Guide to Financial Statements
Guide to Financial Statements Financial Statements are the single most valuable source of financial information on a business
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]]>Capital expenditures (CAPEX) and operating expenses (OPEX) are two important items from a company’s cash flow and income statement (respectively). They are both key financial metrics that companies use to budget, forecast, and analyse their spending. Understanding the difference between CAPEX and OPEX is especially important for making sound investment decisions and properly allocating financial resources.
In corporate finance, CAPEX refers to the money a company spends to acquire, maintain, or improve fixed assets like property, buildings, technology, or equipment. OPEX refers to the ongoing costs a company incurs for running day-to-day operations. Analysing CAPEX and OPEX helps determine where a company is investing its capital and how efficiently it is operating.
Topic | Key Takeaways |
---|---|
Definition of CAPEX | Capital expenditures made to acquire, upgrade long-term assets like property, equipment, technology. Considered an investment, not an expense. Capitalized on the balance sheet, depreciated over time. |
Definition of OPEX | Operating expenses for day-to-day operations. Considered a cost, expensed immediately. Examples include salaries, rent, utilities, marketing. |
Accounting Treatment | CAPEX is capitalized and depreciated over time. OPEX is expensed immediately. |
Tax Deductibility | CAPEX depreciation is deductible over the asset’s life. OPEX is fully deductible when spent. |
Analyzing in Excel | Download financial statements. Create columns for CAPEX and OPEX items. Calculate totals and metrics like % change. Use pivot tables, charts to analyze. |
Importance of Metrics | Operating margin relies on OPEX. Return on capital relies on CAPEX. A balanced CAPEX and OPEX strategy enables growth. |
CAPEX refers to the capital expenditures a company makes to acquire, upgrade, or maintain physical assets such as:
CAPEX investments are made to create benefit for the company over many years, not just in the current period. Examples include constructing a new factory, upgrading to new software systems, or replacing old equipment with newer models.
CAPEX is considered an investment for the future rather than an expense, as these investments will generate returns over the long-term. CAPEX spending is also known as capital spending or capital costs.
OPEX refers to the ongoing, regular expenses a company incurs from its day-to-day operations. OPEX spending is what a company requires to keep the lights on and doors open. Examples of OPEX include:
Unlike CAPEX, OPEX spending is considered a cost and is expensed in the current period. OPEX is also known as operating costs or operational expenditures/expenses.
There is potentially overlap and some ambiguity in the definitions of the two items: OPEX will contain an expense for “Repair and renewal” (R&R). It may be advantageous to classify expenditure as R&R because this will be immediately deductible in full from taxable profit. CAPEX will only be offset against tax over a much longer period. In the UK, the tax authorities draw the line as follows: “if an asset is altered or improved, then it is CAPEX, it is not allowable expenditure” (for tax purposes), i.e. R&R.
For analysts, an important question when looking at CAPEX is to assess whether CAPEX is “maintenance” CAPEX, replacing old worn-out machinery to simply maintain capacity, or is it Investment CAPEX, giving rise to an increase in productive capacity.
Capital expenditures can be presented on a gross or net or gross basis in a set of accounts:
Net CAPEX = Cash spent – Proceeds of Sale of Assets
CAPEX spending is not deducted from the income statement in the year of purchase i.e. it is not “expensed”. Instead, the cost of the asset will be “depreciated” gradually through the income statement over the useful life of the asset. The aim is to match revenues and expenses over time: If a plane will fly for 25 years before it is retired from service, it makes sense to treat 1/25 of the capital cost of the plane as an expense in each year it is in service.
CAPEX does not necessarily tell us the full story about the investment in new capacity made by a company in a year. When a company enters a lease, there is not always any immediate cash impact. Instead, the value of the leased asset and a corresponding amount of lease debt appear on the asset and liability sides of the balance sheet. There is no “CAPEX”. A company may also buy other companies or make investments in joint venture or associates. These may all increase the productive assets under the control or partial control of the company.
The formula for calculating operating expenses is:
OPEX = Cost of Goods Sold + Sales General and Administrative Costs
Where:
In a manufacturing company for example, it is very easy to categorise a lot of costs:
An operating expense is not necessarily recorded in the period when it is paid for in cash.
Using the same “matching principle” mentioned above, we will match revenues and expenses in time. Taking a simple example like insurance:
OPEX is fully deducted in the year it was spent. It is not amortized over time like CAPEX.
CAPEX and OPEX have different accounting and tax implications:
CAPEX is capitalized on the balance sheet. It is recorded as a long-term asset that is depreciated over multiple accounting periods.
OPEX is the proportion of direct and indirect production cost expensed on the income statement in a period. It is recorded as a cost against revenues.
CAPEX deductions are spread over the useful life of the asset. Only the annual depreciation can be deducted each year.
OPEX is fully tax deductible in the period it was spent.
For accounting purposes, CAPEX improves a company’s balance sheet position but hurts the income statement in the near term due to depreciation expenses. OPEX negatively impacts the income statement but does not create a depreciable asset.
For taxes, CAPEX provides deductions over many years while OPEX provides an immediate deduction. Companies can use a mix of CAPEX and OPEX to optimize their tax position.
Typically, to incentivize investment by companies, Tax authorities give accelerated capital allowances. What this means is that whilst a company may depreciate an asset over 8 years, expensing 12.5% of original cost per year, the Tax authorities may allow a bigger deduction for calculating tax. This lowers the tax bill. In the UK, in this case a 25% deduction would be allowed in year one and then an 18.75% deduction in year 2 and a 14.1% deduction in year 3. This reduces the overall tax burden for the first three and a half years after investment.
CAPEX and OPEX spending can be analysed in Excel to track where a company is allocating resources:
This Excel analysis can identify spending patterns and trends to see where resources are being allocated. The mix of CAPEX vs OPEX can be compared to peers.
Some key places where you will examine CAPEX and OPEX metrics in corporate finance include:
A major tech company has been aggressively increasing CAPEX expenditures in recent years to build new data centres, cloud infrastructure, and capabilities. This has lowered near-term earnings due to higher depreciation expenses. However, the tech company’s market share has significantly grown thanks to these investments. This is an example of a growth strategy fuelled by prudent CAPEX spending.
A mature manufacturer has kept CAPEX spending relatively flat in recent years as its assets and capabilities remained adequate. It focused more on reducing OPEX by streamlining operations, cutting excess costs, and improving productivity. This helped improve profit margins through OPEX efficiencies rather than asset investments.
A young startup has been careful to allocate capital raised between essential CAPEX for technology, equipment, and office space while keeping OPEX like marketing and hiring controlled. As the startup matures, CAPEX investments continue enabling growth. The balanced allocation has helped the startup scale efficiently.
Analysing the CAPEX and OPEX strategies in these case studies provides examples of how expenditure optimization promotes long-term success.
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]]>Perpetuities are an important concept in corporate finance and investment analysis. A perpetuity is a constant stream of cash flows that continues indefinitely into the future. Understanding perpetuities allows financial analysts to properly value assets and investment opportunities that involve long-term, ongoing cash flows. They are one the most fundamental tools in valuation alongside concepts such as yield curves and zero-coupon bonds.
Aspect |
Takeaway |
Definition | A perpetuity is a constant stream of cash flows continuing indefinitely into the future |
Formula | The formula for valuing a perpetuity is: Present Value = Cash flow per period / Discount rate |
Discount Rate | The discount rate reflects the time value of money and associated investment risks |
Growing Perpetuities | Growing perpetuities have cash flows that increase at a constant growth rate each period |
Comparison to Annuities | Perpetuities continue forever while annuities have a fixed number of payment periods |
Applications | Perpetuities are used to value financial assets with very long or infinite lives |
Examples | Examples of perpetuity valuation include stocks, bonds, royalties, real estate, settlements |
Key Assumptions | Key assumptions are constant discount rate and growth rate, which may not hold true |
Synonyms | Perpetuity and forever mean the same thing – an unlimited time period |
A perpetuity is a stream of cash flows that continues forever without end. The equal periodic payments can occur at any fixed interval, such as monthly, quarterly or annually. A key feature is that the perpetual cash flows remain constant over time. Their present value and theoretical fair value can be calculated using a standard perpetuity formula.
The formula for the present value (PV) of a perpetuity is:
PV of Perpetuity = Cash flow per period / Discount rate
Where:
For example, if a perpetual bond pays $100 annually, and the discount rate is 5%, the present value is:
This means an investor should be willing to pay $2,000 today to receive $100 every year forever, assuming a 5% discount rate. The lower the interest rate, the higher the present value of the perpetuity.
The discount rate is a critical component in perpetuity valuation. It reflects the time value of money and is typically influenced by factors like the risk-free interest rate, market conditions, and specific risks associated with the cash flow. For instance, a higher discount rate is used for riskier cash flows, which lowers the present value of the perpetuity.
A variation on a standard perpetuity is a growing perpetuity, where instead of fixed cash flows, the periodic payments increase at a constant growth rate. The formula for a growing perpetuity PV is:
PV = C / (r – g)
Where:
For example, if the initial cash flow is $100, and payments grow at 3% annually at a 5% discount rate, the PV is:
PV = $100 / (0.05 – 0.03) = $5,000
With a growth rate of 4%, the value of the perpetuity would rise to $10,000.
This shows how faster growth can increase the present value of a perpetuity versus flat or slowly growing cash flows.
Perpetuities and annuities, while similar, differ mainly in their length.
Perpetuities have infinite payments, while annuities have a fixed number of payment periods.
One key assumption in perpetuity valuation is that the discount rate is constant over time, which might not hold in dynamic market conditions. Similarly, growing perpetuities assume a constant growth rate, an assumption that may not always reflect real-world scenarios.
For example, with an ordinary annuity certain, payments are made for a set term like 20 years. But a perpetuity continues making equal payments forever into the infinite future.
Their formulas also differ accordingly, with perpetuities using a simple 1/r discount rate divisor and annuities using a discounted cash flow approach based on the total number of periods. Still, both tools serve a similar purpose in determining the present value of future cash flow streams.
Perpetuities have many practical applications in corporate finance and investment analysis:
In these cases, being able to accurately value cash flows continuing far out into the future is critical.
The perpetuity concept and related formulas are important tools financial analysts rely on to properly value these kinds of long-term assets and cash flow streams.
In summary, perpetuities represent future cash flow streams continuing indefinitely. Their valuation relies on a simple, straightforward formula using the constant periodic payment divided by the discount rate.
Perpetuities are useful in finance for analysing assets with very long or infinite lives. Understanding the perpetuity concept is key for corporate analysts and investors looking to properly value long-term equity dividends, bonds, royalties, annuities, and various other assets and cash flows.
A note to be wary of is that textbooks will show two different formats of the formula, where:
The latter is the standard one used in finance, while our formulae is standard for the valuation of a perpetuity today, where the first payment happens one time-period (a year, quarter etc) from now.
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]]>The discount rate is a crucial concept in corporate finance and investment appraisal. It is used to determine the net present value (NPV) of future cash flows thus accounting for the time value of money and enabling the comparison of projects and investments with cash flows spread over different time periods.
Takeaway | Description |
Definition | The rate applied to future cash flows in order to calculate their present value. Accounts for the time value of money and investment risk. |
Impacts | Critical in investment appraisal, project timing, capital rationing, financing choices, and business valuations. |
Comparison to Other Metrics | Broad term that covers a number of more specific metrics such as cost of capital, interest rates, and hurdle IRRs. |
Common Ranges | Varies widely by industry and project risk – from low single-digit percentages for stable assets (e.g. government bonds) to double-digit percentages for higher risk assets (e.g. startups, technology ventures.) |
Uses in Excel | Input into the NPV formula. |
The discount rate is the rate used to determine the present value of future cash flows. It can also be considered as the rate of return that could be earned in alternative investments of equivalent risk. The discount rate reflects the impact of the time value of money – the idea that money available today is worth more than the same amount in the future, due to its potential earning capacity.
The higher the discount rate, the larger the sum of money you would expect to receive in the future, if you were to invest the same amount today. As such, it also implies that a certain set of future cash flows are worth less today than if a lower discount rate was used. Corporations apply discount rates to determine the present value of long-term projects and investments, and thus is crucial in capital budgeting and net present value analysis.
Net Present Value (NPV) measures the difference between the present value of cash inflows and outflows over the lifetime of a project or investment. The NPV is calculated by discounting the projected future cash flows to their present value, using the discount rate.
If the NPV is positive, the discounted future cash flows exceed the initial investment, and the project is likely to be profitable. If the NPV is negative, the initial investment is higher than the present value of future cash inflows and the project is likely to be unprofitable.
The discount rate can be used in Excel within the NPV formula:
=NPV(discount_rate, cash_flow_series)
Where:
The discount rate significantly impacts capital budgeting and corporate finance decisions, including:
The term discount rate is a broad one that can often be used to cover a number of more specific metrics, including:
The discount rate is a fundamental concept in corporate finance that reflects the time value of money and risk. By applying suitable discount rates, corporations can accurately assess the profitability of long-term projects and investments.
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]]>Liquidity ratios are an important set of financial metrics used to analyse a company’s ability to cover its short-term obligations.
Companies fail not due to lack of profits in most cases, but due to their inability to meet their short-term cash requirements – i.e. they fail to pay suppliers, tax, bank loans or other financial obligations. The suppliers stop supplying, the banks recall their loans, the government gets angry at not receiving tax and the company goes bust.
Ratios in themselves do not give you definitive answers to questions, but they can highlight when problems are potentially arising, and companies are beginning to struggle.
To do this, you need to be able to pick up a set of financial statements and use the information intelligently. By comparing a company’s most liquid assets to its short-term liabilities, liquidity ratios provide insight into whether a company has enough cash on hand to cover its upcoming financial obligations. Monitoring liquidity ratios helps stakeholders understand a company’s financial health and resilience.
Liquidity refers to the ability of a company to convert assets to cash in order to pay off short-term liabilities and debt as they become due. Liquidity ratios evaluate a company’s capacity to meet short-term financial demands and provide insights into the adequacy of working capital.
Topic | Key Takeaways |
Liquidity Ratios | Compare liquid assets to current liabilities to assess ability to cover short-term obligations. Higher ratio indicates greater liquidity and lower liquidity risk. |
Types of Ratios | – Cash ratio: only cash and equivalents vs liabilities
– Quick ratio: cash, equivalents, receivables vs liabilities – Current ratio: all current assets vs liabilities |
Analysis | Compare ratios over time and to industry averages. Analyze trends and benchmark against peers. Consider influence on other financial metrics. |
Applications | Assess short-term cash positions and working capital. Guide financing, inventory, and cash flow decisions. Evaluate loan applications and set credit terms. |
Liquidity ratios are calculated by comparing a company’s liquid (cash or near-cash) assets to its current liabilities. Liquid assets are balance sheet accounts that can be easily converted to cash within a short period of time, say within 90 days or less. This includes cash and cash equivalents (like short-term investments), accounts receivable, inventory, and marketable securities.
Current liabilities are a company’s debts or obligations that are due within one year. This includes accounts payable, wages payable, taxes payable, short-term loans, accrued expenses, and the current portion of long-term debt.
By comparing liquid assets to current liabilities, liquidity ratios show a company’s ability to repay new and existing short-term debt. The higher the liquidity ratio, the larger the margin of safety to cover short-term debts. One question this pose is “what is a high ratio?”. Ratios are only meaningful when compared to the same ratio over time or compared to similar companies. Is it deteriorating or improving? Is it better / more liquid than its peers?
There are three primary types of liquidity ratios used in financial analysis:
Let’s look at each of these ratios in more detail:
The cash ratio is the most conservative liquidity ratio. It measures only cash and cash equivalents against current liabilities. Cash equivalents refer to assets that can be quickly converted into cash, typically within 90 days or less. This includes treasury bills, short-term certificates of deposit, and marketable securities.
(Cash + Cash Equivalents) / Current Liabilities
If cash / current liabilities >1, then the company can cover all its liabilities out of its existing cash reserves.
A higher cash ratio indicates a greater ability to pay off short-term obligations without needing to liquidate other assets, wait for customers to pay their invoices, or take on new loans. However, holding excessive cash can also mean a company is not maximizing its investment opportunities.
Also known as the ‘acid-test’ ratio, the quick ratio measures a company’s capacity to pay current liabilities without needing to sell inventory or get additional financing. It provides a more conservative view of liquidity position than the current ratio by excluding inventory from current assets. This is particularly relevant for a manufacturing company where, perhaps, much of the inventory is in the form of Raw Materials, or Work-in-Progress, in which case the company has to work through the entire operating cycle before that inventory can be sold. And then the company, if selling on credit terms, has to wait even longer to collect the cash from its customers. So, it is conservative to ignore inventories.
(Current Assets – Inventory) / Current Liabilities
The quick ratio focuses on assets that can be most readily converted to cash, which includes cash equivalents, marketable securities, and accounts receivable. A higher ratio indicates greater liquidity and lower liquidity risk.
The current ratio compares all current assets to current liabilities and is the broadest liquidity ratio. Current assets include cash, inventory, accounts receivable, and other assets that can be converted to cash within one year.
Current Assets / Current Liabilities
This ratio provides the most comprehensive assessment of a company’s ability to cover short-term obligations with its liquid assets. A relatively high current ratio indicates good short-term financial health while a low ratio may indicate greater liquidity problems.
Each of the three primary liquidity ratios provides a slightly different perspective on a company’s financial health. Generally, the following guidelines can be used when interpreting liquidity ratio results:
However, liquidity ratios should also be compared to industry peers and trends over time to get a better gauge of appropriate levels. The optimal current, quick, and cash ratios vary across different industries.
For illustration, here are some sector medians for liquidity ratios for public companies in the US:
Manufacturing: | Retail: | Transport & Utilities: | |
Cash ratio | 1.26 | 0.32 | 0.24 |
Quick ratio | 1.55 | 0.61 | 0.75 |
Current ratio | 2.88 | 1.27 | 1.08 |
Along with assessing liquidity, financial analysts also examine liquidity ratios trends over time and compare ratio values to industry benchmarks. This provides a more in-depth evaluation of financial health.
Key aspects to analyse include:
Unusual fluctuations or divergence from industry norms requires further investigation into the underlying drivers and factors affecting liquidity.
Here is an extract from the 2023 interim financial statements of Sainsbury’s plc, the UK supermarket chain which also has a financial services division:
Cash ratio = Cash / Total Current Liabilities = 2,067/11,594 = 0.18, (prior year 0.14)
Quick ratio = Current Assets excluding inventories / Total Current Liabilities = (8,389 – 2,187)/ 11,594 = 0.535 (prior year 0.536)
Current ratio = Total Current Assets / Total Current Liabilities = 8,389 / 11,594 = 0.724 (prior year 0.70)
The ratios might look ‘low’ compared to the average corporate, but with such a rapid cash conversion cycle, you will find that supermarkets liquidity is low compared to other sectors.
Also note that the ratios are in line with, or slightly improved, compared to 2022. This is a good sign – the business is stable in its liquidity position, and it has not caused problems in the past.
The other thing you might want to do here is compared to peers, but before doing so you would probably want to remove the Financial Services assets and liabilities as this is a different business operation. Including this will give a ‘blended’ ratio that makes it harder compared to other supermarkets.
Economic cycles significantly influence the financial performance of companies, and liquidity ratios are no exception. You can expect companies to have volatile ratios during economic swings,
During growth phases, companies have more cash and receivables, enhancing their ability to cover short-term liabilities. Conversely, in recession periods, sales and cash flow may decline, putting pressure on liquidity ratios. Companies might face challenges in meeting their short-term obligations, leading to lower liquidity ratios.
Liquidity ratios hold particular importance for small businesses, which often operate with tighter cash flows and limited access to credit compared to larger corporations.
For small businesses, maintaining a healthy liquidity ratio is crucial for ensuring operational stability and financial flexibility. A higher liquidity ratio generally indicates that a small business has enough liquid assets to cover its short-term liabilities, which is vital for sustaining operations, especially in times of financial uncertainty or slow business periods.
However, it’s important for small businesses to balance liquidity with efficiency. Excessive liquidity might mean that resources are not being utilized effectively for growth opportunities. Therefore, small business owners must carefully manage their assets and liabilities to maintain optimal liquidity levels that support both short-term stability and long-term growth.
Liquidity ratios have many practical uses for assessing real companies:
For example, let’s say a company has $100,000 in cash, $200,000 of accounts receivable, $250,000 in inventory, and $150,000 in current liabilities. Its liquidity ratios would be:
This demonstrates how the current and quick ratios of this hypothetical company indicate good short-term liquidity. However, the low cash ratio highlights how it may run into trouble covering liabilities with only its cash on hand. Analysing all three ratios together paints a more complete picture of liquidity.
Evaluating liquidity through current, quick, and cash ratios provides vital insights into a company’s financial health and flexibility. Assessing liquidity trends over time and against competitors allows stakeholders to identify improving or deteriorating liquidity. With a comprehensive understanding of these fundamental ratios, financial analysts and managers can better monitor short-term financial performance.
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]]>The post Time Value of Money (TVM): Examples, Relevant Formulas and Interpretation appeared first on Capital City Training Ltd.
]]>Time Value of Money (TVM) is a core corporate finance concept that refers to the principle that money available now is worth more than the same amount in the future, due to its potential earning capacity today. The TVM concept underlies all calculations and decisions involving time and interest rates in both business and personal finance. Understanding TVM is crucial for corporate finance professionals and investors to properly evaluate cash flows that occur at different points in time.
Concept | Key Takeaways |
Time Value of Money (TVM) | – Money available earlier is worth more than the same amount later due to earning capacity.
– TVM underlies calculations/decisions involving time and interest rates. – Critical concept in corporate finance and investing. |
TVM Calculations | – Present Value (PV)
– Future Value (FV) – Net Present Value (NPV) – Internal Rate of Return (IRR) |
Importance of TVM | – Enables comparison of cash flows over time.
– Evaluates long-term projects. – Determines if investments have positive value. |
TVM and Inflation | – Inflation reduces purchasing power over time.
– Use real interest rates and cash flows to account for inflation. |
Applications of TVM | – Capital budgeting, valuation, stocks, bonds, risk management, retirement planning. |
Advanced Concepts | – Compounding periods impact returns.
– Continuous compounding used in certain models. |
The time value of money concept can be seen more clearly when looking at the formula for future value:
FV = PV (1+r)n
Where:
This formula calculates how an amount of money today (PV) can earn interest over time at a specified rate, resulting in a future value (FV) amount. The longer the time period and higher the interest rate, the higher the future value.
For example, $100 invested today at an annual interest rate of 5% for 10 years would result in a future value of $162.89.
This demonstrates that $100 today is worth more than $100 ten years later, because the money today can be invested to start earning interest immediately and be worth more in ten years time.
There are four key calculations used in corporate finance where the TVM concept is utilised:
Understanding the time value of money concept is crucial in corporate finance for several reasons:
In summary, TVM is a fundamental corporate finance concept underlying many analyses and decisions. Managers need a firm grasp of TVM to make sound long-term financial choices and properly value potential investment opportunities.
Inflation, or the tendency for the prices of goods/services to increase over time, impacts the time value of money. As inflation rises, the purchasing power of money decreases.
To account for inflation, calculations involving the TVM concept may use a real interest rate alongside real cash flows. The real rate is the nominal interest rate minus the inflation rate, whilst real cash flows will also exclude any inflationary impact. Being consistent with type of rate used and the cash flows used ensures TVM calculations reflect the real purchasing power of the cash flows over time. This is crucial for obtaining an accurate picture of investment worth and returns.
For example, with 5% inflation and 6% nominal interest rate, a 1% real interest rate can be used in TVM based calculations alongside cash flows that have been adjusted to exclude the impact of inflations. Failing to account for inflation consistently can lead to poor financial modelling and uneconomic investment decisions.
Time value of money has many applications in corporate finance:
Overall, time value of money concepts are commonly applied in corporate financial modelling, valuation, risk management, and long-term decision making.
The Time Value of Money calculations often vary based on the frequency of compounding. Whether interest is compounded annually, semi-annually, quarterly, or monthly, it significantly impacts the final amount. For example, £1,000 invested at an annual interest rate of 20% compounded semi-annually (i.e. 10% every six months) will yield a different value than if it were compounded annually. This is because more frequent compounding periods result in interest being calculated on interest more often.
A more complex extension of the above concept is continuous compounding, where interest is calculated and added to the principal at every possible instant. The formula for continuous compounding is FV = PV * e^(rt), where e is the base of the natural logarithm, r is the annual interest rate, and t is the time in years. This concept is particularly relevant in certain financial models and theoretical scenarios.
Here are some real-world examples that demonstrate the time value of money principle:
In summary, the time value of money is universally applicable across finance. Corporations, governments, financial institutions, and individuals all leverage the power of TVM in modelling, valuation, markets, and decision making. A thorough understanding of this concept is essential for all finance professionals and managers.
To learn more about Compound Annual Growth Rates and other financial metrics, take our Financial Maths Bootcamp course.
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]]>The post Net Present Value (NPV) Explained: Definitions, Formula and Examples appeared first on Capital City Training Ltd.
]]>Net present value (NPV) is a core concept in corporate finance and investment analysis. It is a project / investments appraisal technique that is considered to be fundamentally the most robust, and consistent with the concept of enhancing shareholder value in investment appraisal. By calculating a NPV, companies can analyse the profitability of projects or investments whilst taking the time value of money (TVM) into account. Some investment appraisal methods fall short by ignoring TVM – for example the Payback Period.
The NPV calculation helps determine if a project will result in a net positive once allowing for the cost of capital invested in the project – thus assisting with making good investment decisions.
Key Takeaway | Description |
Definition | NPV is the difference between the present value of cash inflows and outflows over time. It accounts for the time value of money. |
Formula | NPV = ∑ Present Value of Cash Flows over n time periods |
Positive vs Negative NPV | Positive NPV indicates value creation. Negative NPV indicates value destruction. |
Uses | Evaluating investments, capital projects, acquisitions, capacity expansion, asset purchases, product pricing. |
Excel Calculation | Use the NPV function, entering discount rate and cash flows as inputs. |
Annuity NPV | Can calculate NPV of equal cash flows (annuity) using an annuity factor. |
Limitations | Dependent on accuracy of cash flow estimates. Does not remove all uncertainty. |
Best Practices | Use NPV along with other metrics like IRR and payback period for full analysis. |
Net present value, or NPV, is defined as the difference between the present value of cash inflows and the present value of cash outflows over a period of time. It compares the present value of cash flows at any point in time relating to an investment project, taking required returns (%) into account. The NPV calculation uses a discount rate to bring future cash flows back to present day dollars. The discount rate is commonly taken as the Weighted Average Cost of Capital (WACC) for the business – i.e. what is the average cost of funding our business, taking the cost of debt and the required return on equity into account?
A positive NPV indicates projected value-added on the investment, over and above the cost of capital. A negative NPV indicates value-destruction, or a project that does not generate sufficient returns for investors. To clarify, a negative NPV does NOT necessarily mean a project isn’t profitable: it means that it is not generating sufficient returns to satisfy the expected returns of investors.
The formula for calculating NPV is:
NPV = Present Value of Cash Inflows – Present Value of Cash Outflows
Or
NPV = ∑ Present Value of Cash Flows over n time periods
Where:
To find the present value of each cash flow, the formula is:
Present Value = Cash flow * Discount factor
Where the Discount Factor is (1 + discount rate) ^ n
For example, if the cash flow in year 1 is £100, and the discount rate is 5%, the present value of the year 1 cash flow is:
Present Value = £100 * (1 + 0.05)^1 = £100 / 1.05 = £95.24
This brings the £100 cash flow back to today’s dollars, accounting for the 5% discount rate. Doing this calculation for each cash flow and summing them gives you the NPV.
NPV is easy to calculate in Excel using the =NPV function. The inputs are:
Be careful about the way this function works when selecting cells referring to the project cash flows. The NPV function will discount ALL selected cash flows and assumes the first cash flow in the series is 1 year after the start of the project – so make sure not to include the initial investments in the selected data for the NPV function. An illustration will help.
For example, take a project with an initial investment of £1000, then annual cash flows of +£300, +£500, +£650, +£700 respectively. The company has a cost of capital of 8%
As you can see, the resulting NPV is £737, and note that the initial investment of £1000 is NOT included in the NPV function but is taken off at the end – we don’t want to discount the initial investments as it is already a present value!
Many analysts prefer to show the discount factors separately, to ensure transparency in their calculations: the same example giving us:
NPV has many practical applications in corporate finance and investment analysis:
Essentially, whenever a business is allocating capital, NPV helps management make better financial decisions.
Annuities are a series of equal cash flows made over a number of periods. The NPV of an annuity can be calculated using an annuity factor:
NPV of Annuity = (Annual Annuity Amount) x (Annuity Factor)
The annuity factor is based on the number of periods and discount rate, and tables to look up the factor are readily available. Having said that, Excel is much more convenient!
Practical applications of discounting annuities include bond valuation and determining the present value of pension obligations.
Some common misconceptions about NPV include:
NPV is an important and useful calculation, but should be applied carefully with other tools to support strategic financial decisions.
A leading energy company was evaluating an investment in a large-scale solar power project. The project required an initial investment of £500 million with expected annual cash inflows from energy sales of around £80 million for 20 years. Using a discount rate of 8%, which reflected the project’s risk and the company’s cost of capital, the NPV calculation showed a positive value, indicating that the project was a viable investment. This analysis played a crucial role in the company’s decision to proceed with the project.
A pharmaceutical company considered investing in the research and development (R&D) of a new drug. The project involved an initial investment of £200 million and promised potential cash inflows from drug sales after regulatory approval. Despite high initial costs and the uncertainty of drug approval, the NPV analysis, which incorporated various scenarios of success and failure, showed a significantly positive NPV for the most likely scenario. This gave the company confidence to invest in the R&D project.
A multinational corporation was considering the acquisition of a smaller competitor. The acquisition was priced at £1 billion, with expected synergies and cost savings leading to additional annual cash inflows. By calculating the NPV of the projected cash flows, using a discount rate that accounted for the acquisition’s risks and financing costs, the corporation determined that the acquisition would have a positive NPV, leading to the decision to go ahead with the purchase.
In summary, NPV is a crucial metric in corporate finance that compares the present value of cash inflows to outflows to analyse profitability. The NPV calculation requires estimating cash flows, choosing a discount rate, and determining present values. It has widespread applications in investment analysis and drives many capital budgeting and resource allocation decisions. While a powerful tool, NPV should be complemented with other metrics and applied with care to ensure sound financial decisions.
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]]>The post Buy-Side vs Sell-Side appeared first on Capital City Training Ltd.
]]>The expressions “Buy-side” and “sell-side” are a commonly-used piece of market shorthand to describe the kind of business a finance firm is involved in. The main activity of the financial markets is originating securities – bonds, shares and instruments like Syndicated loans – and distributing them to investors. The originators are the “Sell-Side”, the buyers, the “Buy-Side”.
The financial markets involve many more activities, mergers and acquisition advice, trading of securities once issued, the trading of futures, options and derivatives and currencies, but this origination and distribution is the core.
Origination involves several different groups in an investment firm:
Aspect | Buy-side | Sell-side |
Definition | Institutions buying securities for their own account or in their role as a fund-manager. | Firms involved in originating, promoting, and selling securities. |
Examples | Mutual funds, pension funds, insurance companies, hedge funds, State superannuation funds, Sovereign wealth funds. | Investment banks, stock-broking firms, securities firms. |
Primary Goal | To invest own money or funds on behalf of clients to generate returns. | Earn fee income for arranging and placing securities; providing research; advisory services. Make profits from market-making |
Roles & Responsibilities | Asset management, research, determining assets to buy/sell, portfolio management. | Client coverage, origination, broking, sales & trading, equity research. |
Career Pathways | Specialized roles, starting often on sell-side as researcher in a specific asset class, Quantitative research or supporting a portfolio manager, progressing to portfolio manager. | Diverse roles in different “silos”: coverage, origination in ECM or DCM, credit, syndicate, sales and trading. Starting as analysts, progressing to senior positions in banking, trading, or research. |
Interaction | Uses sell-side services for research, executing trades, leveraging resources. | Provides research, trading services to buy-side, aims for commissions, league rankings, and revenue. |
Real-World Applications | Using sell-side research reports for investment decisions, executing trades. | Offering IPO advisory, M&A due diligence, valuation advice, and negotiation assistance. |
Key Example | Pension funds, hedge funds investing based on research, executing through trading desks | Investment banks like Goldman Sachs providing research, trading services. |
The buy-side refers to institutions that buy securities for their own account or as third-party fund-managers. Some of the main buy-side entities include mutual funds, pension funds, insurance companies, State superannuation funds and hedge funds. Their primary goal is to invest money on behalf of their clients and generate returns by making investments in various securities like stocks, bonds, derivatives etc.
Conversely, the sell-side entities are involved in creating, promoting and selling those securities to the buy-side. Investment banks, brokerage firms, and securities firms are examples of sell-side institutions. Their main role is to connect buyers and sellers, distribute securities, provide research and advisory services, provide liquidity to investors through their trading capabilities.
In essence, the buy-side buys and manages securities while the sell-side originates and sells those securities and related derivatives.
On the buy-side, the main roles involve asset management and research. Portfolio managers and analysts conduct research on securities to identify investment opportunities. They determine which assets to buy, hold or sell to construct portfolios that aim to maximize returns for their clients. Traders on the buy-side then execute the trades to implement the investment decisions.
The sell-side connects the buyers and sellers to facilitate transactions. Key roles on the sell-side include investment bankers who provide capital raising and M&A advisory services. Brokerage and sales traders interact with buy-side traders to execute orders and manage client relationships. Equity research analysts publish research reports on securities to provide insights and recommendations to the buy-side.
On the buy-side, roles tend to be more specialized. Many portfolio managers and analysts start their careers on the sell-side before transitioning. The career path often involves interning at a mutual fund or hedge fund, then becoming a junior analyst, and working up to a portfolio manager role. Traders also begin as execution traders before managing their own book.
The sell-side offers diverse roles from investment banking, trading, research, and sales. New graduates often start in analyst programs or internships. The career path usually involves progressing from analyst to associate, vice president, director, and managing director roles. Traders also progress from junior to senior trader positions.
There is significant interaction between the two sides. Sell-side firms pitch ideas and provide research to buy-side clients. Traders collaborate to execute orders and negotiate prices. Investment bankers interact with buy-side clients for deals like IPOs, follow-on offerings, and M&A.
The sell-side aims to provide services that are valuable to the buy-side in exchange for commissions and fees. Having buy-side clients is crucial for the sell-side in terms of league table rankings, bonuses, and overall revenue. The buy-side leverages the sell-side’s resources to identify opportunities and access liquidity.
A common example is a pension fund portfolio manager using research reports from a sell-side firm to inform investment decisions about investing in an IPO or in shares already in issue. The portfolio manager may then execute trades through the sell-side’s trading desk to implement their strategy.
In investment banking, a private company looking to go public would hire an investment bank for advisory services on the IPO. The process of going public is lengthy and labour intensive and is a complex project management exercise. The private company taps into the bank’s expertise on legal, marketing and pricing aspects to maximize value in the offering. The issuer also mobilises substantial specialised resources in preparing research, documentation and in distributing the securities.
For M&A, a private equity firm (buy-side) acquiring a company may hire an investment bank (sell-side) to underwrite and distribute syndicated loans or bonds to finance the acquisition. This leverages the bank’s origination and distribution resources.
In this case the bank might offer the following range of services:
In summary, the buy-side and sell-side play complementary roles in financial markets. With the buy-side focused on managing investments and the sell-side on facilitating transactions, they interact extensively to enable efficient markets. Though differing in their roles, both are essential in the functioning of corporate finance and global financial markets.
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]]>The post Guide to Financial Statements appeared first on Capital City Training Ltd.
]]>Financial Statements are the single most valuable source of financial information on a business – providing valuable insights into a company’s financial health and performance.
As a manager, investor, shareholder, employee, supplier, customer, government, or a creditor, having the ability to analyse and interpret financial statements is a critical skill for making informed decisions about a business.
This guide will walk through the key components of 3 key financial statements at a high level, including:
We’ll also mention briefly the role of the ‘other two’ – that is the Statement of Changes in Equity and the Statement of Comprehensive Income. In the US, the Statement of Retained Earnings is also often referred to, and we will explain where that fits in. We’ll also look at some financial statement analysis techniques – without crunching numbers.
With the right knowledge and techniques, financial statements can reveal the underlying story of a company’s success – or otherwise!
Financial Statement | Purpose | Key Takeaways |
Balance Sheet | Shows assets, liabilities, and equity at a point in time | – Assesses liquidity, leverage, working capital, net asset value
– Analyze composition and trends in assets, liabilities, equity |
Income Statement | Shows revenues, expenses, and profit/loss over a period | – Analyze revenue growth, profit margins, expense trends
– Compare to industry and past performance – Identify variances and underlying causes |
Cash Flow Statement | Shows sources/uses of cash during a period | – Analyze cash flow trends and categories (operations, investing, financing)
– Assess cash flow vs. net income – Evaluate cash flow sustainability |
Statement of Changes in Equity | Details changes in equity accounts | – Analyze drivers of equity changes (earnings, dividends, share issuance etc.) |
Statement of Comprehensive Income | Shows profit/loss and other comprehensive income | – Assess impact of items not included in net income (foreign currency adjustments, hedges etc.) |
The first step is to understand the components of financial statements and their purpose. The three primary financial statements are:
While these core statements are prepared using standardized accounting principles to enable comparability between companies and across reporting periods, it’s important to note that variations in accounting policies and interpretations can still lead to differences. Investors should be aware that these variations can affect the direct comparability of financial statements across different companies, making it crucial to understand the specific accounting practices employed.
Financial statements are rich with data, yet extracting meaningful insights requires not only practice but also a deep understanding of the industry context and prevailing economic conditions. It’s essential to analyse these statements within the broader industry and economic framework, as sector-specific factors and macroeconomic trends can significantly influence financial performance and outlook.
Focus on year-over-year trends and be wary of relying too much on results from a single year, which may not be indicative of longer-term trends. Also, read the accompanying footnotes which explain policies and provide additional details that may significantly impact the interpretation of the financial statements.
The balance sheet provides the base for financial analysis. At the highest level, it is simply an ‘equation’:
Assets = Liabilities + Equity
Or:
Assets – Liabilities = Equity
Broken down, these are:
Of course, the balance sheet presented in the financial statements shows a lot more detail than this simple equation, and the assets, liabilities and equity are broken down into component elements, the details of which are further explained in the ‘Notes to the Accounts’.
The Assets section of the balance sheet has categories for Non-Current Assets and Current Assets. Current assets are resources that are cash, near cash, or expected to be converted into cash in the short term (less than one year). This includes cash, accounts receivable, inventory, and short-term investments. Non-current assets are long-term resources like plant and machinery, IT equipment, long-term investments, and perhaps intangible assets like brands, licences. They are assets that are invested in for the long-term (more than just the current accounting period)
Similar to the categorisation of assets, liabilities are split into two headings:
Comprised of paid-in capital from stock issuance and accumulated earnings from profitable operations (or ‘retained earnings’ meaning it is profit reinvested in the business assets and not paid out as dividends).
Financial analysts will use a balance sheet to understand the company’s:
Intangible assets like intellectual property, brand value, and customer relationships can be significant drivers of a company’s value. However, these assets are often not captured in traditional balance sheet metrics. This is because of strict accounting rules relating to ‘self-generated’ assets. Analysing these assets requires a qualitative (and thus subjective) approach, considering factors like brand strength, market position, and customer loyalty, which can provide a more complete picture of the company’s assets.
While the balance sheet shows a snapshot in time of assets owned and liabilities due, the income statement details performance of the business over a set (usually 1 year) period. It outlines revenues earned and expenses incurred to arrive at net profit or loss for the company over the reporting period. Generally, income statements span one quarter or one year. Note that revenue ‘earned’, and expenses ‘incurred’ doesn’t necessarily mean the cash is received or paid. Hence the need for the Cash Flow Statement, to identify those differences.
Starting at the top line of the P&L and working down the statement, the order of items is consistently presented. The top line shows operating revenues – those earned from the company’s core business activities (delivering services or selling goods). They do not include earnings from selling non-current assets, for example, or investment income.
Common expenses include cost of goods sold, sales and marketing costs, research and development costs, and general and administrative expenses.
Revenue less Cost of Goods Sold gives what is known as Gross Profit. Note that Cost of Goods Sold is named as such for a very good reason! – it is only the cost of the goods sold to customers that is included, not the cost of what has been purchased in the period. Then subtracting other operating expenses (sales, marketing, distribution) from revenues gives operating profit.
Then finance-and tax related items are added / deducted to arrive at the final net profit (also ‘net income’) or loss.
Using the income statement, analysts and investors will typically:
This will provide some insight as to whether the business is improving, deteriorating and whether management strategy is working to improve returns to shareholders
Non-recurring items, which are unusual and infrequent in nature, can significantly impact a company’s income statement. It’s important to identify and understand these items, as they can distort the true operating performance. Adjusting for extraordinary items provides a clearer picture of a company’s recurring profitability and operational efficiency. Adjusting for these, we essentially remove ‘noise’ from our analysis. Of course, you cannot ignore them altogether as they can be ‘red flags’ that require further interpretation or analysis. But by removing them it does help clarify the picture of underlying performance. We often talk about underlying earnings, or underlying EBITDA.
While income statements show profitability – based on the ‘accruals’ concept, cash flow statements depict actual cash generated and used. Profit does not equal net cash flow for a number of reasons. For example, you may spend cash on inventory, but the inventory only gets recognised in the P&L when sold (‘Cost of Goods Sold’). There is also consideration of non-cash expenses like depreciation. Cash flow statements account for these disparities.
Cash flows arise from three activities – operations, investing, and financing, and these are the three sub-headings in the Cash Flow Statement.
Just this categorisation of cash flows makes for tremendous value-added in analysing liquidity in a business. For example, you can see how much cash is generated purely from operations. A business’ cash balance may have increased from one year to the next, but is it organic, self-generated or is it due to borrowings or selling off valuable assets?
On a cash flow statement, we can:
Healthy companies generate sufficient operating cash flow to fund expansion and dividends. Rapidly growing companies will generate healthy operating profit, but the incremental investment in working capital and fixed assets may be a significant drain on cash. The cash flow statement will highlight these points quickly and clearly. Beware dependency on external financing which can be difficult to secure and isn’t necessarily appropriate.
In cash flow analysis, distinguishing between operating and non-operating cash flows is crucial. Operating cash flows arise from a company’s primary business activities, while non-operating cash flows relate to financing and investing activities. This distinction helps in assessing the sustainability of cash flows and the company’s ability to generate cash from its core operations.
Finally, a few points around the other elements of financial statements – firstly the Statement of Changes in Equity. Equity is typically a significant number in the balance sheet. Companies will normally have significantly more equity than debt – but there are always exceptions (such as banks!) The Statement of Changes in Equity provides additional details on changes to this equity account over the reporting period. As well as the impact of profits on Equity (retained earnings), it shows other details that are not part of the P&L It shows, as main points:
The overall statement will help us analyse what has caused changes in shareholders’ equity – is the company profitable? Issuing new shares? Buying back stock? Paying dividends? The statement provides greater clarity into these dynamics.
Shareholders’ equity plays a critical role in company valuation. It represents the residual interest in the assets of a company after deducting liabilities. In valuation, equity is often analysed in conjunction with earnings and cash flow metrics to determine a company’s worth. However, do note that the number in the Balance Sheet is not the market value of equity, it is a historic value based on capital paid in, net income (earnings) and dividends paid out. However, a deep dive into the components of shareholders’ equity can reveal insights into a company’s financial health and growth potential.
The Statement of Comprehensive Income is like a 2^{nd} P&L. It shows net income from the P&L, but then adds into the mix any other gains/losses to equity earnings that are not considered to be part of the core business / financing of the business and are as yet to be crystallised (i.e. they aren’t at a fixed value yet!). These items are called Other Comprehensive Income (OCI).
A couple of examples of Other Comprehensive Income might help.
More sophisticated analysis involves calculating financial ratios for cross-company comparisons and examining statement components. Useful ratios include profitability, liquidity, leverage, valuation, and efficiency ratios. Component analysis examines accounts like receivables, inventory, debt, capital expenditures, and research and development expense.
Percent change analysis tracks line items across reporting periods to identify large swings. Trend analysis examines increases or decreases over consecutive periods. Common-size analysis scales statements to make comparisons easier, like expressing all income statement accounts as a percent of total revenue. Ratio analysis measures relationships between statement accounts, like the current or quick ratios for liquidity.
Financial statement analysis is a cornerstone in making informed investment decisions. By dissecting the balance sheet, income statement, and cash flow statement, investors can gauge a company’s financial health, growth prospects, and risk profile. This analysis, combined with an understanding of market conditions and industry trends, can guide investors in identifying undervalued or overvalued stocks.
People who are new to reading financial statements are often looking for a pro-forma framework to crunch numbers and tell them what they need to look at. The thing is, every business is different and crunching numbers won’t give you answers, but the ratios will tell you where to ask further questions and seek explanations.
One rule of thumb for generating the analysis is to look at a line item in the P&L, Balance Sheet, or Cash flow statement, and ask yourself:
For example, look at the Revenue in the P&L and consider:
All numbers in the financials have a ‘linked’ corresponding number to help put it into context, so you need to know enough about financial statements to find the other number(s) and see if they stack up. It’s not a formula, it’s logic and understanding.
To find out more about interpreting and analysing financial statements, take a look at Capital City Training’s eLearning courses: Finance for the Non-Financial Manager and Financial Accounting & Analysis.
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]]>The post Bond Duration Guide: Definitions, Concepts and Examples appeared first on Capital City Training Ltd.
]]>Bond duration is a key concept in investment management and corporate finance that allows investors and financial professionals to measure the sensitivity of a bond’s price to changes in interest rates. Understanding duration is crucial for assessing the amount of risk associated with a bond investment and for structuring bond portfolios to achieve specific investment objectives.
Concept | Description |
Bond Duration | Measures the sensitivity of a bond’s price to changes in interest rates, assessing risk and guiding portfolio structure. |
Types of Duration | Macaulay Duration: Weighted average time until a bondholder receives cash flows. Unit of measurement: time (years)
Modified Duration: Measures bond price sensitivity to interest rate changes across the yield curve (i.e. a shift in rates for all maturities – see Key Rate Duration below, in contrast) Unit of measurement: % Effective Duration: For bonds with options, adjusts for potential changes in cash flows. Dollar Duration: Measures dollar change in bond price for a percentage interest rate change. PV01: is a sub-set of Dollar Duration, measuring the price change of a bond resulting from a 1bp (0.01%) change in rates Key Rate Duration: Measures sensitivity to yield curve changes at specific maturities, rather than all maturities |
Calculating Duration | Utilizes various formulas to determine different types of durations – see below for an Excel example |
What is a ‘Good’ Bond Duration | This varies depending upon the context. Short durations are preferred in rising interest rate environments; longer durations beneficial when rates are expected to fall. |
Short-term Bonds and Duration | Short-term bonds have a maturity of 5 years or less and are less sensitive to interest rate changes but offer lower yields. |
Duration Risk | Higher duration gives higher interest rate sensitivity, all other things being equal. This can be managed through diversified bond portfolios and hedging strategies. |
Practical Applications | Used to compare interest rate risks, match bond portfolio durations with liabilities, employ bond immunisation strategies, assess bond yields versus risks, and hedge against duration risk. |
Examples for Calculation | Below, you will find examples on the calculation of Macauley Duration and Modified Duration. |
Bond duration, in its simplest sense, measures the average time period it will take, in years, for an investor to be repaid the bond’s price by the bond’s total cash flows. In other words, duration is the weighted average life of a bond’s cash flows, taking the time value of money into account.
The amazing thing is that this same measure of duration Is very close to being the % change in a bond’s price resulting from a 100bp (1%) change in yield on that bond. A higher duration means the bond’s price is more sensitive to yield changes, whilst a lower duration means the bond’s price is less sensitive.
Understanding the various types of bond duration is crucial for investors seeking to manage the interest rate risk inherent in fixed-income investments. Here are the most commonly used duration types:
Macaulay Duration, named after Frederick Macaulay who introduced the concept, is the weighted average time until a bondholder receives the bond’s cash flows. It is a fundamental measure used to determine the sensitivity of a bond’s price to interest rate changes. The Macaulay Duration is calculated by summing the present values of all cash flows, each multiplied by the time until receipt, and then dividing by the current bond price.
Modified Duration is a derivative of Macaulay Duration and provides a direct measure of a bond’s price sensitivity to interest rate changes. It is calculated by dividing the Macaulay Duration by one plus the yield to maturity per period. This adjustment transforms the Macaulay Duration into an elasticity measure, estimating the percentage change in price for a 1% change in yield.
Effective Duration is particularly relevant for bonds with embedded options, like callable or putable bonds. It considers potential changes in cash flows due to these options. Effective Duration is calculated under the assumption that the bond’s cash flows may change as interest rates change, providing a more accurate measure of interest rate risk for these types of bonds.
Dollar Duration measures the actual dollar change in a bond’s price for a one percentage point change in interest rates. It is the product of a bond’s modified duration and its price. This metric is useful for investors who wish to understand the change in their portfolio’s value in monetary terms, rather than in percentage or years.
Key Rate Duration assesses a bond’s sensitivity to changes in the yield curve at specific maturities. For example, it can measure the change in a bond’s price in response to a 1% change in the yield for 5-year Treasury bonds. This type of duration is important for gauging the impact of non-parallel shifts in the yield curve.
The most commonly used formula for calculating bond duration is the Macaulay duration:
Macaulay Duration = (t*CF)/[(1+y)^t]
Where:
This formula sums the present values of each individual cash flow, weighted by the timing of the cash flow. The result is expressed in years.
Modified Duration is equal to Macaulay Duration divided by one plus the yield to maturity divided by the number of compounding periods per year:
Modified Duration = Macaulay Duration / (1 + (Yield to Maturity / Number of Compounding Periods per Year))
There is no intuitive link here, but some simple calculus on a bond price expression could get us there. Here’s we’ll spare you the pain of going back to school with differentiation but get in touch with us and we’ll send you the simple proof!
Key Rate Duration for a specific maturity is calculated by taking the percentage change in the bond’s price and dividing it by a small change in the yield for that maturity.
Key Rate Duration at specific maturity = (Change in Price / Initial Price) / Change in Yield at that Maturity
Dollar Duration is calculated by multiplying the Modified Duration by the bond’s price and then by 0.01:
Dollar Duration = Modified Duration * Bond Price * 0.01
“Good” bond duration depends on the investment context.
For example, in a falling rate environment, bond prices will rise. Wouldn’t it be nice to invest in bonds that responded more to that fall in rate? That would be long Duration bonds! The converse is true in a rising rate environment. What you will find is that portfolio managers will shorten the duration of their portfolios in anticipation of rates rising.
Have a look at a bond fund fact sheet (you can find one at many investment manager websites – e.g. BlackRock) and see how the duration of the portfolio compares to the benchmark – it is likely to be shown, but not always.
By ‘short-term’ we commonly mean bonds with a maturity of 5 years or less. But there is no fixed interpretation. A bond can never have Duration any longer than its maturity. For a coupon-paying bond, the Duration will always be less than its maturity.
So, as well as shorter maturity, short-term bonds will have lower duration than any longer-term bond, and thus be less risky than longer maturity bonds, as their prices are less sensitive to interest rate changes.
However, short duration bonds typically have lower yields compared to longer maturity bonds. So any given change in rates will have a proportionately larger impact.
Remember that Duration does not measure the likelihood of any change in rates, it purely measures the impact should rates change.
It is worth noting that, although short-term bonds have lower rate sensitivity, short term rates can be more volatile. Duration does not take into account the likelihood of rate movements – it is purely a measure of “if rates change, this tells you how sensitive your bond investment(s) is.
Duration indicates the interest rate risk inherent in a bond investment. Bonds with higher durations involve more risk, as their prices will fluctuate more widely with interest rate shifts.
Investors can manage duration risk by constructing a bond portfolio with an overall optimal duration fitting their risk tolerance and market outlook. This often involves holding bonds with a range of individual durations.
Duration risk can also be addressed through the use of bond futures, interest rate swaps, and other hedging strategies. Reducing a portfolio’s duration means reducing its sensitivity to the potentially negative impact of rising interest rates.
Understanding duration has several applications for fixed income investing:
Let’s look at some step-by-step examples of computing duration using the formulas discussed earlier:
Calculate the Macaulay duration of a 5-year bond with a 12% annual coupon rate and a $1,000 face value.
Assume the current market price is also $1,000 – what is the modified duration? Use this to estimate the change in value if rates increase by 50bp.
Then we can use this to determine the modified Duration (the % change in bond price, given a 100bp change in yield):
So, if rates increase by 50bp, from 12% to 12.5%, the approximate change in value is:
So the new price should be approximately $1000 – $36 = $964.
In fact, if we discount the bond cashflows at the new yield of 12.5% we get $982. This is quite some ‘rounding error’!
What you find is that, in fact, Duration is only a good measure of the change in value of the bond price for SLIGHT changes in rates.
This is because it measures sensitivity of the bond price at a single (current) yield. As soon as rates move, not only does the price change, but so does the Duration.
So to work out the true change in bond price we need firstly to measure Duration, then the rate of change of Duration as rates move! This ‘rate of change of Duration’ is known as Bond Convexity.
A 10-year semi-annual coupon bond has a 6% coupon rate and 8% yield to maturity. What is its approximate Macaulay duration?
These examples demonstrate how to calculate bond duration based on the timing and size of its cash flows. The duration metric provides critical insights for managing bond interest rate risk.
In summary, duration is a key tool for measuring interest rate risk, constructing bond portfolios, and implementing bond investing strategies. The accurate calculation and interpretation of duration can help investors reach their desired risk-return profile.
What are the three primary factors driving the Duration of a bond?
Well, take these illustrations:
So, remember, which bonds have higher duration?
Longer maturity
Lower coupon
Lower rate environments.
Start learning the core skills you’ll need in the world of investment banking with our free Investment Banking Fundamentals course, drawing in core modules from our wider course catalogue to get you started on a career in finance.
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]]>The post Derivatives, Swaps and Options: A Guide appeared first on Capital City Training Ltd.
]]>Derivatives are financial contracts that derive their value from an underlying asset or index – in fact, anything that has an objective, independent measure of value. They have become essential tools in corporate finance and risk management. Swaps, forwards, futures and options are common types of derivatives used by companies to hedge risks, but can also be used by traders to speculate on asset prices. This article provides an introduction to derivatives, swaps, and options, explaining key concepts and formulas used in valuing and applying these important financial instruments.
Aspect | Description | Types | Key Formulas/Concept |
Derivatives | Financial instruments deriving value from an underlying asset, used for hedging risks and speculation. | Futures, Options, Swaps, Forward Contracts | Derivative is a generic term that applies to all types of financial contracts that derive their value from some ‘underlying’ asset, index or event. |
Options | Give the holder the right, but not the obligation, to buy/sell the underlying asset at a specified price. | Call Options, Put Options | Black Scholes, Binomial Option Pricing |
Swaps | Contracts where two parties exchange financial instruments or payments. | Interest Rate, Currency, Commodity, Equity, Credit Default Swaps | Present value of future cash flows exchanged |
Forwards | Agreements to buy/sell an asset at a future date for an agreed price, not traded on exchanges. | Currency Forwards, Commodity Forwards | Forward price = Spot price x (1 + interest rate) ^ time |
Futures | Contracts to buy/sell an asset at a future date and price, traded on exchanges. | Commodity Futures | Mark-to-market based on daily settlement price |
As mentioned, derivatives are contracts that derive their value from the performance of an underlying financial asset, index, or other investment. Companies use derivatives to hedge risks and/or enhance returns, while speculators also trade derivatives to profit from price movements in the underlying asset – without having to purchase the underlying asset, and with the use of leverage. The value of a derivative contract is driven by the price of the underlying asset.
Some key features of derivatives:
Initial investment requirements for derivatives can vary. For instance, options often require a premium to be paid upfront, reflecting the cost of acquiring the right represented by the option. In contrast, some swaps might not necessitate an upfront payment, as their value is derived from the mutual obligations of the parties involved.
A forward contract is the simplest of derivatives to explain and the best place to start. It is an ‘over-the-counter’ agreement between two parties to fix the price upfront to buy or sell an asset at a specified future date. Forwards are negotiated between the parties ‘over the counter’ meaning there is no standardisation or the contracts – the terms are whatever is negotiated.
Forwards allow companies and investors to lock in prices and manage cash flow risks, but they can be used to speculate on price movements too. The most common forward contract – and the single biggest (by trading volume) derivative is the currency forward – used to trade / hedge currency prices i.e. exchange rates.
The simplest way to see how they work is by giving an illustration:
Note that the company isn’t trying to make a gain in doing this transaction – it’s not about speculation. The motivation is purely to eliminate market price risk.
Because the agreed rate might be less favourable than the market price turns out to be, the brokers will ask the company to pay a deposit, or ‘margin’ upfront, typically 5-10% of the contract value. Large corporates will often have credit lines with banks that mean they don’t have to pay the margin – but the bank will be taking on the risk of the company defaulting.
Futures are similar to forward contracts, but they are standardized contracts traded on regulated exchanges. Large companies commonly use commodity futures to hedge input costs, while investors speculate on price changes in the underlying asset to make a profit. For example, an airline operator may buy an oil futures contract to hedge the price of jet fuel (jet fuel prices are strongly correlated to the price of oil)
The way that these futures work is that the buyer (the airline operator) doesn’t actually want to take delivery of the oil, so it ‘closes out’ the trade at a later date by selling the contact back via the exchange, cancelling out its purchase obligation. If the price has risen, the airline operator will receive the price difference as cash. This ‘profit’ can be used to reduce the cost of its jet fuel, which is strongly correlated to oil prices.
Options are slightly more flexible than forwards or futures as they give the holder the right, but not the obligation, to buy (or sell) the underlying asset at a fixed price at a later date.
The option to buy is called a ‘Call Option’, whilst the right to sell is called a ‘Put Option’.
This optionality essentially means the company buying the option has the choice to either take the pre-agreed fixed price under the option agreement, or just walk away (‘abandon’ the option) and transact at the current market price, which might be more favourable. This flexibility doesn’t come for free – and buyers of options have to pay a premium upfront, like you would with an insurance contract.
The leverage effect in options is a significant aspect of their appeal and risk. A relatively small investment in the option’s premium can control a much larger value of the underlying asset. This leverage amplifies potential gains, but it also increases potential losses, making options a high-risk, high-reward investment.
Swaps are analogous to a series of forward contracts, extending over a longer time period. Forwards will have settlement dates going out not more than around 12 months, but Swaps can have lives of 20-30 years. Having said that, they are most commonly used to hedge interest rate risk on loans which have lives of 3-5 years. Other swaps include currency swaps, commodity swaps, equity swaps, and credit default swaps. Swaps allow companies to hedge different types of longer-term risks.
There are various formulas used to price different types of derivatives. But even the term ‘price’ needs clarifying. For a forward, future or swap, the price is the pre-agreed fixed rate quoted by the bank or their broker. Howeverm the ‘price’ of an option is the up-front premium to be paid to have the option to buy the underlying at the fixed rate. Slightly different. The key factors are:
Some key derivative pricing formulas:
Companies use derivatives like swaps, futures, and options to hedge risks as part of their risk management strategy. For example, an airline may utilize oil futures to lock in fuel costs and hedge against rising oil prices. A software firm could purchase currency put options to limit exchange rate risk.
Speculators aim to profit from derivatives trading based on their view of market movements. For instance, a fund manager may buy S&P 500 index call options in anticipation of rising stock prices. Swap rates can provide insight into market expectations of risks.
On the balance sheet, derivatives are presented at their fair value. Positive fair values are financial assets while negative values are financial liabilities. Fair values of derivatives fluctuate based on related market risks, and this can affect earnings. Companies must also meet regulatory requirements for reporting derivative instruments.
Leverage refers to the situation where the amount of capital required to trade a derivative contract is less than the market exposure it gives. For example, using our currency hedging example from earlier, where the company was expecting to receive $20,000.
Derivatives are powerful tools for risk management. Companies often use them to hedge against various risks, such as currency fluctuations, interest rate changes, and commodity price volatility, as already explained. For example, an importer might use currency forwards to hedge against the risk of currency depreciation. Understanding how to strategically use derivatives for risk management is key for corporate finance professionals.
Misuse of derivatives for hedging has cost of lot of money to companies in the past – have a quick search for Metallgesellschaft and see for yourself! Derivatives are not ‘dangerous’ in themselves unless they are in the hands of people who don’t understand them. The issue with using derivatives is that although they may hedge market price risk effectively, they can give exposure to other types of risk – notably liquidity and counterparty risk.
The regulatory landscape for derivatives has evolved significantly, especially following the financial crisis of 2008. Regulations now focus more on transparency, reporting requirements, and reducing systemic risk. This includes the mandatory clearing of certain derivative contracts through central counterparties (to address counterparty risk and to help with centralised data) and reporting trades to trade repositories. Staying abreast of these regulatory changes is vital for companies and investors involved in the derivatives market.
Let’s look at some exercises and examples to understand how derivatives like swaps, futures, and options work:
Futures Contract – A company enters into a futures contract to buy 10,000 barrels of oil for $80 per unit in 6 months. It plans on buying the equivalent volume in jet-fuel in 6 months time and the current price of Jet Fuel is $100/bl. When it comes to closing the futures contract, the price on the same contract has risen to $93/bl and Jet Fuel has risen to $119. What is the net settlement on the forward contract, and if applied to the Jet Fuel purchase, what is the net cost of the jet fuel?
Under the forward contract:
For the jet fuel, the cash price turns out to be $119/bl, but the company has gained $13/bl on the futures contract, so it’s net cost is only $106/bl equivalent. It didn’t manage to fully hedge the price increase in Jet Fuel, but remember there are other factors to consider. Most significantly, the company used Oil futures to hedge the price of Jet Fuel – known as a ‘proxy’ hedge. Jet Fuel futures are not so accessible in the market and Oil is considered to be a good proxy (due strong correlation in price movements). Although a strong correlation, the prices are not the same!
Option Payoff – An option to buy Stock XYZ has a strike price of $25. This is the fixed, agreed purchase price the option holder can buy the stock at. What are the possible payoffs at expiration if XYZ is trading at $20 and $30? The payoffs are the gain to the option holder. If there is not gain, they will not exercise their option and the payoff is zero!
If XYZ = $20, then option to buy the stock at $25 is worthless. The payoff would be zero.
If XYZ = $30; then the option to buy the stock at $25 has some intrinsic value – buying an asset worth $30 for only $25 means $5 of value. This $5 would be the pay-off under the option. This is an example of ‘cash settlement’ where rather than delivering the stock (worth $30), the option seller can just settle the difference between the stock value and the agreed price. $30-$25 = payoff $5.
Derivatives are invaluable but complex tools in current finance markets. Options, swaps, forwards and futures allow companies to hedge risks and enhance returns but only with informed usage. In the hands of the ignorant, they can be “financial weapons of mass destruction” (quote Warren Buffett). Just ask Robert Citron, Treasurer of Orange County, California! If you speak any French whatsoever, you’ll see the immediate irony there, but it’s true!
Speculators aim to profit from derivative trades based on market views. By understanding key concepts, valuation models, and risk interpretations, both corporate finance officers and investors can effectively leverage derivatives, like futures, swaps and options, in line with their objectives.
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