# The Hurdle Rate

The hurdle rate is also called minimum acceptable rate of return (abbreviated MARR) or break-even yield. It refers to the minimum rate of return that is required before any project can be undertaken. The hurdle rate is used in the capital budgeting and is the same as the required rate of return in the discounted cash flow analysis of long-term investment opportunities. It is a discount rate used when different investment alternatives are considered.

If the expected return on the proposed investment is below the hurdle rate, than the investment is not acceptable and vice versa. Sometimes the hurdle rate also refers to the minimum internal rate of return (IRR) for the project to be undertaken.

The hurdle rate should be equal to the marginal cost of capital, which is also referred to as the incremental cost of capital. The hurdle rate is also a rate of return which is necessary to maintain market value of the firm. The market value of the firm refers to the firm’s current market price of shares.

Organizations use hurdle rates to evaluate long-term investment projects using discounted cash flow techniques (capital budgeting). This allows assessing potential projects more systematically. Such evaluation allows having better confidence that selected long-term investments will at least have returns equal to the marginal cost of capital.

Hurdle rates should be set for each project or at least for each business unit or division to account for differences in risk profiles across the enterprise.

# Overview of financial ratios

Liquidity ratios

Current ratios measure liquidity, which refers to the ability of the firm to meet its short-term debt obligations. The formula for current ratio is as follows:

Current ratio=Current assets/Current liabilities

A positive current ratio is a must. A current ratio of at least two is generally advisable. If a company has current ratio of two, it means that it has current assets which would be able to cover current liabilities twice.

Activity ratios

Total asset turnover calculates how efficiently assets are used to generate sales. In other words, how efficiently the balance sheet is managed.

Total asset turnover=Sales/Total assets

The health of this ratio is an important factor which contributes to a healthy return on investment (ROI/ROA).

Inventory turnover ratio measures the liquidity of a firm’s inventory. It measures how many times the company turns over (sells, uses or replaces) its inventory during a period, such as the financial period.

It is calculated by dividing cost of goods sold by inventory.

Inventory turnover ratio = Cost of goods sold/Inventory

The result of this ratio is only meaningful in comparison. It can be compared to industry averages, to firms past inventory turnover ratios and to inventory turnover ratios of competitors.

Industry averages differ significantly between industries for inventory turnover ratio. Inventory turnover is positive (higher than zero) as long as firm has any inventory. Generally high inventory turnover is considered to be a good indicator.

However, the norm would differ significantly between industries. If industry turnover is too high compared to the norm within the industry, it may mean the company keeps too little inventory and, therefore, may lose some sales.

Debt ratios

Debt ratio measures how many of firm’s assets are financed by debt. The formula for debt ratio is as follows:

Debt ratio=Total liabilities/Total assets

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.

Debt-equity ratio measures how much of equity and how much of debt a company uses to finance its assets.

Debt-equity ratio = Total debt / Equity

If the debt-equity ratio is less than one, then it means that equity is mainly used to finance operations. However, if the debt-equity ratio is more than one, then it means that debt is mostly used for financing. If the debt-equity ratio is equal to one, then it means that half of financing comes from debt and half from equity.

The more debt compared to equity the firm uses in financing its assets, the higher the financial risk and the higher potential return. Financial risk refers to risk of firm being forced into bankruptcy if the firm does not meet its debt obligations as they come due.

Times Interest Earned Ratio (Interest Coverage Ratio)

Times Interest Earned Ratio (Interest Coverage Ratio) measures the ability of the enterprise to meet its financial obligations (interest payments on debt that come due). The formula for the Times Interest Earned Ratiois as follows:

TIER=EBIT/interest charges

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

For example, assume that ABC 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

One should also compare ratios of individual firms to industry averages, to obtain a better understanding. It is generally advisable that TIER should be between 3 and 5.

ABC’s TIER 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 the firm takes is lower than average, but so is the return.

Profitability ratios

Operating profit margin measures how much of each sales dollar remains after all costs except for interest, tax and preferred dividends are deducted.In other words it measures how efficient the business manages its operations or how efficiently the firm manages its income statement (keeping a healthy balance between sales and costs).

Operating profit margin = Operating profit/Sales

For example, if ABC has a operating profit of \$500,000 and sales of \$3,000,000 then the operating profit margin is calculated as follows

Operating profit margin = \$500,000/\$3,000,000

Operating profit margin = 0.167 or 16.7%

The higher the operating profit margin, the better it is.

Return on total assets (ROA) is also called return on investment (ROI). It refers to how effective management is in generating returns on assets of the firm.

ROA/ROI=Earnings available for common stockholders/Total assets

For example, if ABC’s total assets are \$3,500,000 and the earnings available for common stockholders is \$400,000 than

ROA/ROI=400,000/3,500,000

ROA/ROI=0.11

This means that for every dollar of assets, ABC earned 11 cents. The more the firm earns on every dollar of assets the better.

# Using CAPM (Capital Asset Pricing Model)

In addition to Gordon Model, another way to find the cost of common stock is by using Capital Asset Pricing Model (CAPM). CAPM allows us to ascertain the relationship between required return and non-diversifiable risk, which is measured by the beta coefficient (b).

Beta coefficient (b) refers to the index that measures non-diversifiable risk (risk which a company cannot eliminate through diversification). It indicates how an asset’s return will react to the changes in the market return, which in turn shows the return on a portfolio of all securities in the market.

Capital Asset Pricing Model (CAPM) is simple, as long as you know the formula and have the information necessary for the formula. The formula is as follows:

rs= Rf+(b*(rm-Rf))

Where:

rs – required return (return on a portfolio or a security)

Rf – risk free rate (e.g. rate on the U.S. Treasury bill)

b – beta coefficient

rm – market return

EXAMPLE:

If Rf (risk free rate) is 5%, beta is 2 and market return (rm) is 12%, the rs (required return or cost of common stock) can be found as follows:

Rs=5%+(2*(12%-5%)

Rs=19%

# Test yourself

Assuming we know that beta (company’s market risk coefficient) is 2, market return is 13%, risk free rate of return is 7%, current dividend is \$4 and dividend growth over the past 5 years is 5% and the same growth is expected in the future. With CAPM, find the price of the ordinary share.

SOLUTION:

First, using CAPM, we find rs:

rs= Rf+(b*(rm-Rf))

rs=7+(2*(13-7))

rs=19%

Next, we use the Gordon model (P0=D1/(rs-g)) to find the price of the ordinary share:

Po=(4*(1+.05))/(.19-.05)

Po=4.2/0.14

Po=\$30

Test yourself:

ABC’s financial manager prepared the following information. The dividend which were paid in the current year was \$5. The growth of dividends over the last 5 years were 7% and the same growth of dividends is expected to be in the future. Risk free rate is 8%, market rate is 14% and beta coefficient is 2.

Required: What is the market price of ABC’s ordinary shares?

Solution:

Firstly we need to find required return (rs) with the help of the capital asset pricing model (CAPM).

rs= Rf+(b*(rm-Rf))

rs=8+(2*(14-8))

rs=20

Next, we need to use Gordon model:

Po=D1/(rs-g)

Po=5*(1+0.07)/(0.20-0.07)

Po=5.35/0.13

Po=41.15

The price of the ABC’s ordinary share is \$41.15. Note that we determined D1 (dividend within the next period) by taking known D0 (last dividend) and multiplying it by (1+ growth rate).

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# Annualized Net Present Value (ANPV)

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.

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# Risk in Capital Budgeting

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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# The Difference Between IRR and NPV

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)

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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# Net Present Value Method

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

NPV is a sophisticated capital budgeting technique. Theoretically, Net Present Value (NPV) is the best technique out of sophisticated capital budgeting techniques but it is difficult to use it in practice. Sometimes Net Present Value method is referred to as the “gold standard” for investment decisions.

It is very easy to use Net Present Value with the help of a financial calculator if all necessary data is available. However, it is important to firstly understand the logic behind this calculation. NPV is determined by finding present value of cash inflows and then subtracting an initial investment.

NPV=Present value of cash inflows – initial investment

Now, after we understand the logic behind usage of Net Present Value method, we can calculate NPV using a financial calculator. We will always use a HP 10bll financial calculator throughout the website. Other calculators are similar but may have some small differences.

Before you make any calculations, make sure that you:

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

2 – Ensure that it is set for end if cash flows occur at the end of the period and that it is set for beginning if cash flows occur at the beginning of the period.

To set for end/beginning – press second function followed by beg/end. If it is set for the beginning than word “begin” will be displayed. If it is set for the end than no word will be displayed.

Majority of calculations will be with the “end” setting (used when cash flows occur at the end of the period). Therefore, it is important to acquire a habit of re-setting your calculator to the “end” setting after every calculation with the “begin” setting. Otherwise, you are running a risk of forgetting to re-set the calculator and obtaining an incorrect result from future calculations.

NPV FOR ANNUITY IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

Annual cash inflow: amount, CFi1

Number of periods: number of periods, second function, Ni

Cost of capital: number, i

Find NPV: second function, NPV

NPV FOR A MIXED STREAM IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

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

Cost of capital: number, i

Find NPV: second function, NPV

If NPV is higher than zero than we know that this project will earn returns higher than the business’s cost of capital. Further, the owner’s wealth will increase by the amount equal to NPV.

### Test yourself

ABC Corporation has an option to invest in projects A. Project A has aninitial investment of \$15,000, and operating cash inflows of \$3,000 over the economic life of the project, which is 8 years. The cost of capital (also called discount rate or rate of return) is 8%.

Find the net present value (NPV) of project A?

SOLUTION:

With the use of a financial calculator, we can find the net present value (NPV) as follows:

Clear the calculator by pressing second function followed by “C ALL”.

Make sure calculator is set to the “end”. This setting is used because in this problem cash flows occur at the end of each period. It is commonly accepted that if problem does not state when cash flows occur, you need to assume that cash flows occur at the end of the period, not at the beginning of the period.

WE KNOW THAT NPV FOR AN ANNUITY IS CALCULATED AS FOLLOWS:

Initial investment: amount, minus sign, CFi

Annual cash inflow: amount, CFi1

Number of periods: number of periods, second function, Ni

Cost of capital: number, i

Find NPV: second function, NPV

NOW YOU NEED TO PLUG IN THE NUMBERS:

NPV for annuity:

Initial investment: 15000, minus sign, CFi

Annual cash inflow: 3000, CFi1

Number of periods: 8, second function, Ni

Cost of capital: 8, i

Find NPV: second function, NPV

= \$2,239.92

The above calculation makes it clear that project A is an acceptable project for ABC because the NPV is higher than zero (\$2,239.92).

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# Unsophisticated capital budgeting techniques

Simple (unsophisticated) capital budgeting techniques include average rate of return (ARR) and the payback method (also called PB or payback period).

### Average Rate of Return

Average Rate of Return (ARR) is an unsophisticated budgeting technique and generally considered to be ineffective. Average Rate of Return (ARR) evaluates relative profitability of the investment. In other words, it evaluates how project affects accounting profits. Average Rate of Return (ARR) is calculated as follows:

ARR = Average income / Average investment

Average income refers to annual average net profits after tax (refer to income statement to see how net profits after tax are determined). Annual average net profits after tax is found by taking total net profits after tax over the useful life of the project and dividing it by number of years over useful life of the project. Average investment refers to average investment over the economic life of the project. The ARR capital budgeting technique does not consider the time value of money. It also considers net profits rather than cash inflows. Consequently, the technique overlooks the possibility of reinvestment of returns.

The positive side of this technique, as compared to payback period discussed below, is that it considers returns on investment over entire useful life of the project. However, this technique is generally not recommended.

### Payback method

Payback period (PB), also called a payback method, is another unsophisticated budgeting technique. It determines how long it takes to recover the initial investment by taking into account cash inflows from the investment. If we deal with an annuity (an equal periodic cash flow over a specific period) than all we need to do is to divide initial investment by an annuity.

However, if we deal with a mixed stream of cash inflows (unequal cash flows during specific period with no precise pattern) than we need to add up cash flows until the initial investment is recovered.

Management needs to subjectively determine the maximum payback period and then projects are evaluated according to this. If the project’s payback period is below maximum than the project is acceptable and vice versa.

The payback period budgeting technique measures business’s risk exposure because the project’s risk level depends on how long it takes to recover the initial investment. However, it does not explicitly consider the time value of money.

Moreover, this budgeting technique is weak because it is subjective in nature since the minimum payback period is subjectively determined. Furthermore, it does not take into account the cash flows that occur after the payback period.

A variation of payback period capital budgeting technique allows to account for time value of money and risk (due to usage of discount rate which incorporates risk). Such variation is called discounted payback period technique. This technique determines how long it takes for discounted cash flows to recover the investment. However, this variation still does not consider cash flows after the payback period.

### Test Yourself

ABC Corp has a proposed project A, which has expected cash inflows of \$4,000 over 10 years period. The initial investment is \$30,000. Find the payback period.

SOLUTION:

Payback period = 30,000/4,000 = 7.5 years

This means that it will take 7.5 years for ABC to recover its investment in project A.

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# Capital Budgeting Techniques

The Capital budgeting techniques discussed here focus on financial considerations, although, there are financial and non-financial considerations that should be taken into account when selecting a project for capital expenditure.

There are unsophisticated (simple) and sophisticated (advanced) techniques.

1 – Unsophisticated techniques include payback period (PB, also called payback method) and average rate of return(ARR).

2 – Sophisticated techniques include net present value (NPV), internal rate of return (IRR), equivalent annual annuity (AEE) and profitability index (PI).

Out of this range of techniques, payback period is the most popular unsophisticated technique. From the sophisticated techniques, the most popular methods are net present value (NPV) and internal rate of return (IRR).

Capital budgeting techniques used to select most profitable projects for capital expenditure, which is aligned with enterprise’s objective of maximizing shareholder’s wealth. Sophisticated techniques are considered to be the most effective means of selecting the most appropriate projects for capital expenditures. Such techniques take into account risk, the time value of money and focus on cash flows rather than on accounting profits.

The result of educated usage of capital budgeting techniques knowledge generated on which projects and in which order should be accepted based on the available funds for investment.