and Balance Sheets.
You’ll get the most benefit from using efficiency ratios, when you use them to compare businesses in the same industry. The first efficiency ratio is Receivables Turnover ratio, which measures how many times a company’s accounts receivable turn over in a period – typically one year. When companies extend credit to clients, it results in accounts receivable.
So how’s it calculated? You divide Net Credit Sales for the year by the Average Accounts Receivable for the year. Only credit sales should be included in the net sales figure. Generally, a higher receivables turnover is better, since that means there’s a shorter time to collect. A simple evaluation is for management to take the average number of days taken by customers to pay debts and compare it to the number of days in the credit terms. For example, an average collection period of 33.46 days would indicate good efficiency for payment terms of 45 days for credit sales.
The second ratio is the Inventory Turnover ratio, which measures the number of times a company sells and replaces its inventory in a given period. It indicates how fast a company can sell its goods. And is useful because it helps manage “frozen cash”, which is cash invested in in-process and finished inventories.
It’s calculated with the formula Cost of Goods Sold (COGS) divided by the Average Inventory. The higher the turnover, the better. The goal is for the Inventory Turnover Ratio to increase over time so that there’s less investment in stock. The turnover rate should be high enough that cash can come in from customers before suppliers need to be paid.
The third ratio is the Operating Cash Flow to Sales Ratio, which gives you an idea of a company’s efficiency in turning sales into cash. It’s expressed as a percentage and shows the relationship between cash generated from operations and sales made over a specified period. Operating cash flow is the net cash generated from operations, which includes both net income and changes in working capital. It’s found on the Cash Flow Statement. The formula used is Operating Cash Flow divided by Net Sales which is found on the Income Statement.
Cash is just as important as profit because a company needs cash to pay dividends, suppliers, and creditors, and to purchase assets. The higher the Operating Cash Flow to Sales Ratio, the better. After all, a company’s sales and operating cash flow should grow in parallel.
Efficiency ratios let you analyze the efficiency of a company’s management of resources and investments.
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Liquidity Ratio Analysis
Learning Objective
After completing this topic, you should be able to
• recognize how to calculate the values of liquidity ratios
1.
[Topic title: Liquidity Ratio Analysis] Liquidity brings to mind the idea of flowing water. In finance, liquidity means having cash, as well as the ability to quickly convert assets into cash. For a business this means cash flows freely enough so it can pay off its current liabilities quickly with what it has. Liquidity ratios, which are sometimes called working capital ratios measure the availability of cash.
When thinking about liquidity, you should also consider solvency. Solvency is all about business risk. For example, the inability of business to pay off debts and investments from its assets and cash flow on a long-term. Both liquidity and solvency ratios use elements of the Balance Sheet: a statement of financial position, which gives a snapshot of a company at a given point in time. It typically lists assets, liabilities, and capital.
Liquidity ratios measure the short-term solvency of a business; gauging the company’s ability to meet its credit obligations. There are two commonly used liquidity ratios.
The Current ratio expresses how well a company is able to pay its creditors from its current assets. As one of the best-known measures of financial strength, it answers the question “Are there are enough current assets to meet the current liabilities with a margin of safety?” It’s worth mentioning that current assets are assumed to be convertible into cash within one year, and current liabilities are short-term debts that are due in one year or less.
The formula is Current Assets divided by Current Liabilities. In general, a Current ratio of around 2.0 is good for a lender or creditor. Higher or lower values might be a cause for concern.
You know that the Current ratio includes all Current Assets. The Acid Test ratio includes only the most liquid current assets. It’s also called the Quick ratio because it only includes cash and current assets that can quickly be converted to cash. It’s more accurate in measuring true liquidity because it doesn’t include inventory and prepaid expenses. This ratio answers the question, “If all sales income were to stop, could the business still meet its current obligations with the quickly convertible funds it has on hand?”
It’s calculated with the formula Liquid Assets divided by Current Liabilities. Liquid assets are cash, marketable securities, and accounts receivable. As a rough guide, the Acid Test ratio should be 1.0 or higher. When the ratio is 1.0, it means that liquid assets are pretty much equal to the liabilities owed. So the company can pay what it owes without needing to sell its inventory.
But what does it mean if it is less than 1.0? Possibly the company isn’t solvent for the short term. But, in some industries, 0.7 might be acceptable. These companies have liquid assets available to cover just less than three quarters of the current liabilities.
So a company that is highly liquid inspires confidence as their short term financial situation is secure.
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Analyzing Solvency Ratios
Learning Objective
After completing this topic, you should be able to
• identify how to calculate the values of solvency ratios
1.
[Topic title: Analyzing Solvency Ratios] It takes hard work to pay off debts for both businesses and individuals. In financial terms, solvency means being able to pay all legal debts even if you have to convert assets to cash. Basically, debts can be dissolved by the assets. Liquidity ratios relate to what’s currently happening. But solvency ratios take a longer-term approach and help you determine if a company is financially overextended. There are two commonly used Solvency ratios, which both use elements of the Balance Sheet.
The first one – Debt to Total Assets – includes both short-term and long-term debt as well as tangible and intangible assets. It’s calculated by adding up the company’s Total Debt and then dividing by Total Assets. This ratio measures the percentage of assets financed by creditors, as opposed to the percentage financed by owners. It gives you an idea of a company’s ability to withstand losses while still being able to cover its obligations.
A high Debt to Total Assets ratio might be a red flag that the business may not be able to meet its long-term obligations. This business might be called highly debt leveraged. A ratio under 1.0 means that most assets are financed through equity and earnings, while a ratio above 1.0 means they’re financed more by debt.
For example, total liabilities of $110,000 divided by Total Assets of $200,000 gives you a ratio of 0.55. This isn’t bad –about half of the company’s assets are financed through equity. But it could also indicate a conservative approach to opportunities of leveraging on potentially low interest debts.
The Debt to Equity ratio on the other hand compares debt to owners’ equity instead of comparing debt to assets. When you calculate how much the company is leveraged in debt, you can find the relationship between what is owed and what is owned.
The shareholders’ – or owners’ – equity is the claim stockholders have to a company’s assets once all creditors and debtors have been paid. It’s the company’s net worth, and it’s calculated by subtracting total liabilities from total assets. The Debt to Equity ratio is the tool that highlights the extent to which debt is covered by shareholders’ funds
The formula for the Debt To Equity ratio is Total Liabilities divided by Total Shareholders’ Equity. Sometimes, only interest-bearing, long-term debts are considered instead of total liabilities in the calculation. For example a Total Liabilities of $110,000 divided by the Total Shareholders’ Equity of $90,000 results in a ratio of 1.22. This is a relatively high ratio.
As a rule of thumb, a high Debt to Equity ratio may indicate high risks – such as interest rate increases and creditor nervousness – and even financial weakness. The company may have been too aggressive in financing its growth with debt.
You can now use the power of solvency ratios to check whether a company’s longer-term obligations can be met easily or not.
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Horizontal Analysis
Learning Objective
After completing this topic, you should be able to
• recognize examples that are characteristic of horizontal analysis
1.
[Topic title: Horizontal Analysis] Let’s face it – it’s not always easy to interpret all the figures in financial statements based on their values alone. [A sample Balance Sheet is displayed.] For instance, can we say that a company with a liability of $20,000 is less exposed to risk compared to another company with liabilities of $200,000? Not really. The riskiness depends in part on the size of the company and how much it has in assets. And also on the nature of each company’s business.
When dollar amounts vary greatly, it’s difficult to compare the performance of two companies. Even evaluating the performance of one company over time becomes harder. To remedy this, you can use horizontal and vertical analysis of financial statements. Very cleverly, these types of analyses use dollar amounts converted to percentages. A vertical analysis expresses each item as a percent of a base amount.
But a horizontal, comparative, or trend analysis, is the process of examining how specific items in a financial statement vary over time. Think of when you compare financial information for two or more years, you follow a single line item – such as sales revenue – in a straight line across each year’s statements. [Two sample Financial Statements are displayed side-by-side.] As well as checking actual dollar amounts, it lets you compute percentage changes from year to year for all balances. Because it looks at trends over years, it helps spot areas of divergence that can alert you to problems or changes.
It’s helpful to look at industry averages as these give you an idea of what values are normal and acceptable. So to perform horizontal analysis and highlight trends–whether positive or negative – you take a base year as a reference and calculate how other years vary from it.
After selecting the base year, you calculate the percentage of variance from the base year’s data. First, you set consecutive Balance Sheets, Income Statements, or Cash Flow Statements side-by-side, and look out for any changes. Then you restate the amounts of each item, or group of items, as a percentage of the base year amount. The base year figures will always be 100%, and the changes from the base year expressed in relationship to that.
Suppose you’re reviewing inventory from year 3 of a business. Year 3 is the base year. Year 1’s inventory of $121,000 is divided by Year 3’s inventory of $83,000 to get a percentage of 146%. This indicates that the amount of inventory at the end of Year 1 was 146% of the amount it was at the end of Year 3. Year 2’s inventory of $100,000 is also divided by Year 3’s inventory of $83,000 to get a percentage of 120%. So inventory is 120% of the base year at the end of Year 2.This allows you to examine how each item has changed in relationship to the changes in other items.
Now you can use horizontal analysis to examine financial statements and check what has changed over time.
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Vertical Analysis
Learning Objective
After completing this topic, you should be able to
• identify examples that are characteristic of vertical analysis
1.
[Topic title: Vertical Analysis] Trying to compare data from companies that differed in size used to be an absolute nightmare. Luckily for us vertical analysis became our savior. Just as in horizontal analysis, all of the amounts are converted into percentages. The difference lies in what pieces of data are set as 100%.
In vertical analysis, the items given base values of 100% are the most important pieces of financial data. Everything else gets converted to percentages of those items. Just like that, size isn’t an issue anymore. And the relative composition of assets, total liabilities and equity, and revenues and expenses is revealed. Both Income Statements and Balance Sheets can be analyzed in this way. Depending on the source document, the percentage figures result in the output of a common-size Balance Sheet or common-size Income Statement.
For a vertical analysis of a Balance Sheet, total assets are set as the base value, and every other asset is expressed as a percentage of it. The total liabilities and equity amount is also assigned 100%, and each liability and shareholders’ equity account is expressed as a percentage. In the Income Statement, net sales is the base value having 100%.
The vertical analysis of a Balance Sheet shows how assets, liabilities, and equity are related. For example – what mix of assets generates income? What mix is from financing? Whether by liabilities or by equity. What percentage of total assets is inventory? What happens if that percentage changes significantly? What mix of various expenses a company has incurred? What percentage of total assets is made up of equity? What percentage is from liabilities? And what percentage of total assets comes from accounts receivable?
Vertical analysis calculations let you examine the composition of each of the elements on a financial statement. For an Income Statement, it reveals how many cents of each sales dollar are absorbed by various expenses. For example, if expenses in a company equal 57.3% of total net sales, it means for every $1 in sales earned, more than 57 cents goes to the costs of goods sold.
The vertical analysis of multiple years of financial statements can help you determine if significant changes have occurred. Similarly, you can also compare between financial statement items in companies of different sizes. The first step is to transform a given year’s balance sheet amounts into percentages of total assets and total liabilities. When the calculations are complete for all years, the sum of the percentages for the individual asset accounts needs to equal 100%. Then, because assets equal total liabilities plus equity, the sum of the percentages for the various liability and equity accounts will also equal 100%. It’s more meaningful when the percentages are compared with competitors’, or industry averages – or over a longer period of time for one company.
Using vertical analysis you can make certain financial comparisons between companies, regardless of size or dollar amounts.
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Resources: Discounted Cash Flow Valuation
• PRINT
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o Seeking Alpha. (2016, March 28). Does Warren Buffett use discounted cash flow? https://seekingalpha.com/instablog/5969741-the-value-pendulum/4868716-warren-buffett-use-discounted-cash-flow
o Ross, S. A., Westerfield, R. W., Jaffe, J. F., & Jordan, B. D. (2021). Corporate finance: Core principles and applications (6th ed.). McGraw-Hill. Available in the courseroom via the VitalSource Bookshelf link.
 Chapter 4, “Discounted Cash Flow Valuation,” pages 82-128
Resources: Impacts to Common Stock Prices
• PRINT
•
• Ross, S. A., Westerfield, R. W., Jaffe, J. F., & Jordan, B. D. (2021). Corporate finance: Core principles and applications (6th ed.). McGraw-Hill. Available in the courseroom via the VitalSource Bookshelf link.
• Chapter 6, “Stock Valuation,” pages 164-193. Find out how the valuation of these securities determines the ultimate value of the entire enterprise.
• Edspira. (n.d.). Capital stock (common stock and preferred stock) [Video] | Transcript https://www.youtube.com/watch?v=TZ2uWgtQXBo
• APITAL STOCK (COMMON STOCK AND PREFERRED STOCK)
• Speaker 1: The stockholders equity section of the balance sheet is a little tricky for some people to understand. You get used to seeing things like in the liability section, just accounts payable, it’s $100. You get salaries, wages payable is $200, and then all of a sudden, you get to the stockholders equity section, and you see something like this. You see common stock, or preferred stock. You see a par value. You’re wondering what that is. Shares authorized; issues outstanding; and you got basically a bunch of words, and all these things that make it a little bit more complicated than what you see on the right, which is just a number. You’re wondering maybe how do they get that 200, and what do all these words over here mean?
• Basically, this is the capital stock section of the balance sheet, and for a lot of firms, you could just go ahead and call it the common stock section because some firms don’t have preferred stock or anything like that. More generally, we just refer to it as capital stock, and it’s basically how the firm gets financing. When we think of things like let’s say you hear about a firm having an IPO or something like that. They’re basically raising money for the firm by issuing shares. They’re issuing shares of stock in their firm, and so this is the section where we’re accounting for that. The firm has to disclose certain types of things, one of which is the par value, another of which is the number of shares that have been authorized.
• What does that mean? The firm has a board of directors, and the board of directors votes to say, “Okay, how many shares are we going to authorize in this offering of stock to the public?” In this case, it was 100,000, so there are a 100,000 shares that the board of directors has authorized. However, that’s different from the amount of shares issued and outstanding. Here’s why. Just because the board said, “Hey, theoretically, we can issue up to 100,000 shares,” they’ve only actually issued 20,000. Now, they reserve the right to issue that additional 80,000, that difference between these two. They can do that down the road, but they haven’t done that right now. Right now, the amount of shares issued has been 20,000. In this case, actually, also, there’s 20,000 outstanding.
• You might say, “Well, why is that different or potentially different? Here it’s the same, but why could that be different? Why, if they issued 20,000, would there not just automatically be 20,000 shares outstanding and in the public?” That’s because the firm can buy back shares, which is called treasury stock. The firm can go and actually have a stock buy-back, and buy some of those shares that were issued, and just hold onto them, and then maybe reissue them later or give them to employees, or a number of things.
• In any event, the amount of shares authorized, issued, and outstanding, you can actually have three different numbers. Basically, when we talk about the par value, what we wanna drill down is focus here on this problem on these 20,000. We’re not concerned with the amount that we’re authorized. That hasn’t been issued. They’re not outstanding. We wanna say, “Okay, well, this par value.” Now, we say, “Okay, well, what does this par value even mean?” Theoretically, in the old days, it was kind of a value … Let’s just draw here. You’d have a little certificate of stock. Now, it doesn’t necessarily work that way. People can buy stock online and never even have a piece of paper, but you have this certificate of stock in this company, let’s say Coca Cola, and there would be a value on here, that par value. Theoretically, that value is the amount that you could go to the company at any time, and say, “Look, I have this par value here, and I demand that amount of money for my stock.”
• Now, realistically, stock prices fluctuate up and down. We have no idea where the stock price is gonna be six months from here, a year from now. Coca Cola doesn’t know what its shares are gonna be worth. What they do nowadays is they just put a par value that’s really, really low, in this case, one penny per share, and sometimes it’ll be 1/100 of a penny per share, really, really low par value because it doesn’t really matter. It’s just kind of this archaic tradition or what-have-you. The par value is deliberately set really low, and you basically just … In this case, we’d take that 20,000 and multiply it by the one cent par value per share, and that’s gonna give us 200. 200 would what the firm would have under its common stock. If you think of a journal entry, so they’re raising money, they would have a credit … They’d have a cash amount. Obviously, they’re debiting cash for some amount.
• Okay, that’s the actual money they get from the people who buy their stock, and then there’s gonna be a credit to common stock for that 200. Then, now you might be wondering, “Okay, but the firm is gonna get more than one cent per share when they go ahead and actually issue the stock, right?” Maybe they get $35 a share. In that case, that’s where we’re gonna have this … To make this entry here balance … Let’s say this cash was 800, for example. We’ve got this 600 here, and we’re wondering, “Well, what is that?” To make that entry balance, we’re gonna have a thing called additional paid in capital, I’ll just abbreviate APIC, and that’s actually gonna make this entry balance, and APIC is gonna be a lot bigger than the common stock, typically, on that shareholders equity section of the balance sheet because again, this is deliberately set low. It’s just representing the par value, maybe the same … You do preferred stock the exact same way. You’d have a cash, then preferred stock.
• In any event, that kind of explains kind of the rationale for why we have this common stock and what it is. In the next video, we’re gonna go through an actual example and calculate how you would go about doing the journal entry and everything in a case where you have significant additional paid-in capital, and talk about-
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• TheFinCoach. (2012). Session 08: Objective 1 – common stock valuation [Video] | Transcript https://www.youtube.com/watch?v=uajW4BWh_zY
ESSION 08: OBJECTIVE 1
Common Stock Valuation
Greg Pierce: Welcome to Corporate Finance.
Speaker 2: We’re rolling.
Greg Pierce: Welcome to introduction to Corporate Finance session number eight on stock valuation. I’m Greg Pierce your finance coach, and we’re here to talk about how do we value a stock. We know now how to value bonds. And what are some of the general models, generic models for valuing stocks. The general case, just in general you’re gonna see that stocks are much more difficult to value than bonds, there are several models.
We don’t know a lot about the stock as much as we do about the bond. The bond we know the face is $1,000 and we know the required rate of return of all the bonds in the market. So a lot of knowns in the bond world, but in stocks we just don’t know if a company will pay a dividend, when it will pay the dividend, when it might begin to pay the dividend, and how long the dividend will continue.
So there are … And we do not know the stock price in the future to discount those back to today to get a handle on the stock price. So, we’re gonna go over several cases that will help us to value stock. There are many, many others that are a lot more complex. These are very good general cases. First of all, what I’m gonna call the general stock valuation equation, and I’ll call it wildly fluctuating. It’s where dividends are all over the place.
They may grow at a super normal rate for several years and then, step back a more normal rate. So we’re gonna call that one the wildly fluctuating or, general stock valuation model. It’s the first equation you see here. Another equation you should memorize is the zero dividend growth case. So what happens if GM who used to pay $2.00 a year continues to pay $2.00 forever? So $2.00, $2.00, $2.00, $2.00, $2.00, we know that, that’s an annuity. Hopefully it will go on forever, we know in GM’s case it hasn’t.
They’ve stopped paying their $2.00 dividend due to financial difficulties. But if there were a company to come about that would pay a constant dividend every year, same amount each year, that becomes an annuity. If it goes on forever it’s perpetuity. And we remember from session six that present value of a perpetuity is C or R. So here we just substitute the dividend value in there and then you get D over R for the stock price today.
If we have a constant dividend growth. McDonald’s recently announced that they are going to pay a constant four percent growth in dividends. Try to anyway, that was their model and their plan. And so, if we have a constant dividend growth rate G, we know that the price of the stock today is equal to the next dividend over R minus G where G is the constant growth rate in the dividends. We’ll talk more about that model.
If we have super normal growth again, where a company grows very, very fast to begin with, and then starts to level out, we’d go back to the general stock valuation equation or what I call wildly fluctuating, where the present value or price of the stock today is equal to the future dividends discounted back to today. Plus some price of the stock at some time T, discounted back to today.
And, finally, the two components of required return we want to memorize, D1 over P0 plus G. So if we switch around that constant growth equation for P0 and solve for R, we get the required return of any stock. What do you want when you buy a stock? You want dividend yield plus capital gains yield, and those are the two required elements of required return. Looking at our learning objectives, we have three for this chapter. We want to know and learn how to value common stock and we’re gonna go through some of those models.
What are some of the features of common stock and preferred stocks, and how are they different? And finally, where do we buy our stocks? And the answer on the stock markets and we’ll go over some of the stock markets. Common stock valuation is a little bit more difficult than bond valuation as I’ve said. We don’t have any promise cash flows what so ever, unlike a bond where you have a promised coupon. You don’t know if the company will be in financial difficulty or not, the life of the investment is forever. You hope the corporation goes on forever.
So there is no maturity unlike a bond, which has … A corporate bond has a 30 year maturity date. There is no easy way to look at the required rate of return as you can with a bond market. So, little bit more difficult to value. So what is the price of the stock today? It’s equal to present value of the dividends, plus some price in the future, all discounted back to today. And we can go on and on, discount all the dividends back. Dividend one, dividend two, dividend three, dividend four, dot, dot, dot.
And if we push out that P sub T, the price of the stock out far enough it kind of falls off the map because it’s discounted by such a large factor that there isn’t much value. So we could say in general, the price of the stock today is equal to the present value of all of it’s future dividends in a very simple model. Model number two again, that’s the general stock valuation equations. If we have no growth in dividend as I said, the price today is simply equal to D over R, which looks like a perpetuity equation C over R from session number six.
So, same amount each year in dividend. The price of the stock is simply the dividend divided by required rate of return. In model number three, constant dividend growth model, we have a constantly growing perpetuity. We have a growth rate, a constant fixed growth rate that’s declared by the company, and therefore we can look at the price of the stock today as being a next dividend D1 over R minus G.
Another way to look at the price of the stock at any time T, like P15 is equal to D16 over R minus G. Again, next dividend over R minus G. If we have some information on the price today, this stock price today, then the price at any time T is simply the price today times 1 plus G to the T. It looks very much like the present value, future value equation. In general in dividend growth model, the price of the stock at any time T, is equal to next dividend over R minus G.
So again, if we wanted to do a P4 price of the stock and time four is equal to D5 over our minus G. Price of the stock at time 10 is equal to D11 over our minus G. And this only applies when dividend is growing at a constant rate G, like in the case of McDonald’s. They’ve recently looked at a four percent targeted growth rate. This works mathematically if required return is greater than G. So we don’t have a negative denominator.
Super normal growth rates can exceed the required return over some future length of time. Again, a company may grow very, very rapidly. And again, we have to go to when we see this, when we see what I call a wildly fluctuating dividend model, we go to equation number one and that is the general stock valuation equation. When I’m looking at P sub T out there to the right, we know it’s equal to dividend sub T plus one over dividend at the next growth rate, divided by R minus G.
So P sub T, what I do is I step back one year. So, if it says that the stock dividend will grow constantly in year four, then we go step back to year three and calculate P sub three, and P sub three is D4 over our minus G, and that takes care of all future dividends almost as if it were P0 out there. And again, so sometimes these stocks will grow at let’s say, 30% very quickly when the company’s starting up and growing rapidly, and then taper off to a five percent more common and reasonable growth rate.
Again, if that happens in year four where the growth goes constant, we step back and calculate P3 at the end of that equation and P3 is equal to D4 over R minus G. Components of required return look at, what do you require when you buy a stock? Well hopefully, you get some price appreciation and your stock goes up. This is called, referred to as capital gains yield. And if it’s constant growth rate can be … It can use a terminology G, same as the growth rate in dividends.
And dividend yield is D1 over P0. So when I buy a stock, hopefully some day it pay me a dividend and dividend yield breaking up that constant growth model into pieces gives me dividend one over P0. So, percent R is equal to D1 over P0 plus G. Dividend yield plus capital gains yield, and that’s what I look for when I buy a stock.
REFERENCES
• The Finance Coach:Introduction to Corporate Finance with Greg Pierce, published on June 25, 2012, from TheFinCoach.
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• Harper, D. (2018, February 18). Forces that move stock prices. https://www.investopedia.com/articles/basics/04/100804.asp
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Resources: Bond Valuation
• PRINT
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• Ross, S. A., Westerfield, R. W., Jaffe, J. F., & Jordan, B. D. (2021). Corporate finance: Core principles and applications (6th ed.). McGraw-Hill. Available in the courseroom via the VitalSource Bookshelf link.
• Chapter 5, “Interest Rates and Bond Valuation,” pages 129-163. This chapter illustrates the employment of time value of money concepts to determine the value of corporate debt/bonds and common/preferred stock.
• McCracken, M. (n.d.). Bond valuation [Video] | Transcript http://www.teachmefinance.com/bondvaluation.html
BOND VALUATION
Speaker 1: A bond is when a company of a government borrows money from the public or banks, who are the bond holders, and agrees to pay it back later. Par value is the amount of money that the company or the government borrows. Usually it’s $1000. Coupon payments are like interest, the company or the government makes regular payments to the bond holders, like every six months or every year. The indenture is the legal stuff, it’s a written agreement between the company and the bond holder. They talk about things like how much the coupon payments should be and when the money, the par value, will be paid back to the bond holder.
The maturity date is the date when the company pays the par value back to the bond holder. The market interest rate is the current interest rate for a bond and it changes every day. Okay, the thing about bonds is that the interest rate, or the coupon payments, are fixed. They don’t change. If you have $1000 bond and you’re getting 10% interest, well, you’re getting $100 payment every year for as long as the bond lasts. In the meantime, interest rates in general go up or down.
Okay, say interest rates went up, and say that bonds are now paying 15%. Well, your bond will be less valuable because yours is only paying 10% while current bonds are paying 15%. On the other hand, let’s say that the interest rates went down to 8%. Well, now your bond is more valuable because your bond is paying 10%, while bonds that are issued today are only paying 8%. Okay, let’s say again for the example that you have a bond with a par value of $1000 that pays 10% interest, and the current market rate is 8%. Well, perhaps you’d like to sell that bond to someone else.
The question is how much should you sell it for? In other words what is the present value of the bond? Okay, basically there are two parts of a bond and by adding these two parts together we can figure out what the present value of a bond is. The first is the present value of the coupon payment. Now, this is basically just an annuity. The second is the present value of the par value. This can be calculated using the time value of money.
Let’s do an example. Let’s say that you have a bond with a par value of $1000 and the maturity date is in five years. The annual coupon payments are for $100, which is 10%, and the market interest rate is, like we said before, 8%. In other words, the market interest rate has dropped from 10% to 8% since the bond was issued. If you go to this page and learn about annuities you’ll find that it comes to $399.27. We won’t go through how to figure the present value of annuity again right now because you can go to the other page, but if you’re going to figure it out yourself for the interest rate use 8%, and for the number of compounding periods use five, and for the payment use the $100.
Using this information you’ll find that the present value is $399.27. The present value of the par value is the $1000 that you’re going to get, discounted by 8%, which is the market interest rate. To understand this you have to use the time value of money information that we taught you earlier. If you don’t remember it you can go to this page, which will explain it to you again. The equation would look like this, $1000, the future value, equals the present value times 1.08 to the power of five, 1.08 to the power of five equals 1.4693280. So, you divide both sides with that number and you get $680.58.
Okay, now you just add these two numbers together. The present value of the coupon payments, which as an annuity is $399.27. The present value of the par value, which you figured out using time value of money, is $680.58. When you add these two numbers together the present value of the bond is $1079.86. Now, it’s logical that the present value of the bond is more than the bond’s par value because the interest rates have dropped, which means that your bond is now more valuable than the bonds being issued today at the lower interest rate.
REFERENCES
• Copyright 2008 by TeachMeFinance.com. All rights reserved.
CREDITS
Subject Matter Expert:
Robert Wagner
Interactive Design:
Ginny Yahnke
Instructional Design:
Mo Yang
Project Manager:
Jay Austin
esources: Capital Budgeting Tools
• PRINT
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• Ross, S. A., Westerfield, R. W., Jaffe, J. F., & Jordan, B. D. (2021). Corporate finance: Core principles and applications (6th ed.). McGraw-Hill. Available in the courseroom via the VitalSource Bookshelf link.
• Chapter 7, “Net Present Value and Other Investment Rules,” pages 194-228. This chapter introduces the process of capital budgeting, which determines the value of a potential investment/project to a firm. That is, it weeds out good investments from the bad. Evaluating capital budget projects is a critical function for any business professional involved with finance decisions.
• Chapter 8, “Making Capital Investment Decisions,” pages 229-261. The key to valuation of investments and projects is the cash they generate. This chapter illustrates the way to figure the all-important cash flows from investment projects.
• Van Dalsem, S. (2017). Capital budgeting cash flows tutorial [Video] | Transcript https://www.youtube.com/watch?v=X6HvKl__rLY&t=19s
• View the segment, 12:36-27:36.
CAPITAL BUDGETING CASH FLOWS TUTORIAL
Speaker 1: In this video, I’m going to work through the calculating project cash flows tutorial. This is out on D2L along with a spreadsheet that I’m going to use. This spreadsheet is actually in the tutorial. I’m gonna show you how to work through the spreadsheet in Excel and also demonstrate how to calculate all the different capital budgeting tools that we’ve learned previously in Excel.
So let’s get started with the tutorial here. This is the problem. You’re interested in the purchase of a machine that costs $65,000. Installation of the machine will cost an additional $15,000. The machine has an economic life of four years with the three years makers depreciation. However, you expect to sell it after three years at a salvage value of $23,000. The machine requires an initial increase in working capital of $20,000. While in operation, the machine will generate $40,000 in revenues and will cost $5,000 to operate in the first year.
The expected rate of inflation is 2.5%. Revenues, operating costs, and the required networking capital will increase by the rate of inflation for years two and three. So year one is $40,000 in revenues, $5,000 in cost, $20,000 in network capital. We’re gonna increase those by 2.5% in years two and three. If the corporate tax rate is 40% and the firms weighted average cost in capital is 12%, should the firm invest in the project. So that’s our problem. Now I’m gonna work through the solution.
So the way we define the project cash flow is this is the project operating cash flow, minus the project change in networking capital, minus the project capital spending. The project capital spending … the depreciable basis of the investment into the machine includes both the cost of the machine and installation cost. So you get to depreciate not only the machine itself, but any kind of installation costs and transportation costs that come with putting that machine in place.
And so we … this is reflected in the worksheet as an investment a year zero. So I’m gonna go over here to this spreadsheet and at time zero, year zero, I’m gonna put in negative $80,000. And then it says, “The project change in networking capital, the investment in working capital reflects an expected permanent increase in network and capital for the duration of the project.” So in this case, we’re buying a machine to produce goods. In order to produce goods from that machine, we have to have inventory. So there’s going to be a permit increase in inventory that lasts for the life of the project.
And then at the end of the project, we actually wind down that inventory, we stop buying new inventory. When we get close to the … or new raw materials when we get close to the end of the project and just use up what’s left and reclaim our investment. And I’ll demonstrate how to do that later on. So I’m gonna go over here. Our network and capital investment is $20,000 and that also occurs at time zero because the day we get started, we wanna have that inventory in place. Project operating cash flows. Since the purpose of calculating cash flows of the project is to determine if the firms investors would receive an adequate return.
We want to calculate the free cash flows that would be available to all of the firms investors. So the term free cash flows means that these are the cash flows left after we paid off all the operating expenses of the firm, we paid for our inventory, we paid for our employees to work, we paid for utilities, and everything that’s left over in terms of cash is now available to pay out to the firms investors. This does not include paying out money for interest expense because the bond holders are investors to the company.
So we don’t include financing cost, meaning interest expense in our calculation. Instead we discount the cash flows back at the weighted average cost of capital, which is constructed using the financing cost. So our operating cash flow is equal to the earnings before interest in taxes, plus depreciation, minus the taxes. Depreciation expense for each year is calculated from the maker schedule and that stands for modified accelerated cost recovery system. So it’s accelerated depreciation. And I put the table from the IRS website here for the half year convention.
And the half year convention works like this. This is from the IRS website. The half year convention, under this convention you treat all property, place, and service or disposed of during a tax trade has placed in service or disposed of at the mid point in the year. So we assume that any time we purchase a fixed asset, it’s purchased in the middle of the year so we take, at the beginning, a half a year of depreciation, and at the end we have a half a year depreciation. Now the makers half year convention table assumes that it’s placed in the middle of the year.
So we don’t have to adjust it there. Where we adjust it is at the end. So let’s say we have a, well in our case, a project that lasts three years, it has a three year depreciation life, but you’ll see here that it goes out for four years. That’s because we have a half year here at year one, we have a half year at year four. For a five year project, we have a half year at year one and a half year at year six, sorry. For seven year, half year at the beginning, half year at the end.
That’s why there’s always an additional year on these because we’re assuming that we’re putting the asset in place in the middle of the year. So we’ll use this schedule. The end of project cash flows. The final cash flows from the project come from the sale of the fixed asset investment and unwinding the investment in working capital. There are two effects on cash flows from the sale of the equipment. The first is the cash received on the sale, the second is the tax paid on the … gain from sale.
The gain of sale of equipment is calculated at the sale price of the equipment minus the remaining basis value. So that’s a key word there. The basis value is how we normally refer to as the book value, but because we’re dealing with tax statements, for tax purposes, we don’t refer to it as book value, we refer to it as the basis value and that’s how we tell the difference between what’s on the books, the financial statements of the firm, what you and I see as investors and what the firm is actually reporting to the IRS.
The reason why we’re interested in what they’re reporting to the IRS or what we assume they’re reporting to the IRS is because that’s what they’re actually paying cash taxes on. And so we’re interested in cash flows here because that’s going to determine how much value it’s creating for the company. So the remaining basis value of the equipment is calculated as the original out paid less the accumulated depreciation expense and we’ll work through that here in a minute. Figure three shows the calculation for this sample problem.
So let’s go to our spreadsheet and what we’re gonna do now is we’re going to put in the project operating cash flows and then we’re gonna put in, to this point, the end of project cash flows. We’re gonna work through figure three here after we get our project cash flows in. So our revenues for the first year are $40,000, our working capital investment stays the same, there’s no change in it, our operating expense for the first year are $5,000, our depreciation, what I’m gonna do here is actually put in our depreciation percentages on this spreadsheet.
So I’m gonna go back here. And this has a three year life, if you read the introduction again. We have 33.33, 44.45. So I’ll put those in right down here. .3333, .4445, .1481, and 7.41%. I’ll make these look a little nicer. So these are my depreciation rates. So my depreciation for the year is equal to the fixed asset investment and that asset investment alone, not the working capital investment, multiplied by … oh, actually I’m going to go back here.
I’m gonna press F4 and that’s gonna lock that in place. That’s gonna make life a little bit easier. And multiply it by the depreciation rate for the first year C30. And then I’m just gonna drag this over so I don’t have to put that in again. I can drag it over for the first year. And then for the second … so that’s the $80,000 multiplied by the 44.45. For the third year, because of the half year convention, I need to multiply this by .5 because I’m only depreciating it for half a year.
If we went out to year four to the end of the life of the asset for depreciation reasons, we wouldn’t multiply it by .5 because the schedule is already taking that into account. Our rate of inflation is 2.5% so I’m gonna make a sell up here so as inflation rate and gonna put 2.5% here. I’ll make that into a percentage. And here’s a nice trick in Excel if you’re not familiar with it. You can name cells. So I’m gonna name this one, so I’ve selected cell F7 and then I go up here to the name box and I’m gonna name this one inflation.
So I can actually just type in the word inflation. And it’s going to give me that rate. So I put an equals, the previous years revenues, multiply by one, plus the rate of inflation here, and it gives me that $41,000 and I go add another year. I’m gonna pull that over. Gonna do the same thing. It’s got the previous year D15, multiply one plus the rate of inflation. I’m gonna make these look better. Here we go. My operating expense should actually be negative. So put negative there. Gonna do the same thing with the rate of inflation is equal to the previous year, multiply it by one plus inflation.
And pull that over again. And so I’ve got my revenues, I’ve got my operating expenses, I’ve got my depreciation expense. My working capital investment expense is also going to increase by the rate of inflation. So my change in working capital is the amount of additional working capital I have to invest in for each year and it makes sense that this should go up because the cost of goods sold per unit that we sell, for every piece of inventory we bring in, is going to also increase by the rate of inflation.
Our sales are increasing by the rate of inflation so our accounts receivable should also increase by the rate of inflation. So our change in working capital investment. In year one we’re not going to put an increase, in year two we’ll increase it by the rate of inflation. So up here I’m gonna put in equals the previous years working capital investment multiplied by one plus inflation. So it goes up by $500. And then I’m gonna pull this over one more year and it’s going to increase by $512.50.
So what I’m gonna put down here is that this represents a cash flow. We’re going to put more money out, we’re going to increase our inventory expense. So I’m to put in here equals the change in the working capital investment. See it’s negative. It’s going to be a use of cash. I’m gonna do the same thing for year three. So our cash flow isn’t the $20,500, it’s actually just the difference, it’s the change from one year to the next. Our earnings before tax … interest in taxes. So our earnings before interest in taxes do not include the change in the working capital investment.
And the reason being is that this is not tax deductible. So our EBIT is equal to $40,000, minus the $5,000, minus the $24. So I get $8,336 for year one. For year two I get $315, and then for year three I get $30,847.88. My tax rate, according to the problem, is 40% if the corporate tax rate is 40% so I’m gonna put that in here. I’m gonna make that negative because that’s going to be an expense. And then we add back depreciation. So I’m gonna put equals negative and then highlight the depreciation expense. So the reason we did that, the reason why we take out depreciation then add it back in is because depreciation is a non-cash expense.
So we get to take it out and we like to take it out because it decreases our taxable income. So we take it out so we’re not taxed on it and then we add it back in because it wasn’t really a cash expense. However, tax is a cash expense. We actually have to pay that. And so it’s beneficial for firms to do this, to have depreciation, take it out, and add it back in afterwards because this is a non-cash expense, but it affects our cash because we reduce our taxable income by that amount. So after we add back depreciation, we calculate our operating cash flows, as our change in work capital, plus the EBIT, subtract out the tax, but it’s negative on here so we use a plus sign, plus the depreciation.
So change in working capital investment, plus EBIT, plus tax, plus the adding back the depreciation, and for year one we get a cash flow of $31,665, for year two we get a cash flow of $35,249, and in year three we get a cash flow of $23,920.23. So the next step is to determine what the cash from the sale of the equipment is. So going back to the tutorial, it says here, “The end of project cash flows, the final cash flows from the project come from the sale of the fixed asset investment and unwinding the investment in working capital.”
“There are two effects on cash flows from the sale of the equipment. The first is the cash received on the sale.” So in our case, we expect to sell it for $23,000, and the second is the tax paid on the gain from the sales. So I wanna make it clear here, you’re not paying tax on the sale amount, you’re paying tax on the gain on the sale. The gain on sale of equipment is calculated as the sales price or the sale price of the equipment minus the remaining book value of the equipment. The remaining basis value … excuse me, remaining basis value of the equipment.
The remaining basis value of the equipment is calculated as the original amount paid less the accumulated depreciation expense. Figure three shows the calculation for the sample problem. So we’re going to calculate this, but we’re gonna do it in Excel to make it a little easier. So I’m gonna go up here to the top. Our fixed asset investment was the $80,000. So that was our basis value. And now we put in our depreciation for each year. So for year one, it was $26,664, for year two it was $35,560, and for year three it was $5,924. So here are accumulated depreciation.
I’m gonna put in equals the sum of these three. And if you’re thinking of like a balance sheet, and this helps me out. I think of the gross fixed asset value of $80,000, the accumulated depreciation value would then be $68,148, and then the net fixed asset value would be the remaining value after we take out the accumulated depreciation. So $11,852. So the gain on the sale of the investment … is equal to what we sell it for $23,000, minus the remaining basis value. So the gain on the sale of investment is $11,148. The tax on the gain is our tax rate at 40%, minus the gain on the sale.
So our tax is $4,459.20 and again, I’m not taxing the $23,000 I’m receiving, I’m taxing the gain on the sale of the investment. What I’m receiving that is above the book value or the basis value of that equipment. So the cash flow from the sale of the equipment, there’s two pieces to it. What we sell it for, and we sell … or we expect to sell the equipment for $23,000, minus our tax on the gain, $4,459.20. So our cash flow from the sale of the equipment is expected to be $18,540.80. So our cash from the sale of the equipment is equal to $18,540.80.
And then at the end of the project our recovery of the working capital investment. So what happens here, and let me go back to the tutorial. The gain on the sale of the investment, I’ve already put these in here. And I’m going to show them again to you. So the gain on the sale is the $23,000 minus the taxes we paid. So it’s $11,148. So that’s our gain on the sale. And the tax on the gain is $4,459.20. So the cash flow from the sale of the equipment would be our $23,000, which is what we receive, less the amount we paid out, which was the $4,459.20. And so that’s equal to $18,540.80.
The second end of project cash flow is recovering the working capital investment. Throughout the project, a level of investment remains in networking capital that is unwound in the final year as last piece of inventory are converted to sales and accounts receivable are paid and no new investment is into working capital takes place. So imagine that your near the end of the project and you’re probably in the last three months of the project. You’ve got enough inventory, raw materials inventory on the shelf to make new products for the next three months.
So you’re not planning on buying any additional inventory. So unwinding the investment takes place in this way, that we use up that inventory on the shelf. We don’t reinvest and we receive the cash back without reinvesting it when we sell the product. Additionally, when we look at accounts receivable, it’s the same idea. We’re selling things on credit. And when we’re done at the end of the project, we’re not selling any more of the product on credit, so we’re not increasing or we’re not even maintaining the amount of accounts receivable from the project, we’re winding them down, we’re collecting the cash from the accounts receivable without generating any new accounts receivable.
So we’re decreasing our inventory, we’re decreasing our accounts receivable, and as we do that, we get cash in it’s place. So we’re unwinding the investment and we’re collecting the cash we have invested in the working capital. So the way this works on our project cash flows, if I go down here. Recovery of the working capital investment, that’s gonna be equal to, I’m gonna put equals negative the working capital investment, just for that last year because this is just accumulating every year. We’re not investing $20,000 a year one and than $20,500 in year two.
We’re only investing $500 in year two. And an additional $51,250 in year three. So we’re getting all that cash we have invested in inventory and accounts receivable back at the end of year three. So we end up project cash flows look like this. At time zero or year zero, we receive … or we invest $100,000 at year one, our operating cash flows are $31,665.60. Year two, they’re $35,249 and that also includes the investment we have up here in the working capital. And then in year three, we have our operating cash flows $23,920.23, plus the cash from the sale of the equipment, plus the recovery of the working capital investment.
So this is what our cash flows look like. You wanna make it look like something you’ve seen before. We can copy it. We can put it in this order. I have my cash flow and I have my year. And that’s what we were doing in the previous chapter. So now we’re gonna calculate the NPV, the IRR, the MIRR, the profitability index in the pay back period. NPV’s a little bit different in Excel because we don’t want to include the time zero cash flow or the year zero cash flow in the NPV function.
So I’m gonna put equals and then the negative $100,000, plus NPV, the discount rate is the weighted average cost of capital. So in this case it’s 12% from the tutorial. And then I’m going to highlight, put a comma and highlight the rest of the cash flows. So it looks like this. And the reason we don’t put the $100,000 in here, in the NPV function, is because the first cash flow that NPV sees, it discounts back by one year. So what it assumes that first cash flow occurs at year one, the second at year two, and the third at year three.
And I get an NPV of $1,552.35, my IRR equals IRR. I highlight all of it and I get 13% there. Let’s take it out. 12.8%. My modified internal rate of return is equal to MIRR. I highlight all my cash flows again. And then it gives me two options here. The finance rate, and this is going to be your weighted average cost of capital. So it’s 12%. And the reinvestment rate. This is the rate that you assume you’re going to reinvest the cash in flows at. So the rate we assume we’re going to reinvest the $31,665.60, the $35,249, and so on.
We’re also going to use the weighted average cost of capital here. And I get an MIRR of 12.58%. So the profitability index, I’m gonna calculate this as the NPV and then I’m going to add the initial investment of $100,000. And if you look at what I’m doing, I’m actually taking minus that amount because it’s a negative number and then I’m gonna divide it by the negative … by a negative and then the negative $100,000. And I get a profitability index of 1.02.
So the pay back period … so we just add back the cash flows and so that’s what I’m gonna do here. Equals my $31,660 … excuse me, my negative $100,000, and I’ll put a plus $31,665 while we still have $68,334 to pay back. So I’m going to take that, plus my year two cash flow, and now we only have $33,085 to pay back. So I’m going to divide that by my year three cash flow. And I get .5212. So my pay back period is 2.52 years. Okay. So the question is would we accept this?
And it looks like we would. The NPV, while not huge, is positive $1,552.35, the IRR is greater than the weighted average cost of capital, the MIRR is as well, the profitability index is 1.02 so it’s greater than one, and we expect it to pay back in 2.52 years. So that’s it for this tutorial. Please let me know if you have questions about it.
REFERENCES
• Capital Budgeting Cash Flows Tutorial, published March 21, 2017, from Shane Van Dalsem.
• Licen