Category Finance

Capital structure decisions

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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.

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Degree of total leverage (DTL)

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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.

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Risk Adjusted Discount Rate: Dealing with Risk in Capital Budgeting

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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.

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Risk Scenario Analysis: Dealing with Risk in Capital Budgeting

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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

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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.

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Using a financial calculator

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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.

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Profitability index (PI)

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Profitability Index (PI) is another sophisticated technique used in capital budgeting decisions. PI is related to NPV as it indicates the net present value (NPV) per each dollar invested. PI is calculated as follows:

PI =

Total present value (PV) of cash inflows divided by Initial investment.

PI is an especially advantageous technique if the company operates under capital rationing. If the PI is greater than one, the project is acceptable.

 

Equivalent Annual Annuity Approach (EAA)

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Equivalent Annual Annuity approach (EAA) is another sophisticated technique used in capital budgeting decisions. EAA determines the annual cost of the project over its economic life. It is determined by dividing net present value (NPV) of the project by the present value interest factor for annuity (PVIFAr,n) for a specific period and at a specific discount rate. PVIFAr,n can be found in financial tables.

EAA is helpful when a project has to be selected from mutually exclusive projects with unequal lives. The project with the highest Equivalent Annual Annuity (EAA) is more attractive. If two mutually exclusive projects have equal EAA than the project with the shorter economic life is more acceptable.

 

The Difference Between IRR and NPV

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This article answers two questions:

1 – What is important difference between IRR and NPV?

2 – Based on these differences and other considerations, which method is more popular and which method is theoretically superior?

What is important difference between IRR and NPV?

Net Present Value method assumes that cash inflows are reinvested at cost of capital, which is more realistic than assumption made in Internal Rate of Return method (IRR) that cash inflows are reinvested at IRR.

Based on these differences other considerations, which method is more popular and which method is theoretically superior?

Theoretically, it is advisable to use the Net Present Value method because it assumes that cash inflows are reinvested at cost of capital. However, in real life, the Internal Rate of Return method is more common because it considers the rate of return instead of dollar amount considered in the Net Present Value method and the former seems to be more intuitive to users of techniques. There are, however, ways to deal with shortcomings of Internal Rate of Return method and therefore IRR is still considered a sophisticated and reliable technique.

Internal Rate of Return method (IRR)

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Sophisticated capital budgeting techniques include Net present value method (NPV), Internal Rate of Return method (IRR), Profitability index (PI) and Equivalent Annual Annuity (EAA). Internal Rate of Return method (IRR) is discussed below.

Internal Rate of Return (IRR) is a widely used technique.

It is also very easy to utilize Internal Rate of Return with the help of a financial calculator. It is much more challenging to calculate it by hand. Again, as in utilizing the NPV method, it is important to first understand the logic behind the calculation.

In simple terms, the IRR is the rate of return that would equate NPV with zero. If IRR higher than cost of capital than project should be accepted and vice versa. If IRR at least equals cost of capital than we know that business will earn at least rate equal to its cost of capital on this particular project.

Below is shown how to calculate IRR using the financial calculator.

IRR for annuity is calculated as follows:

Initial investment, minus sign – CFi

Annual cash inflow – CFi1

Number of periods – second function Ni

Second function IRR

IRR for a mixed stream is calculated as follows:

Initial investment, minus sign – CFi

Put in each cash inflow separately following with CFi1, CFi2 etc

Second function IRR

Both NPV and IRR will show whether the project is acceptable. However, the ranking of specific acceptable projects may differ between two techniques.

Test yourself

ABC have an option to invest in project B. The initial investment for project B is $35,000. Operating cash inflows from project B expected to be $5,000 per year for 8 years. The cost of capital of ABC is 5%.

What is the Internal Rate of Return (IRR) for project B?

Find out if project B is acceptable based on IRR calculation.

Solution:

With the help of financial calculator, we can determine IRR of project B as follows:

CFio: -35,000

CFi1: 5,000 (annual operating cash inflow)

Second function Nj: 8 (8 years)

Second function IRR: calculate – 3.07

The IRR of project B is 3.07%. The cost of capital of ABC is 5%. Since IRR (3.07%) is below cost of capital (5%), the project is not acceptable.

Test yourself

ABC have an option to invest in project D. The initial investment is $300,000. The operation cash inflows are expected to be $100,000 at the end of year 1, $110,000 at the end of year 2 and $130,000 at the end of year 3. The cost of capital of ABC is 10%.

  1. Calculate IRR
  2. Recommend if based on IRR technique project D is acceptable.

Solution:

1. With the help of financial calculator, the calculation is as follows:

Clear calculator: second function followed by C ALL

CFo: -300,000

CF1: 100,000

CF2: 110,000

CF3: 130,000

Second function IRR: calculate – 6.24%

2. Since cost of capital of ABC is 10% and IRR is only 6.24% (less than cost of capital), based on IRR technique, project D is not acceptable.

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