It therefore shows how much profit (attributable to the shareholders) in dollars (or any other currency) can be distributed to the shareholders for every dollar of common stock.

The formula to calculate the return on equity ratio is very simple. You will need two numbers, the net income available for distribution to the shareholders which can be found on the income statement and the shareholders equity which can be found on the balance sheet – statement of financial position.

The formula is: ( Net Income/Common Stock Equity)%

It is worth pointing out that in order to calculate ROE, the net income is after deducting any dividend that needs to be paid out to investors that hold redeemable preference shares. However, these dividends are already deducted before arriving to the net income, since redeemable preference is debt and the “dividend” is included in the finance expense line (on the profit and loss statement).

The following example will help us calculate and understand the return on equity ratio. It’s a straightforward scenario for two different companies that have a different capitalization and different income.

[table id=21/]

Company A has a lower net income but also a significantly lower equity. At the same time, Company B has a higher net income but a significantly higher shareholders’ equity figure.

Therefore, the return on equity ratio for company A (2,000,000/15,000,000) is 13% while the ROE for Company B is 10% (5,000,000/50,000,000).

Based on the example above, we can see that while Company B has a higher net income, ROE takes into account the “size” of equity too.

As a result, ROE for company A is higher than for Company B. This means that Company A has managed to generate more profit per dollar of equity than Company B.

Investors usually follow company that have a high ROE because it shows that the company is able to potentially pay out high dividend. However, high ROE and does not necessarily mean high dividends too. In other words, a company might be able to generate high profits compared to the equity funds used, but it might be choosing to either retaining them or re-investing them instead of distributing them.

Another point that is worth noting is that ROE can be manipulated by raising debt instead of capital. If a company used more debt, then the shareholders’ equity will be lower and therefore the ROE (return on equity) will be higher. However, higher debt also means higher interest expense (among other things).

Finally, a variation of the Return on Equity is the Return on Common Equity which excluded preference shares (both the dividend paid to preference shares but also the funds raised by issuing preference shares).

The online calculator below can be used to calculate the return on equity. Just fill in the blanks!

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The internal rate of return is the discount rate which makes the costs to undertake a project equal the profits that this project will generate. In other words, the internal rate of return is the discount rate that gives a zero net present value.

The idea is that if the cost of capital which is also the interest rate that a company pays to borrow money is less than the internal rate of return, then the project can be accepted.

As noted above, if the internal rate of return is lower than the cost of capital then the project should be rejected since it costs more money for the company to invest in this project than the return that the project is expected to bring.

We will use one example in order to illustrate how the internal rate of return can be calculated and the approach is. Let’s say that company A uses the internal rate of return to evaluate investment opportunities and make a decision regarding the profitability and viability of a project.

There is one potential project that Company A wishes to appraise with the following characteristics:

-An initial investment of $50,000 is required during the first year.

-The project will last for four years and the cash inflows during these four years will be:

- Year 1 : $15,000
- Year 2: $20,000
- Year 3: $25,000
- Year 4: $18,000

The company has a cost of capital of 15% and wishes to appraise this project and decide whether to proceed or not.

There are two different approaches that can be followed to calculate the internal rate of return.

From the IRR definition, we know that the IRR is the discount rate that makes the present value of the cash flows become $nil. We can therefore use a trial and error approach and start increasing the discount rates until we get to a present value that is $nil.

The following table illustrates the calculations.

[table id=19 /]

As we can see from this table, a discount rate of 19% gives around $500 NPV while a 20% discount rate gives a $-462 NPV. We can therefore understand that the IRR is somewhere in the middle or around 19.5%.

There is another approach we can use to calculate the internal rate of return (IRR) and involves a formula (see below). The idea is that we use two different discount rates for which one will give a positive net present value and another that we believe will result in a negative net present value. It might sound complicated but follow the example below which should help you understand what are the steps you should follow.

IRR= Ra + (NPVa/(NPVa-NPVb))*(Rb-Ra)

where

Ra is the discount rate that gives the positive net present value, NPVa is the positive NPV, NPVb is the negative NPV and Rb is the discount rate that gives the negative NPV.

Let’s proceed with a table that can illustrate what’s written above in an easier to follow way:

[table id=20 /]

The table is part of the first table and we can see that a 10% discount rate gives a positive NPV and a 20% gives a negative NPV. We can therefore use the formula above and calculate IRR as:

IRR= 10+(11,242/(11,242+462))*(20-10)=19.6%

As you can see both methods will give the same IRR (more or less) but most people prefer to calculate IRR by using the second approach since it involves less calculations.

The internal rate of return is a very robust capital appraisal method but there are certain limitations. For example:

- When a project has positive cash flows, followed by negative and then followed by positive cash flows again, there will be more than one IRR (more than solution).
- IRR is not very reliable when comparing projects that have significantly different time horizons (i.e project A will last for 5 years while project B will last for 15 years).
- Due to the limitations explained above, IRR is mostly used a decision tool (accept or reject) and not as a comparison tool (project A vs project B).

There are however certain advantages that IRR has which make it one of the most preferred capital appraisal methods.

- It’s an easy way to decide to accept or reject projects.
- It’s a robust method that can be used to monitor how a project is performing based on the actuals vs the budgets and how that compares to the cost of capital.
- It takes into account the time value of money compared to other methods (payback period for example) that do not.

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Shareholder funds are not interest bearing but they dilute the ownership of the company. In addition, investors expect some kind of return on their investment which usually takes the form of dividends.

On the other hand, debt does not dilute the ownership but it requires interest payments. In addition, debt holders come first when a company is being liquidated. Finally, debt usually requires a fixed or floating charge.

There are two different formulas that can be used. Both of them are valid and as long as there is consistency, the results from your analysis should be comparable.

The first formula includes the interest bearing debt in the numerator and the share capital plus the retained earning in the denominator. So, the first formula for the gearing ratio is:

Gearing Ratio (%) = (Interest Bearing Short and Long Term Debt/Share Capital+Retained Earnings) *100%

The second formula that can be used to calculate the gearing ratio is pretty much the same apart from the fact that the debt that is included in the numerator is also added in the denominator.

In other words, the formula is:

Gearing Ratio (%) = (Interest Bearing Debt)/(Share Capital + Retained Earnings+Interest Bearing Debt)

Where interest bearing debt one should include bank loans, overdraft facilities, loan notes issues and other forms of debt that has been issued.

In order to understand the gearing ratio, two examples will be used.

Company A has a $1,000,000 bank loan that is due in 5 years. In addition, the shareholders funds as per the latest statement of financial position appear to be $750,000. Similar companies in the industry usually have a gearing ratio of 40% to 50%.

Using the above formulas (the first one), we can calculate the gearing ratio for this company which is 75% (1,000,000/750,000). Apart from analyzing the historical data for the same company, it’s also useful to compare the results with similar companies in the sector. The reason for that is that different sectors have different characteristics.

For this example, we can see that Company A has higher gearing since other companies in this sector have around 50% financial gearing.

Company B operates in the same sector with Company A. Company B has a $500,00 bank loan and $1,500,000 shareholder funds. Therefore, we can calculate the gearing ratio which is 33.33%.

While for simplicity, we don’t use historical information for Company A and B, we can say that both companies could improve their financial leverage.

For example, Company A is highly geared with the gearing ratio being higher than the industry average by 25%. At the same time, company B has a significantly lower than the industry financial leverage.

So what does that mean? For company A, a high gearing ratio means that the company will have to pay interest on an annual basis (higher than what’s normally paid by same companies in the sector), adhere to bank covenants and risk breaking these covenants when the financial results are not so good. Of course, all of the above are not ideal for a company.

Increased gearing ratios are risky and when a company is unable to repay it’s debt, it can lead to bankruptcy.

At the same time, Company B has a very low gearing ratio when compared to other similar companies in the same industry. This is also not ideal since the cost of debt is lower than the cost of equity.

The cost of debt is cheaper because as already mentioned, debt holders are more secured then shareholders (in the event of a liquidation). Of course, as we saw from the first example, that does not mean that companies should only raise debt. This is also risky and can lead to unpleasant events.

Companies should find a balance that is in line with the needs of the company, the ability to raise debt or capital (creditworthiness), the needs and desires of its shareholders and also in line with the industry and market standards.

As explained above, there are reasons for which a company might want to increase the gearing ratio. There are different ways to achieve that:

- Raise additional debt (bank loans, loan notes, overdraft etc.)
- Buy Back part of the shares that are issued
- Pay Dividends from the retained earnings reserves

Similarly, there are situations where a company might have to or want to lower the financial gearing which can be done by:

- Repaying part of its interest bearing debt (by selling unused assets or by using cash reserves)
- Issuing new shares which can be also used to repay bank loans or buy back loan notes which can be then cancelled.

Finally, a gearing ratio online calculator is included below which can be used to calculate the financial gearing of a company using the first formula (debt/equity).

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There are many companies nowadays that try to achieve capital appreciation by investing the profits generated in other projects that will bring more profits and so on. The dividend payout ratio for these companies are lower compared to companies that choose to return their profits back to the shareholders.

You can find the dividend payout ratio with two different (but similar) formulas. The first formula is :

Dividend Payout Ratio= (Total Dividends Paid/Net Income Available to the shareholders)

The second formula works on a per share basis and it is as follows:

Dividend Payout Ratio=(Dividend Per Share/Earnings Per Share).

Of course, both formulas will give you the same number.

As explained above, the dividend payout ratio shows the dividend that a company distributes compared to the net income generated during the year.

So what does a high dividend payout ratio mean? It means that a company chooses to distribute a big part of its income to the shareholders instead of investing in projects. Of course, this can be both good and bad. It’s good because the investors get a return on the funds they have invested and it’s also bad because it means that a company might be unable to find profitable projects or that it operates in a mature industry with limited opportunities.

Dividends used to be the standard form of profits distribution but nowadays companies also use share repurchases. Therefore, when the dividend payout ratio is calculated and it appears to be low, it might be the case that a company prefers to buy-back its shares instead of paying out dividends.

As noted above, it’s not that uncommon for companies to choose not to pay dividends (for many years in certain occasions). Apple and Microsoft are two good examples. Apple paid dividends in 2012 after around 7 years. In addition, Microsoft paid a dividend in 2003 but went public back in 1986. However, both companies had impressive capital appreciation so the investors had a decent return on their investment.

Therefore, when analyzing the dividend payout ratio, it’s important to understand if a company offers buybacks, if there is capital appreciation and above all, if the dividend payout ratio fluctuates. A dividend payout ratio that changes a lot over time can mean either that the company does not have stable profits or that the dividend policy is not consistent.

Both scenarios are not ideal since investors are interested in knowing when they will recoup their investment and what this return will be. For this reason, the market seems to be less forgiving for companies that have dividend payout ratio that changes a lot over time.

The dividend payout ratio calculator found below uses the second formula which calculates the dividend payout ratio based on the earnings and the dividends distributed per share.

Therefore, the only input needed is the dividend per share for the numerator and the earnings per share for the denominator.

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So what are the components of working capital. First of all, working capital can be calculated as:

Working Capital = Current Assets – Current Liabilities

Current Assets Include:

- Cash and Cash Equivalents
- Accounts Receivable
- Stock
- Other Short Term Current Assets *

The reason that the other short term current assets have an asterisk is that there are people who prefer to include accounts such as prepaid expenses and other people who prefer not to include them. I personally don’t like including accounts that will not bring cash (there is no cash inflow). Therefore, excluding prepaid expenses from your current assets is a valid option as long as there is consistency.

For example, if a company has low cash, low accounts receivable and high prepaid expenses, the working capital will be distorted by the prepaid expenses while the actual current assets that will bring cash to the company can be low. Therefore, there are cases where excluding the prepaid expenses or other accounts that are not readily translated into cash is a valid option.

Similarly, current liabilities include accounts payable, short term accruals, taxes payable, dividends payable and other short term liabilities that will cause a cash outflow in the short term.

Apart from the components of working capital, it’s also important to understand the sources of working capital. Working Capital can be generated by :

- Sales: Revenue generated increases cash and accounts receivable and therefore increases the working capital.
- Sale of fixed assets: By selling fixed assets that are not being used, a company can increase it’s cash balance. In addition, companies can have the option to sell their fixed assets and lease them back from leasing companies.
- Share Capital Injection: The owners of a company can inject capital in the company increasing the cash and the share equity accounts, therefore increase the working capital.
- Bank Loans: A company can choose to raise long term debt to finance both short term and long term liabilities. If the loan is short term, then the net effect in the working capital will be nil since there will be an increase in cash and an equal but opposite increase in the current liabilities.

There is more than thing that a company can do to manage the working capital. Some of these points are already mentioned above but other options include:

- Negotiate discounts with your suppliers: People usually think that paying your suppliers on time can be a bad thing. However, having good relationships with your suppliers is vital since you can negotiate credit terms, achieve better prices or achieve discounts for bulk orders. Therefore, managing to reduce the accounts payable increases the working capital.
- Manage your inventory to avoid having obsolete stock: It’s not the easiest task especially for big companies that operate in industries such as technology, fashion etc. However, having high stock levels costs and it’s risky. It’s therefore important to be able to forecast the demand and manage your stock levels accordingly. Impaired stock means that the working capital is reduced.
- Alternative Financing: Companies also have the option to effectively discount their long term assets such as accounts receivable by using factors (invoice factoring). Decreasing your long term assets and increase your short term assets directly increases the working capital.

The difference between the current ratio and the quick ratio is that the quick ratio only includes cash, marketable securities (which are easily convertible into cash) and accounts receivable. As explained above, it therefore excludes the stock or inventory.

Therefore, in order to get the quick ratio, you will need to use the following formula:

Quick Ratio (or Acid Test Ratio)= (Cash + Accounts Receivable + Marketable Securities)/Current Liabilities

You can also use the following formula provided that the current assets only include the current assets as per the equation above plus stock:

Quick Ratio (or Acid Test Ratio)= (Current Assets-Stock)/Current Liabilities

Let’s say for example, that company A has the following :

- Cash : $500,000
- Accounts Receivable :$1,500,000
- Current Liabilities: $1,000,000

Therefore, the quick ratio is : (1,500,000+ 500,000)/1,000,000= 2

The quick ratio assesses whether a company will be able to cover its current liabilities from its current assets as they are falling due. Therefore, if you want to analyze the quick ratio, the following apply:

If the quick ratio is higher than 1 (ideally as high as possible), the company appears to be able to repay its current liabilities as they are falling due.

If the quick ratio is lower than 1, then the company might be unable to repay some of its current liabilities and the company might face liquidity squeeze.

The calculator below will help you find the quick ratio by taking the current assets less the inventory and dividing it by the current liabilities. To be more precise and as explained above, the quick ratio only includes cash, marketable securities and accounts receivable. However, most companies only have the above assets plus stock. Therefore, by taking the total current assets and deducting the stock, we get the same figure.

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It might be easier to just start with the formula of the break even point. First of all, the break even point is the point where you make no profit but you also incur no losses. In other words, it’s the point where the total profit that a product generates equals the total fixed costs. So, the break even formula is:

Break Even Point= (Fixed Costs)/(Sales Price-Variable Costs)

As explained above, the break even point is calculated by divided the total fixed cost by the contribution of each unit. By saying contribution, we mean the revenue per unit less the variable costs per unit. In terms of analyzing or explaining the break even point, a high break even point or in other words a large number of units necessary to cover the fixed costs can mean either that the contribution is low (low price per unit or low margins) or the fixed costs are high.

For example, if your company is thinking of launching a new product that will have $500,000 fixed costs while the sale price for one unit is $10 and the variable costs (such as materials and supplies) will be $5, then the break even point will be:

$500,000/($10-$5) or 100,000 units. In other words, using this example, you will have to product and sell 100,000 units to break even.

A second example might be more illustrative. Let’s say that you have two products that you can develop. However, you can not develop both products at the same time. You need to choose either Product A or Product B.

Product A has these characteristics:

- Sales price : $2 per unit
- Variable Costs : $1.5 per unit
- Fixed Costs: $5000

Product B has :

- Sales Price : $4 per unit
- Variable Costs $2 per unit
- Fixed Costs: $20,000

The break even point for product A is : (5,000/0.5) or 10,00 units to break even. The break even point for product B is : (20,000/2) or 10,000.

So which product would you choose to develop? You will need exactly the same amount of sales to break even for both products and product B has a higher contribution as well.

There is definitely more than one factor that I would take into account such as the reliability of the information that I am using to perform my analysis but me, being a risk averse, I would choose product A. The reason? If I lose, I will only lose $5,000. The second scenario is a bit more risky due to the high fixed costs. Of course, this is a matter of preference and the way people assess and perceive risk.

A simple calculator to help you find out how many units of a product you will need to sell to break even. Break Even analysis is a straightforward approach to help you understand if the product you are developing is likely to be successful and if you will be able to cover the fixed costs by using the projected sales that you will be able to make.

The only inputs you need are the revenue per unit, the variable cost per unit and the total fixed cost attributed to the development of this product.

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The current ratio formula is very straightforward. The numerator includes the current assets and the denominator the current liabilities. Therefore, the current ratio formula is:

Current Ratio= Current Assets/Current Liabilities

Examples of current assets that are included are cash and cash equivalents, accounts receivable and stock (or inventory). On the other hand, current liabilities include your trade creditors (or accounts payable), your short-term debt (short-term bank loans, overdraft facilities) and other liabilities that are expected to fall due within the next financial year.

As noted above, the current ratio shows whether a company is able to repay the current liabilities as they are falling due. In other words, if the current ratio is higher than 1, then the company is believed to be in a better shape to repay the current liabilities from its current assets. Preferably, a company should have a current ratio higher than 1.5 but comparing this ratio with the industry which the company operates in or with other similar companies is considered more appropriate. Furthermore, when analyzing the a company, it’s suggested to compare the current position with historical data. Preferably, you use a 3-5 years horizon which will enable you to add comparability and identify trends.

A current ratio that is lower than 1 means that the company risks being unable to pay its current liabilities as they are falling due. In other words, it might be the case that the company will be unable to pay its suppliers or the short-term loan and the consequences might not be pleasant.

Example 1: Company A has $500,000 cash and $200,000 stock while the accounts payable is $1,000,000. Now let’s assume that the full $700,000 balance that represents the current assets can be recovered in a short period. The above example company will be unable to pay part (or $300,000) of its suppliers.

Example 2: Let’s say that we have two companies. Company A has $1,000,000 current assets and $500,000 current liabilities. Company B operates in the same industry and has $2,000,000 current assets and $3,000,000 current liabilities.

The current ratio for Company A is 2 (1,000,000/500,000) and the current ratio for company B is 0.67. Therefore, company A seems to be able to cover its current liabilities by utilizing its current assets and there is also a 500,000 headroom. On the other hand, company B might face difficulties repaying all its current liabilities since the current assets are not enough.

The calculator that you will find below calculates the current ratio by dividing the current assets with the current liabilities. Current assets include all assets that are due within the next financial year such as cash and cash equivalents, inventory, accounts receivable and prepaid expenses. Current Liabilities include liabilities such as accounts payable, accruals and short-term debt.

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The dividend discount model is also referred as dividend valuation model, Gordon’s Growth Model or dividend growth model.

As explained above, the value of a stock should be the same as the discounted future dividend payments. The dividend discount model can be used when the dividends distribution is constant, when there is constant growth or even when the growth of the dividends change. For example, most stocks do not have a constant dividend growth but change their dividends based on their profitability or their investment opportunities.

In order to keep things as simple as possible, we assume that there is a constant dividend growth rate. In other words, the dividends are growing at a constant rate per year.

We will use company “A” as an example who just paid $0.5 as an annual dividend. The dividend growth for the past five years has been 5% and is predicted to stay the same. Finally, we were able to use the capital asset pricing model and calculate the cost of equity which is 10%.

Based on the above, the price of one share should be 0.5*(1+0.05)/(0.1-0.05)=$10.5 per share.

The dividend discount model can be used to value a share when the dividends are constant over time. This case can be applicable when you are trying to value preference shares that might offer predetermined annual dividends. Since there is no growth, the formula becomes:

Using the same example as above, the price of one stock is expected to be lower as the total dividends that will be distributed are also lower. Therefore, the value of one share is ($0.5/0.1)=$5.

In reality, the dividend growth is rarely constant over time. Most companies increase or decrease the dividends they distribute based on the profits generated or based on the investment opportunities they have.

For example, it a common for a company to choose to have a high dividend growth rate for some years (after the introduction of a new product for example) which is then expected to be decreased.

Finding the dividend growth rate is not always an easy task. As an alternative, you can use the earnings retention ratio to “benchmark” the dividend growth rate. The assumption is that the dividend growth comes from reinvesting funds that are not distributed. These funds are invested in projects that will increase the profits generated and therefore the dividends distributed.

The growth based on the retention model-ratio can be calculated as the rate of return multiplied by the percentage of the profits retained and not distributed.

For example, if a company distributes 40% of its profits and retains 60% while the projects that the company runs yield a 7% rate of return, the growth of the dividends is 0.6*0.07=0.042 or 4.2%.

As mentioned in the beginning of this post, the dividend discount model is widely used. Some of its uses are:

- To develop a forecast for the price of a stock.
- To calculate the fair value of a stock.
- To value a company.
- To calculate the cost of equity if we know the dividend growth rate, the price of the stock (for listed companies) and the annual dividend paid.
- To calculate the beta of a stock using the capital asset pricing model (by finding the cost of equity).

The dividend discount model is based on the theory that the price of a stock should be the same as the present value of the future dividends. In reality, companies might choose not to pay dividends (Apple for example) or might choose to repurchase their own stock. If a company chooses to reinvest their profits instead of distribute them, chances are that the market will react positively (all things being equal). Therefore, the dividend discount model will be unable to “capture” the increase of the stock price as there will be no increase in the dividends paid.

]]>The accounting rate of return has two different formulas that can be used to derive the return of the project. The first formula is the following:

expressed as a percentage and where:

- Average Annual Profit is the annual cash inflow that the project will generate after deducting depreciation.
- Initial Investment is the capital expenditure that is required to undertake the project.

For the second formula, the initial investment will need to be replaced by the average investment. Therefore, the accounting rate of return becomes:

expressed as a percentage and where:

- Average Investment is the capital expenditure that is required to undertake the project plus the final scrap value of the machinery divided by two.

Example: A company is trying to decide whether is should accept a project with the following details:

- The initial capital expenditure requirements are $100,000 for a machine that will have a five years useful life.
- Depreciation is calculated on a straight line basis.
- The scrap value of the machine is $10,000
- The project is expected to have $30,000 profit

Using the first way to calculate the accounting rate of return, depreciation can be calculated as:

or ($100,000-$10,000)/5=$18,000. Therefore, the annual profit is $30,000-$18,000=$12,000. The accounting rate of return can be therefore calculated as (12,000/100,000)%=12%

Using the second formula (the average investment method), the annual profit will be the same but the denominator will be:

or: (100,000 + 10,000)/2=55,000. Therefore, the accounting rate of return will be:

12,000/55,000=21.8%.

The advantages of the accounting rate of return as follows:

- ARR offers a straightforward way to calculate the required return of the project.
- It offers a certain degree of comparability between projects.

The disadvantages of the accounting rate of return are as follows:

- It does not take into account the time value of money or in other words it does not recognize that $1 now will not have the same buying power tomorrow
- It can not (or should not) be used as the only way to appraise a project. The net present value should be also calculated as calculating only the return of a project can give a distorted image when projects that have significantly different capital expenditure are compared.
- It uses accounting figures which can be affected by judgment, accounting policies and non cash items (depreciation).
- There are two ways to calculate the accounting rate of return which causes a problem of comparability.

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The break-even point is the point where the total contribution of the sales equal to the fixed costs. In other words, the break-even point is the point where the total revenue less the variable costs from the sales made equal to the total fixed costs.

Break-even analysis is the analysis that is performed to identity how many sales a company needs to make to cover it’s fixed cost base.

A simple example might be more helpful. Let’s say that company A sells one product only which is called SuperGlass. The price is the same ($10 per unit) for all customers and it is not expected to change. The material cost $6 per unit while the company has fixed costs of $10,000.

The contribution per unit is $4 ($10-$6) and therefore, the company will need to sell 10,000/4=2500 units to break-even.

or

A more realistic scenario is that a company is producing more than one product. So the question is how to perform a break even analysis for two, three or fifty products. It is actually quite simple!

Let’s say that company A is producing SuperGlass and ExtraGlass and that the company is expected to sell 2 units of SuperGlass for every unit of Extraglass (2:1). The table below summarizes the price per unit, the variable costs and the fixed costs.

[table id=2 /]

The first thing to do is do to add the contribution for both products so that we can create a “combo” that consists of these two products. The total contribution for this combo $10 (4+6).

Therefore, the break even point is 100,000/10 or 10,000 units. The company will therefore need to produce 10,000 * 2 from SuperGlass and 10,000*1 from ExtraGlass to break even.

It is quite easy to create a chart for a simple break even analysis. The first thing to do is to put the fixed costs in Y axis and the Contribution generated for different levels of sales on the X axis. The result is going to be the same as the photo featured in this post.

It is clear from the graph the break even point is where the total income less the variable costs equal the fixed costs.

Break even analysis can only help you to identify the level sales you need to make to avoid being in a loss making position. It can help you to understand if the product you are thinking to develop can be profitable by indicating how many units you need to sell to break even. If in your opinion, the level of sales is easily achievable then the product should be developed. If the necessary to break even level of sales seem to high, then the investment might not be worthwhile.

Break-even analysis has as any other similar analysis tool flaws. Some of them can be summarized as follows:

- It can only help you analyze straightforward scenarios and it is hard to apply it in more complex scenarios.
- It is based on expected sales prices, expected variable and fixed costs which and expectations will not be objective.
- It does not account for the synergies that products can bring.
- It does not account for certain benefits that a product can bring (such as diversified portfolios, enhanced brand name etc.

The application of the adjusted present value is a bit more complicating process when compared with the net present value methodology. The reason for that is that you need to find the cost of raising finance for a company that has no debt (what is called an “ungeared” company”).

You will then calculate the present value of the cash flows and discount them using the discount rate of this hypothetical ungeared company.

The final step is to add the benefit of raising debt which is the tax shield. The tax shield is nothing else from the tax you will save since the interest charges is a tax allowable expense.

To summarize, you should follow these steps to calculate the adjusted present value (APV).

- Calculate the cost of raising finance for an ungeared company
- Calculate the cash flows that the project that is being assessed will bring (including the initial investment)
- Discount the cash flows from the project by using as discount rate the rate derived from step 1 (the cost of equity for the ungeared company)
- The final step is to add the tax shield or the tax saved from the interest accrued.

The scenario:

Let’s assume that a company is considering investment in a project that will need $10m initial investment and will bring $5 annual cash inflows (after tax) for the next three years.

The company is thinking of raising debt to invest in this project. The debt that will be raised is the $10m needed for the initial investment and the interest will be 10%.

The company operates in a country where it pays tax at 20%. The risk free rate is 5% and the return on the market is 3%. The company has $50m debt and $100m equity contributed by the shareholders. The company has been using the capital asset pricing model to monitor the beta which according to recent calculations is 1.2.

**Solution:**

*Step 1: Calculate the beta of the “ungeared company” and then use the capital asset pricing model to derive the cost of equity for this hypothetical company.*

Therefore, using the following formula:

will give us a beta for an ungeared company equal to 0.86. We will then use capital asset pricing model or

which results in a cost of equity equal to 6.7%. This is the rate that we will use to discount

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*Step 3: Calculate and add the tax benefit from the interest charges.*We will pay $10m * 10% interest or $1m per year. The annuity for the three years 10% rate is 2.487.Therefore, the tax benefit is $1m * 2.487 or $2.487m

*Step 4: Add the present value from step 2 and the tax shield from step 4 and interpret the results.*

The total present value for the project is $5.7 without taking into account the impact of the loan repayments. The company should accept the project since it has a positive present value.