Author Firmsconsulting

Annualized Net Present Value (ANPV)

Firmsconsulting Leave a comment

The annualized Net Present Value (ANPV) technique is the best method to use when comparing mutually exclusive projects which have unequal duration. ANPV is the most efficient technique to convert Net Present Values (NPVs) of projects with unequal duration into an ANPV for each specific project, which can then be compared.

To find ANPV, the following calculation must be made:

1 – Find NPVs for each project

2 – Divide the NPV of each project by PVIFAr,n (Present Value Interest Factor for Annuity) at the project’s required cost of capital and number of periods. The amount for PVIFAr,n can be found in financial tables.

3 – The project with the higher Annualized Net Present Value (ANPV) is preferred.

Alternatively, ANPV can be found by using a financial calculator, as shown below:

PV = use NPV

N = Number of periods over the duration of the project (e.g. number of years)

I = required cost of capital (e.g. 10%)

Find PMT = this will be the annualized net present value (ANPV)

Test yourself

ABC Corporation has two mutually exclusive projects A and B that it can invest in. Initial investments investments required for project A and B are $150,000 and $200,000 respectively. The duration of project A is 4 years and of project B is 3 years. Expected annual cash inflows from project A are $40,000 and from project B is $70,000. The terminal cash flows from projects A and B are $21,000 and $34,000 respectively. The cost of capital of ABC Corporation is 9% and both projects have an average risk, which means that alteration for risk adjusted discount rate is not required. The 9% for cost of capital should be used for both projects.

What is the ANPV for projects A and B?

SOLUTION:

By using a financial calculator, we can find the solution to this problem. First we need to establish the net present value (NPVs) for projects A and B.

NET PRESENT VALUE (NPV) FOR PROJECT A:

Clear calculator: second function, “C ALL”

CFo: -150,000

CF1: 40,000

CF2: 40,000

CF3: 40,000

CF4: 61,000 (40,000 + 21,000)

I: 9

Second function, NPV: 5,534.28

NET PRESENT VALUE (NPV) FOR PROJECT B:

Clear calculator: second function, “C ALL”

CFo: -200,000

CF1: 70,000

CF2: 70,000

CF3: 104,000 (70,000 + 34,000)

I: 9

Second function, NPV: 3,444.86

However, because the projects have different duration, we need to convert Net Present Values (NPVs) found above into ANPV for each project.

CONVERTING NPV TO ANPV FOR PROJECT A:

Clear calculator: second function, C ALL

PV: – 5,534.28

N: 4

I: 9

Find PMT: $1,708.26

CONVERTING NPV TO ANPV FOR PROJECT B:

Clear calculator: second function, C ALL

PV: – 3,444.86

N: 3

I: 9

Find PMT: $1,360.91

Since the ANPV of project A ($1,708.26) is higher than that of project B ($1,360.91), project A should be selected.

Blogbschool.com is powered by www.firmsconsulting.com. Firmsconsulting is a training company that finds and nurtures tomorrow’s leaders in business, government and academia via bespoke online training to develop one’s executive presence, critical thinking abilities, high performance skill-set, and strategy, operations and implementation capabilities. Learn more at www.firmsconsulting.com.

Sign up to receive a 3-part FREE strategy video training series here.

EBIT-EPS Capital Structure Approach

Firmsconsulting Leave a comment

The EBIT-EPS capital structure approach focuses on finding a capital structure with the highest EPS (earnings per share) over the expected range of EBIT (earnings before interest and taxes).

The reason why we are interested in finding a capital structure which will permit maximization of the EPS over the expected range of EBIT is because it partially helps us to achieve the ultimate objective of the enterprise. The ultimate objective of the enterprise is to maximize shareholders’ wealth by maximizing its stock price. Two key variables that affect stock price are return (earnings attributed to owners of the enterprise) and risk (which can be measured by required return (rs)). This approach explicitly considers maximization of returns (EPS). However, it is important to note that this approach ignores risk (does not explicitly consider risk).

Major shortcoming of the EBIT-EPS approach

The fact that this approach fails to explicitly consider risk is the major shortcoming of this method. As firm obtains more debt (its financial leverage increases), the risk also increases and shareholders will require higher returns to compensate for the increased financial risk. Therefore, this approach is not completely appropriate because it does not consider one of the key variables (risk), which is necessary for maximization of shareholders’ wealth.

Considering financial risk

As per above, the approach does not explicitly consider financial risk. However, when utilizing the approach, financial risk can be considered in two ways:

1) The approach measures financial risk by the financial breakeven point. The higher the breakeven point the greater the financial risk.

2) The approach also measures the financial risk by the slope of the capital structure line. The steeper the capital structure line the greater the financial risk.

EBIT-EPS graph

It is a graphical approach. EPS is plotted on the vertical axis (x-axis) and EBIT on the horizontal axis (y-axis). By connecting the coordinates for different capital structures (different variations of equity versus debt), capital structure lines for each capital structure are graphed.

We will need to represent EBIT-EPS coordinates (capital structure lines) for different capital structures to ascertain at which levels of EBIT which capital structure is preferred. This will allow us to find a capital structure with the highest EPS over the expected range of EBIT.

For the purposes of this article it is sufficient to mention that to find EBIT-EPS coordinates we can assume particular EBIT values (and associated earnings available for common stockholders values) and calculate EPS in line with such values for different capital structures.

The formula to calculate EPS is as follows:

EPS = Earnings Available for Common Stockholders/ Number of Shares of Common Stock Outstanding Another easy way to find one of the EBIT-EPS coordinates is to use the financial breakeven point calculation. Financial break-even point occurs at the level of EBIT (earnings before interest and taxes) at which EPS (earnings per share) equals zero. At this level of EBIT all fixed financial costs are covered. The formula for calculation of the financial break-even point is as follows:

Financial break-even point = I + PSD/1-T

Where:

I – interest charges

PSD – preferred stock dividends

T – tax rate

***

This capital structure approach does NOT allow us to determine the point where weighted average cost of capital is at a minimum and where stock price is at a maximum (where wealth of the owners of the firm is maximized). The approach focuses on maximizing earnings rather than on maximizing wealth. Therefore, although it is helpful to use when analyzing alternative capital structures, the major shortcoming of this approach should be taken into account.

Blogbschool.com is powered by www.firmsconsulting.com. Firmsconsulting is a training company that finds and nurtures tomorrow’s leaders in business, government and academia via bespoke online training to develop one’s executive presence, critical thinking abilities, high performance skill-set, and strategy, operations and implementation capabilities. Learn more at www.firmsconsulting.com.

Sign up to receive a 3-part FREE strategy video training series here.

Optimal capital structure

Firmsconsulting Leave a comment

Theoretically, enterprises should try to maintain a certain optimal capital structure, a perfect mix of financing (debt and equity), which results in the lowest possible weighted average cost of capital. At this combination of debt and equity, the stock price is at the maximum. Therefore, attainment of the optimal structure is in line with the main objective of the business, which is the maximization of wealth of the owners of the business. The optimal structure is also referred to as the target capital structure. However, it is important to note the optimal structure exists only in theory.

Theory does not yet offer a methodology that would allow firms’ financial managers to find the optimal capital structure. However, financial managers can determine the approximate optimal structure range, which is close to what they believe the optimal structure for the firm is.

As per above, an optimal structure maximizes the value of the firm. To find the value of the firm, we can use the following formula:

V=EBIT*(1-T)/ra

Which simplifies into:

V=NOPAT/ra

Where:

V = is the value of the firm

EBIT = is earnings before interest and taxes (see the income statement for how it is calculated)

NOPAT = is the net operating profit after taxes (calculated by formula EBIT*(1-T)/ra)

ra = is the weighted average cost of capital (WACC)

If we assume that NOPAT is consistent, then the value of the firm is affected by WACC (ra, weighted average cost of capital). WACC is affected by both, the cost of debt and equity.

The cost of equity

The cost of equity is higher than the cost of debt and increases as financial leverage increases. This is because equity suppliers will demand higher return for increasing financial risk due to increasing financial leverage.

The cost of debt

The cost of debt initially is relatively low. The major reason for this is due to the fact that interest on debt is tax deductible. This tax deductibility of interest paid on debt is also commonly called the tax shield. However, as debt increases, at certain debt ratio lenders will begin to require higher and higher interest payments from the borrower. This is undertaken in order to compensate for increasing risk due to increasing financial leverage.

There are two other costs of debt that the firm needs to consider:

(1) Debt increases the probability of bankruptcy. This is because lenders can force the firm into bankruptcy if the firm cannot meet its financial obligations to the lender.

(2) Another aspect to consider is the agency cost. This refers to the fact that lenders usually protect themselves from increases in risk of the borrower by imposing different loan provisions, which place constraints on actions and choices of the firm. Such provisions commonly include, but are not limited to, minimum levels of liquidity to be maintained, limits on compensation of the executives and limitations on asset acquisitions.

***

As debt increases from a zero point onwards, WACC initially decreases to the theoretical optimal capital structure point. Thereafter, the increasing equity cost and increasing cost of debt causes WACC to start increasing again. Therefore the theoretical optimal capital structure is obtained at the point where the WACC is the lowest.

In other words, the theoretical optimal capital structure occurs at the point where the benefits from using debts are in equilibrium (in balance) with the costs of using debt. The optimal capital structure can also be seen as the balance between risk and return where the firm’s stock price is maximized.

 

Capital structure decisions analysis with debt ratios

Firmsconsulting Leave a comment

When analyzing capital structure decisions, external stakeholders can obtain an approximate idea of the capital structure of the particular firm by using information in the firm’s financial statements to calculate various debt ratios.

When analyzing capital structure decisions of firms as outsiders, we need to consider two types of debt measures:

The first type of debt ratio measures the degree of indebtedness. This refers to how much debt the firm has relative to other balance sheet’s amounts. The debt ratio will measure the degree of indebtedness.

The second type of debt ratio measures the ability to service debts. This type of debt ratios measures the ability of the business to meet its obligations associated with debt, as they come due. Times Interest Earned Ratio and Fixed Payment Coverage Ratio will be considered to measure the ability to service debts.

Both techniques are very simple to use and effective at analysing capital structure decisions.

Measuring the degree of indebtedness

THE DEBT RATIO

A direct measure of debt is a debt ratio. Debt ratios provide direct information on the financial leverage of an enterprise. Debt ratios measure how many of the firm’s assets are financed by debt. The higher the debt ratio, the higher the degree of financial leverage (amount of debt) and the higher the risk. The formula for the debt ratio is as follows:

Debt ratio=Total liabilities/Total assets

Example:

For example, assume that ABC’s total liabilities are $1,700,000 and total assets are $4,000,000.

The debt ratio of ABC is as follows: $1,700,000/$4,000,000=42.5%

This means that ABC’s capital structure is 42.5% of debt and 57.5% of equity.

Measuring the ability to service debts

TIME INTEREST EARNED RATIO (INTEREST COVERAGE RATIO)

The Times Interest Earned Ratio (TIER or Interest Coverage Ratio) measures the ability of the enterprise to meet its financial obligations (interest payments on debt that come due).

When analyzing capital structure decisions, we can use the Times Interest Earned Ratio as an indirect measure of the level of debt in the firm’s capital structure. Commonly, the lower the Times Interest Earned Ratio the higher the degree of financial leverage (amount of debt) and the higher the risk.

The formula for the Times Interest Earned Ratio is as follows:

Times Interest Earned Ratio =EBIT/interest charges

EBIT refers to the earnings before interest and taxes, which is also called operating profit (refer to the Income Statement format to see how it is calculated).

EXAMPLE:

Assume ABC Company has an operating profit of $550,000 and interest charges of $100,000.

The TIER of ABC is as follows:

$550,000/$100,000=5.5

It is generally advisable that the Times Interest Earned Ratio should be between 3 and 5.

ABC’s Times Interest Earned Ratio could be too high. It may be possible that the firm is unnecessarily careful in using debt as a source of capital. This means the risk taken may be lower than average, but so is the return.

When using the Times Interest Earned Ratio, it is important to remember that interest is paid with cash and not with income (since some income may still be in the form of accounts receivable). Therefore, the real ability of the firm to make interest payments may be worse than indicated by the Times Interest Earned Ratio. It is also important to remember that debt obligations include repayment of principal debt as well as payment of interest. The calculation above excludes the principal amount borrowed.

Generally, the higher the Times Interest Earned Ratio the lower the risk an enterprise will not be able to meet its contractual interest obligations on time. Therefore, generally, a higher Times Interest Earned Ratio is the better.

However, cognizance needs to be taken of the fact that the higher the Times Interest Earned Ratio, the lower the risk and lower the return. Therefore, at some point, the Times Interest Earned Ratio may be too high. This will occur if the business is unnecessarily careful with taking up debt as a source of financing, which results in very low risk but also a lower return. This is not aligned with the overall goal of the enterprise which is the maximization of the wealth of its shareholders.

FIXED PAYMENT COVERAGE RATIO

Fixed Payment Coverage Ratio measures the ability of the enterprise to meet all of its fixed-payment obligations on time. When analyzing capital structure decisions, we can use the Fixed Payment Coverage Ratio as an indirect measure of the level of debt in the firm’s capital structure. Commonly, the lower the Fixed Payment Coverage Ratio the higher the degree of financial leverage (amount of debt) and the higher the risk.

The formula for the Fixed Payment Coverage Ratio is as follows:

Fixed Payment Coverage Ratio = EBIT+LP/I+LP +((PP +PSD)*(1/1-T))

Where:

EBIT – earnings before interest and tax (operating profit)

LP – lease payments

I – interest charges

PP – principal payments

PSD – preferred stock dividends

T – tax rate

EXAMPLE:

Assume ABC Company has an operating profit of $550,000 and interest charges of $100,000. The lease payments are fixed at $20,000, principal payments are at $60,000 and preferred stock dividends are at $15,000. The corporate tax rate of ABC is 40%.

The Fixed Payment Coverage Ratio of ABC is calculated as follows:

= 550,000+20,000/100,000+20,000+((60,000+15,000)*(1/1-T))

= 570,000/120,000+((75,000)*1.67)

= 570,000/120,000+125,250

= 570,000/245,250

= 2.3

The Fixed Payment Coverage Ratio of ABC is 2.3. Since EBIT is more than two times larger than fixed-payment obligations, it appears that ABC is in a strong position to live up to its fixed-payment obligations as they come due. However, as with all financial ratios, Fixed Payment Coverage Ratio should be compared to industry average before any conclusions are drawn. Generally, the higher the Fixed Payment Coverage Ratio the lower the risk that enterprise will not be able to meet its fixed-payment obligations on time. Therefore, a higher Fixed Payment Coverage Ratio is the better.

However, as with Times Interest Earned ratio, cognizance needs to be taken of the fact that the higher the Fixed Payment coverage ratio the lower the risk and lower the return. Therefore, at some point, the Fixed Payment Coverage Ratio may be too high. This will occur if the business is unnecessarily careful with taking up more debt which results in a very low risk but also a lower return. This is not aligned with the overall goal of the enterprise which is the maximization of the wealth of its shareholders.

***

When analyzing capital structure decisions with the help of debt ratios, one should compare debt ratios of individual firms to industry averages. There is a large variability of debt ratios’ industry averages between industries. This is because different industries have different operations requirements. There is no one perfect ratio. Appropriate ratios to use should determined by the company in question, taking into account company’s ‘s strategy, operating environment, competitive environment and finances.

Blogbschool.com is powered by www.firmsconsulting.com. Firmsconsulting is a training company that finds and nurtures tomorrow’s leaders in business, government and academia via bespoke online training to develop one’s executive presence, critical thinking abilities, high performance skill-set, and strategy, operations and implementation capabilities. Learn more at www.firmsconsulting.com.

Sign up to receive a 3-part FREE strategy video training series here.

Capital structure decisions

Firmsconsulting Leave a comment

Capital structure decisions refer to the decisions businesses have to make with regards to the mix of financing they use. The mix consists of debt and/or equity as sources of capital. In other words, it is a structure of the liabilities and equity side of the balance sheet, excluding current liabilities. Enterprises usually try to maintain a certain optimal mix of financing (debt and equity), referred to as the target capital structure.

The modern approach to capital structures is largely influenced by the work of Franco Modigliani and Merton H. Miller. This is also known as the M and M, or MM work. Their work published in 1958 in American Economic Review (June 1958) entitled “The Cost of Capital, Corporation Finance, and the Theory of Investment” suggests that under condition of perfect markets, capital structure decisions do not affect the value of the firm. Any increase in Return on Equity goes hand in hand with increase in risk. Therefore, weighted average cost of capital (WACC) stays constant.

In their later work, Franco Modigliani and Merton H. Miller introduced taxes into the model. Their further conclusion was that if corporate taxes are present then the value of the enterprise will increase continuously as more debt is added to capital structure.

This is possible because debt interest payments are tax deductible. However, it is evident that personal taxes will decrease the advantage gained. As a result, it is still profitable to use debt financing. However, the advantage gained is lessened by the existence of personal taxes versus existence of just corporate taxes.

Theoretically, enterprises can increase the value of the firm by finding the optimum capital structure (mix of equity and debt). The optimum capital structure refers to capital structure decisions according to which the weighted average cost of capital is at its minimum value and, as a result, the value of the firm is maximized.

Therefore, the optimum capital structure is in line with the main objective of the business, which is the maximization of wealth of the owners of the business. However, it is important to note that the optimal capital structure exists only in theory.

Sources of capital

Sources of capital include debt and equity. Equity is further subdivided into preferred stock and common stock. In turn, common stock is even further subdivided into new common stock and retained earnings.

When making capital structure decisions, it is important to keep in mind that generally debt is the least expensive source of capital. This is due to the fact that the lender takes much less risk than suppliers of the equity capital. This is occurs because:

(1) Debt has obligatory scheduled payments. Whereas, equity suppliers, especially in case of common stock, will only be paid when company can afford to do so.

(2) In case of liquidation, lenders have priority claim on assets of the company over equity suppliers.

(3) If firm misses obligatory interest or principal payments, lenders can force the firm into bankruptcy. Therefore, lenders have more power in ensuring that payments will be made on time.

Moreover, interest on debt is tax deductible, which makes it an even cheaper source of capital for the firm. Overall, and as stated above, debt is generally the cheapest source of capital for the firm.

How capital structure decisions affect the risk of a company?

Enterprises deal with three types of risks: financial risk, business risk and total risk. The capital structure directly affects the financial and total risk of the firm.

FINANCIAL RISK – a chance that firm will not be able to meet its financial obligations, which can result in bankruptcy. Financial risk is directly affected by the firm’s capital structure (its mix of debt and equity financing). The more debt the firm uses in its capital structure mix, the higher the financial risk.

BUSINESS RISK – a chance that firm will not be able to cover its operating costs. There are three factors that affect business risk. These are an increase in the degree of operating leverage, revenue instability and cost instability. Capital structure decisions do not affect business risk.

TOTAL RISK – a combination of financial and business risk. Since capital structure decisions affect financial risk, the total risk is also affected.

Blogbschool.com is powered by www.firmsconsulting.com. Firmsconsulting is a training company that finds and nurtures tomorrow’s leaders in business, government and academia via bespoke online training to develop one’s executive presence, critical thinking abilities, high performance skill-set, and strategy, operations and implementation capabilities. Learn more at www.firmsconsulting.com.

Sign up to receive a 3-part FREE strategy video training series here.

Degree of total leverage (DTL)

Firmsconsulting 1 Comment

The degree of total leverage, which is a way to measure the total leverage of the firm, refers to the relationship between sales revenue and EPS. It (financial and operating leverage) is a measure of how potential total fixed costs (fixed operating costs and fixed financial costs) can enlarge the effect that change in sales (P*Q) has on EPS (earnings per share).

When does a firm have total leverage?

If the (DTL) is greater than 1, than total leverage exists (which is the case as long as the company has fixed operating or/and financial costs). Due to total leverage (existence of fixed operating or/and financial costs), any increase in sales will result in an even larger increase in EPS and any decrease in sales will result in an even larger decrease in EPS. The higher the fixed financial and operating costs, the higher the (DTL). There are three approaches to calculate the (DTL):

1st approach to calculate the (DTL)

To calculate the (DTL), we can utilize the following formula:

(DTL) =% change in EPS / % change in sales

Test yourself

ABC has a change in operating profit of 70%, change in EPS of 310% and change in sales of 60%.

Required:

Find the degree of operating leverage, the degree of financial leverage and the degree of total leverage.

Solution:

Degree of operating leverage:

DOL =% change in EBIT / % change in sales DOL =70%/60% DOL =1.17

Degree of financial leverage:

DFL =% change in EPS / % change in EBIT DFL =310%/70% DFL =4.43

(DTL):

DTL =% change in EPS / % change in sales DTL =310%/60% DTL =5.17

2nd approach to calculate the (DTL)

If we have data on the degree of operating leverage and degree of financial leverage, then the (DTL) can be calculated as follows:

(DTL) = DOL * DFL

Test yourself:

ABC has a change in operating profit of 70%, change in EPS of 310% and change in sales of 60%.

Required:

Find the (DTL) using the second approach.

Solution:

Firstly, we need to find the degree of operating leverage and the degree of financial leverage.

Degree of operating leverage:

DOL =% change in EBIT / % change in sales DOL =70%/60% DOL =1.17

Degree of financial leverage:

DFL =% change in EPS / % change in EBIT DFL =310%/70% DFL =4.43

Now, we can calculate the degree of total leverage.

(DTL):

DTL=DOL*DFL

DTL=1.17*4.43

DTL=5.18

Note that this is aligned with the answer that we obtained while using 1st approach above for calculation of the degree of total leverage.

3rd approach to calculate the (DTL)

There is another formula that can be used to calculate the (DTL). A third approach to calculate the (DTL) is a more direct technique. The formula is as follows:

(DTL) at base sales level Q =

Q*(P-VC)/Q*(P-VC)-FC-I-(PD*1/1-T)

WHERE:

Q – sale quantity in units

P – sale price per unit

VC – variable operating cost per unit

FC – fixed operating cost per unit

I – interest

PD – preferred stock dividends

T – tax rate

Test yourself:

ABC Corporation ascertained that Q=1800, P=$8, VC=$3, FC=$1300, I=$1,800, PD=$3,000 and the tax rate is 40%.

Required:

Find the (DTL) using a more direct formula for calculation.

Solution:

The calculation of the (DTL) of ABC Corporation will be as follows:

Degree of total leverage at base sales level Q = 1800*(8-3)/1800*(8-3)-1300-1800-(3000*1/1-.4)

Degree of total leverage at base sales level Q = 9000/900

Degree of total leverage at base sales level Q = 10

Since the result is greater than 1, ABC Corporation has total leverage.

Related Articles:

Blogbschool.com is powered by www.firmsconsulting.com. Firmsconsulting is a training company that finds and nurtures tomorrow’s leaders in business, government and academia via bespoke online training to develop one’s executive presence, critical thinking abilities, high performance skill-set, and strategy, operations and implementation capabilities. Learn more at www.firmsconsulting.com.

Sign up to receive a 3-part FREE strategy video training series here.

Risk Adjusted Discount Rate: Dealing with Risk in Capital Budgeting

Firmsconsulting Leave a comment

Breakeven cash inflow analyses, risk adjusted discount rate (RADR) and scenario analyses are tools that facilitate better insight into managing risk in capital budgeting.

Risk in capital budgeting especially refers to variability of the returns (variability of cash inflows), because the initial investment is more or less known with some level of confidence. Therefore, we need to ensure that present value (PV) of cash inflows will be large enough to ensure that project is acceptable.

To adjust the present value of future cash inflows for risk embodied in particular project, we can either adjust cash inflow directly or we can adjust the discount rate. Because adjusting cash inflow is highly subjective, we will rather adjust discount rate. This is when risk adjusted discount rate technique comes into play.

RADR is a discount rate that must be earned to compensate an investor for the risk undertaken. Under RADR the value of the firm must be at least maintained or must increase. Risk adjusted discount rate is the most popular risk adjustment technique that utilize NPV.

The higher is the risk of specific project, the higher RADR will be.

The deployment of RADR is best illustrated by the use of an example:

EXAMPLE

Amanda can invest in two shares, A and B. Both shares presently cost $50 and Amanda wants to hold shares for 4 years. Annual dividends from share A expected to be $7. Annual dividends from share B are expected to be $12. However, shares B are more risky. In 4 years time Amanda expects to be able to sale shares A for $55 each and shares B for $70 each. Amanda’s required return is 8%. However, for shares B she adjusts her return so that her risk adjusted discount rate becomes 12%. Calculate risk adjusted net present values (NPVs) of shares A and B and recommend which shares should Amanda purchase.

Solution:

We will use financial calculator to find risk adjusted net present values (NPVs) of shares A and B.

Risk adjusted NPV of shares A:

Clear calculator: second function, C ALL

CFo: -50

CF1: 7

CF2: 7

CF3: 7

CF4: 62 (7+55)

I: 8

Second function, NPV: $15.38

Risk adjusted NPV of shares B:

Clear calculator: second function, C ALL

CFo: -50

CF1: 12

CF2: 12

CF3: 12

CF4: 82 (12+70)

I: 12

Second function, NPV: $30.94

Since investment in shares B offers higher risk adjusted NPV, Amanda should choose to invest in shares B.

The main difficulty in using risk adjusted discount rate (RADR) technique is in determining level of risk and approximating an appropriate risk adjusted discount rate (RADR). There is currently no systematic way to adjust required return to risk adjusted discount rate (RADR). Management usually determines risk adjusted discount rate (RADR) subjectively.

Sometimes risk index is determined which reflects risk adjusted discount rate (RADR) for every subsequent level of risk. For example, risk can be categorized into below average, average, above average and very high. Past experience and CAPM can be used to subjectively determine the risk adjusted discount rate (RADR) appropriate for each subsequent level (category) of risk.

Blogbschool.com is powered by www.firmsconsulting.com. Firmsconsulting is a training company that finds and nurtures tomorrow’s leaders in business, government and academia via bespoke online training to develop one’s executive presence, critical thinking abilities, high performance skill-set, and strategy, operations and implementation capabilities. Learn more at www.firmsconsulting.com.

Sign up to receive a 3-part FREE strategy video training series here.

Risk Scenario Analysis: Dealing with Risk in Capital Budgeting

Firmsconsulting Leave a comment

Another way to evaluate risk of the project is to undertake scenario analysis.

Scenario analysis focus on developing few alternative scenarios and evaluating variability between returns, which can be measured by net present value (NPV).

For example, we can generate 3 scenarios (optimistic, most likely and pessimistic) and than find NPVs for each of the scenarios. When we know net present values for each scenario, we can find the range.

The range here is found by taking NPV of optimistic outcome less NPV of pessimistic outcome, as shown below:

range (1) = NPV of optimistic outcome – NPV of pessimistic outcome

Alternatively, the range is found by taking annual cash inflow from optimistic outcome and subtracting annual cash inflow from pessimistic outcome, as shown below:

range (2) = annual cash inflow from optimistic outcome – annual cash inflow from pessimistic outcome

Range shows us variability between returns.

Risk in Capital Budgeting

Firmsconsulting Leave a comment

When it comes to capital budgeting, risk refers to probability that project will proof to be unacceptable with net present value (NPV) less than zero or internal rate of return (IRR) less than cost of capital. Particularly, it refers to variability of the returns.

To find the minimum cash inflow level acceptable, we need to calculate breakeven cash inflow.

Breakeven cash inflow refers to the minimum cash inflow that it required for the project to be acceptable. It is calculated as follows:

PV – Initial investment

N – number of periods over which cash inflow is received

I – required cost of capital

Find PMT – breakeven cash inflow

Test yourself:

ABC Corporation have an option to invest in project A which requires investment of $120,000. The duration of the project is 5 years and ABC’s cost of capital is 9%. What is the breakeven cash inflow?

Solution:

We can find breakeven cash inflow of project A with the help of financial calculator.

PV: -120,000

N: 5

I: 10

Find PMT: $31,448.94

The above calculation helps us to determine that the minimum annual cash inflow that will be acceptable for project A is $31,448.94.

Blogbschool.com is powered by www.firmsconsulting.com. Firmsconsulting is a training company that finds and nurtures tomorrow’s leaders in business, government and academia via bespoke online training to develop one’s executive presence, critical thinking abilities, high performance skill-set, and strategy, operations and implementation capabilities. Learn more at www.firmsconsulting.com.

Sign up to receive a 3-part FREE strategy video training series here.

Using a financial calculator

Firmsconsulting Leave a comment

Using a financial calculator is a skill, similar to typing. You just need to know which steps to take and then you need to practice to the point when you feel comfortable with using a calculator.

In all explanations with a financial calculator we will be using an HP 10bll. Other financial calculators are similar, yet we find it easier to work with the HP. Most text books use HP calculators when providing guidance on using a financial calculator, so if you have a different calculator you may need to spend more time learning slightly different calculation steps. Before investing further time, it may be wise to get a universally used calculator.

Before using a financial calculator to make specific calculations such as calculating NPV or IRR, it is important to make sure that you:

1 – Clear the calculator – by pressing second function followed by “C All”

2 – Set calculator for the “END” by pressing second function followed by “BEG/END” and ensuring that the word “BEGIN” is not displayed. Exceptions to this rule occur when it is specifically stated in the problem that cash flows occur at the beginning of the period (for example, at the beginning of the year).

Again, if no sign appears on the display then you do not need to reset it as it is set for “END” by default. If it says “BEGIN” on the display, you need to press second function followed by “beg/end.”

When you set the calculator for the “END” of the period you do that because in the problem you are working with, cash inflow or outflow occurs at the end of the period. If the problem does not state when cash flows occur, you need to assume that it occurs at the “END” of the period.

The majority of calculations will require the “END” setting. If it is by mistake set for “BEGIN” but cash flows occur at the end of the period, then incorrect answers will be generated.

Therefore, it is advisable to keep it set for the “END” at all times as a default and only reset it for “BEGIN” when a calculation requires that to be done. Right after a calculation is completed that requires the “BEGIN” setting, it is important to develop a habit to reset it to the “END”.

In the explanations using a financial calculator, for convenience and clarity purposes, we will generally display explanations of calculations as presented in the example below:

PV: -900 I: 7 N: 5 FV: 1,262.3

When using a HP 10bll financial calculator, or using any financial calculator, you need to first insert the number (number, e.g. -900) and then insert the purpose of the number (e.g. PV).

For example, as per above, you need to press:

900 followed by the minus sign followed by PV

7 followed by I

5 followed by N

Than press FV, and the calculator will display the correct answer

Financial calculators sometimes give false answers. It is advisable to check each calculation 3-4 times to make sure that the same answer is given consistently.

Throughout the site, if you ever struggle with a calculation, always come back to this page for some simple tips on using a financial calculator.

Test yourself

ABC Corporation plans to invest in project C which has an initial investmentof $500,000. ABC’s cost of capital is 8%. The operating cash flows to be generated from the project will be as follows:

End of 1st year: $100,000 End of 2nd year: $300,000 End of 3rd year $250,000

1 – What is the Profitability Index (PI) for project C?

2 – What is the NPV for project C?

3 – Taking the NPV found in the previous step into account, is the project acceptable according to the NPV technique?

4 – Based on the Profitability Index (PI), is project C acceptable?

SOLUTION:

1 – First we need to find present values of the mixed stream of operating cash inflows. Using a financial calculator, we need to take the following steps:

End of 1st year:

FV: $100,000

N: 1

I: 10

Calculate PV: $90,909.09

End of 2nd year:

FV: $300,000 N: 2

I: 10

Calculate PV: $247,933.88

End of 3rd year:

FV: $250,000

N: 3

I: 10

Calculate PV: $187,828.7

Next we need to add up all present values from operating cash inflows to obtain the total PV of operating cash inflows:

= $90,909.09 + $247,933.88 + $187,828.7

Total PV of operating cash inflows = $526,671.67

Next we will follow the equation for Profitability Index (PI):

PI = Total present value of cash inflows/Initial investment

PI=$526,671.67/$500,000

PI=1.05

Therefore, the profitability index (PI) for project C is 1.05.

2 – To find NPV, we follow the formula for NPV:

NPV=Present value of cash inflows – Initial investment

Therefore, NPV for project C = $526,671.67 – $500,000

NPV for project C = $26,671.67

3 – Since NPV is more than zero ($26,671.67), project C is acceptable according to NPV technique.

4 – Since Profitability Index (PI) is greater than 1 (1.05), the project may be considered to be acceptable.

Blogbschool.com is powered by www.firmsconsulting.com. Firmsconsulting is a training company that finds and nurtures tomorrow’s leaders in business, government and academia via bespoke online training to develop one’s executive presence, critical thinking abilities, high performance skill-set, and strategy, operations and implementation capabilities. Learn more at www.firmsconsulting.com.

Sign up to receive a 3-part FREE strategy video training series here.