Chapter 6 — Business Finance And Arithmetic

Fig 1 — Educational Diagram: Introduction to Business Finance

What is Business Finance?
Business finance is the study of how a business acquires, manages and uses funds to achieve its objectives. It covers decisions about raising capital, investing in assets, managing day-to-day funds and distributing profits.

Objectives of Business Finance

• Ensure availability of funds when needed (liquidity).
• Acquire funds at minimum cost and optimum mix (cost-efficiency).
• Allocate funds to profitable projects (profitability).
• Maintain solvency and financial stability (safety).

Importance: Proper finance management helps a firm run smoothly, meet short-term obligations, expand operations, survive downturns and maximize owner wealth.

Major Financial Decisions

• Investment (capital budgeting): Which projects/assets to invest in.
• Financing: From where to raise funds (owners' funds, borrowings, or hybrids).
• Dividend: How much profit to distribute and how much to retain.

Sources of Business Finance

• Owned funds (owner's capital, retained earnings) — internal and permanent.
• Borrowed funds (bank loans, bonds, trade credit) — external, may be short or long term.
• Hybrid (preference shares, debentures) and institutional finance (venture capital).

Classification by Duration: Short-term (working capital), medium-term (term loans for equipment), long-term (equity for expansion).

Working Capital: Funds for day-to-day operations — keeping inventory, paying suppliers, meeting wages and other short-term commitments.

Arithmetic topics covered in Class 11: Calculations of profit/loss, break-even point, working capital requirement, simple ratio analysis (current ratio, debt-equity), cash inflows/outflows and basic return measures.

Key Points to Remember

• Choose a proper mix of funds: too much debt increases risk; too little debt may raise cost of capital.
• Maintain adequate working capital to ensure uninterrupted operations.
• Use break-even analysis to know the minimum sales needed to avoid loss.

Fig 2 — Educational Diagram: Functions of Business Finance

What is Business Finance? Business finance deals with planning, obtaining and managing the funds required for running a business and achieving its objectives. It ensures that the right amount of funds is available at the right time, from the right source, and is used in the right place.

Main functions of business finance

• Estimating financial requirements — Assessing how much capital is needed for start-up, expansion, and day-to-day operations. This is done by preparing projected budgets, cash flow statements and capital expenditure plans.
• Capital structure decisions — Determining the mix of debt and equity (long-term finance) that minimizes cost of capital and risk while maximizing owner returns.
• Raising funds — Selecting appropriate sources of finance (equity, preference shares, debentures, long-term loans, retained earnings, trade credit, bank overdraft) and timing of raising funds.
• Allocation and utilization of funds (Investment decisions) — Deciding where to invest funds: fixed assets (plant, machinery) and working capital (inventory, receivables). This includes evaluation methods such as ROI and payback period.
• Working capital management — Managing current assets and liabilities to ensure smooth operations: cash management, inventory control, receivables and payables management.
• Cash management — Ensuring sufficient liquidity to meet short-term obligations while minimizing idle cash through collections, disbursements and short-term investments.
• Profit planning and control (Budgeting) — Preparing budgets and variance analysis to plan profits and control costs.
• Dividend decision — Determining the portion of profits to distribute to shareholders versus retained in business based on investment needs and shareholder expectations.
• Financial reporting and control — Maintaining records, preparing financial statements, and using accounting reports to monitor performance and ensure compliance.
• Risk management — Identifying financial risks (interest rate, credit, liquidity, market) and using hedging, insurance and diversification to manage them.
• Tax planning — Structuring transactions and financing to optimize tax liabilities legally.

How these functions work together: A typical financial decision flow starts with estimating requirements → deciding capital structure → raising funds → allocating funds to projects and working capital → managing cash and receivables/payables → monitoring performance and making dividend/tax decisions. Each function supports financial stability and growth.

Why these functions matter: Proper financial management reduces the cost of capital, avoids liquidity crises, ensures profitable investment decisions, protects stakeholder interests and supports sustainable growth.

Fig 3 — Educational Diagram: Financial Planning

Definition: Financial planning is the process of estimating an enterprise's future fund requirements, determining the sources and form of funds, and planning their effective utilization to achieve business objectives. It ensures that adequate funds are available at the right time, in the right amount, and at a reasonable cost.

Key objectives:

• Estimate capital requirements (fixed and working capital).
• Ensure availability of funds when needed.
• Coordinate different departments to achieve financial efficiency.
• Minimize cost of funds and eliminate wasteful expenditure.
• Prepare for contingencies and growth opportunities.

Main components:

• Fixed capital requirements: Funds for long-term assets (land, building, machinery).
• Working capital requirements: Funds for day-to-day operations (stocks, receivables, cash).
• Capital structure: Mix of debt and equity.
• Sources of finance: Internal (retained earnings) and external (loans, share capital).
• Budgets and forecasts: Cash budgets, profit forecasts, and projected balance sheets.

Process / Steps:

1. Estimate total capital requirement = Fixed capital + Working capital.
2. Decide capital structure: proportion of debt and equity based on cost, risk, and control considerations.
3. Select sources of funds: short-term (bank overdraft, trade credit) & long-term (term loans, equity).
4. Prepare financial plans: cash flow projections, budgets, break-even analysis.
5. Implement & control: monitor budgets, revise plans as business conditions change.

Importance: Financial planning helps businesses avoid shortages or excessive investment in funds, maintain solvency, support expansion, coordinate departments, and improve investor confidence.

Limitations: Reliance on estimates and assumptions, unpredictable external factors (market, interest rates), and costs of preparing detailed plans.

Practical tip for students: Always separate fixed and working capital when estimating needs; prepare a simple cash budget for the first 12 months of a new business to test feasibility.

Fig 4 — Educational Diagram: Sources of Business Finance

What are Sources of Business Finance?

Sources of business finance are the various ways a business obtains money to start, operate, expand or meet short-term needs. Finance can come from owners, lenders, suppliers, or external investors. Choosing the right source depends on amount required, time horizon, cost, control, risk and purpose.

Major classifications

• Internal sources (Owned funds): generated within the business — owner’s capital, retained earnings (reserves), sale of assets, depreciation funds.
• External sources (Raised funds): raised from outside — equity (shares), debt (bank loans, debentures), trade credit, leasing, factoring, venture capital, government grants.

By time period

• Short-term finance (up to 1 year): working capital, bank overdraft, trade credit, commercial paper.
• Medium-term finance (1–5 years): term loans from banks, hire purchase, leasing, public deposits.
• Long-term finance (above 5 years): equity capital, long-term loans, debentures, retained earnings, venture capital.

Owned vs Borrowed funds — key differences

• Owned (Equity): no fixed repayment or interest, dilutes control, more expensive in terms of expected returns, strengthens balance sheet.
• Borrowed (Debt): fixed interest and repayment, does not dilute ownership, tax-deductible interest but increases financial risk (obligation to pay).

How businesses decide

Decision factors include:

• Purpose: long-term projects favour equity or long-term loans; seasonal needs favour short-term credit.
• Cost: compare interest rate (debt) vs expected return demanded by investors (equity).
• Control: owners who wish to retain control avoid issuing new equity.
• Risk & liquidity: debt increases fixed obligations; maintain adequate working capital.

Advantages and disadvantages (summary)

• Internal funds: low cost and flexible but limited in amount.
• Equity: no fixed repayment, strengthens capital base but costly and dilutes control.
• Bank loans/debt: cheaper (tax benefit) and no dilution but increases financial risk.
• Trade credit & commercial paper: quick and low-cost short-term finance but limited and may affect supplier relationships.

Practical tip

Mix sources to balance cost, risk and control. A common target is an optimal capital structure where weighted cost of capital is minimized while maintaining acceptable risk.

Fig 5 — Educational Diagram: Fixed Capital and Working Capital

Fixed Capital and Working Capital

Fixed Capital (also called long-term capital) is the investment in assets that are used repeatedly and continuously in the business for production over a long period — e.g., land, buildings, plant & machinery, furniture, vehicles. These assets are not meant for resale and are used to create production capacity.

Working Capital (also called circulating or short-term capital) is the fund required for day-to-day operations of the business. It finances current assets like cash, inventory, receivables and short-term prepaid expenses that keep the business running.

Key differences

• Purpose: Fixed capital creates capacity; working capital maintains operations.
• Duration: Fixed capital is long-term; working capital is short-term and cyclical.
• Forms: Fixed capital = fixed assets; Working capital = current assets.
• Liquidity: Fixed assets are illiquid; current assets are liquid.

Components

• Fixed capital: land, building, plant & machinery, furniture, office equipment, vehicles, installation costs, pre-operative expenses.
• Working capital: cash & bank balances, inventories (raw materials, WIP, finished goods), trade receivables, prepaid expenses, short-term loans and advances.

Importance

• Fixed capital determines the scale and capacity of production and influences long-term profitability.
• Working capital ensures smooth operations, meeting short-term obligations and avoiding production stoppages.

Factors determining requirements

• For fixed capital: size and scale of business, technology, choice of machinery, production process, degree of automation, location, statutory requirements.
• For working capital: nature of business (manufacturing, trading, service), production cycle, credit policy (to customers and from suppliers), seasonal fluctuations, inventory levels, growth rate of sales.

Estimation methods

• Fixed capital: prepare a list of required fixed assets and estimate their purchase/installation cost (replacement cost method); use capacity-based estimate (cost per unit of capacity × required capacity); or use a projected balance sheet method.
• Working capital: use the percentage of sales method (current assets or working capital as % of projected sales); operating cycle method (determine working capital tied up in each stage of the cycle); or use projected cash flows and forecasted current assets & liabilities.

Relationship between the two

Both are interrelated: increasing fixed assets (to raise capacity) often raises working capital needs (more raw materials, higher receivables). Financing decisions must balance long-term and short-term funding sources.

Long-term vs Short-term finance sources

• Fixed capital is financed mainly by long-term sources: owner's equity, retained earnings, long-term loans, debentures.
• Working capital is financed by short-term and sometimes long-term sources: trade credit, bank overdraft, short-term loans, commercial paper; permanent working capital may be financed by long-term funds.

Conclusion: Proper estimation and management of both fixed and working capital are essential for profitability and solvency. Fixed capital builds capacity; working capital keeps that capacity running smoothly.

Fig 6 — Educational Diagram: Working Capital Management

Definition: Working capital is the capital required for day‑to‑day operations of a business. It is the amount of funds invested in current assets such as cash, inventory and receivables. Working capital management means planning and controlling current assets and current liabilities to ensure smooth running of the business and to maintain adequate liquidity.

Types:

• Gross working capital: Total current assets (e.g., cash + inventory + receivables).
• Net working capital: Current assets minus current liabilities (CA - CL).

Objectives:

• Maintain adequate liquidity to meet short‑term obligations.
• Ensure uninterrupted operations (raw materials, pay wages, etc.).
• Optimize the balance between profitability and risk — too much working capital lowers return, too little risks insolvency.

Determinants / Factors affecting working capital requirement: Nature of business (manufacturing needs more than services), production cycle length, credit policy (to customers and from suppliers), business size, seasonal fluctuations, growth rate, operating efficiency and statutory requirements.

Classification by duration:

• Permanent (or fixed) working capital: Minimum amount required always.
• Temporary (or variable) working capital: Additional funds needed for seasonal or cyclical peaks.

Key techniques of working capital management: Cash budgeting and forecasting, inventory management (EOQ, ABC), receivables management (credit policy, ageing analysis), payables management (negotiating credit terms), accelerating collections and delaying payments without harming relationships, and short‑term financing planning.

Cash Conversion Cycle (Operating cycle): Measures how long cash is tied up in operations before conversion back to cash. Shorter cycle = better liquidity.

Practical tips for students: Always compare current ratio and quick ratio with industry norms; prepare a simple cash budget to forecast shortfalls; identify seasonal peaks and plan short‑term borrowing in advance.

Simple numeric examples (illustrative):

• If current assets = ₹200,000 and current liabilities = ₹120,000, then net working capital = ₹200,000 - ₹120,000 = ₹80,000.
• Cash conversion cycle example: Inventory days = 30, Receivable days = 45, Payable days = 20. CCC = 30 + 45 - 20 = 55 days. This means cash is tied up for 55 days.

Fig 7 — Educational Diagram: Capital Structure and Cost of Capital

Definition & overview: Capital structure is the mix of different long‑term sources of finance used by a business — mainly equity (owner’s capital), preference shares and debt (loans, bonds). Cost of capital is the average rate of return a company must pay to finance its assets; it is used as a benchmark for investment decisions.

Why it matters: The choice of capital structure affects risk, return to shareholders, tax liability and the firm’s overall cost of funds. The goal is an optimal capital structure — the mix that minimizes the company’s overall cost of capital and maximizes value.

Main sources of long‑term finance:

• Equity capital (owner’s funds, retained earnings): no fixed obligation to pay, but returns expected by owners.
• Preference shares: fixed dividend, ranked above equity for dividends and liquidation.
• Debt (loans, debentures, bonds): fixed interest obligation, interest is tax‑deductible (creates tax shield).

Key concepts:

• Gearing/Leverage: extent of debt in capital structure (high gearing = high debt proportion). Enhances return to equity when business profit is sufficient, but increases financial risk.
• Trading on equity: using debt to try to increase return on equity. Works when return on assets > cost of debt.
• Optimal capital structure: balance of debt and equity that minimizes Weighted Average Cost of Capital (WACC) and maximizes firm value.

Cost of each source (conceptual):

• Cost of debt (Kd): effective interest rate paid on debt. After tax cost = Kd × (1 − corporate tax rate) because interest is tax‑deductible.
• Cost of preference capital (Kp): preference dividend divided by net issue price.
• Cost of equity (Ke): expected return required by shareholders. For a no‑growth dividend, Ke = Dividend / Net proceeds. With growth, the Gordon model: Ke = (D1 / P0) + g.

Weighted Average Cost of Capital (WACC): the average cost of all sources of finance weighted by their market value proportions. WACC is used as the discount rate for evaluating projects.

Simple numeric example (illustrative):

• Equity (E) = 600,000; Debt (D) = 400,000; Total value V = 1,000,000.
• Cost of equity Ke = 12% ; Cost of debt Kd = 8% ; Corporate tax rate T = 30%.
• After‑tax cost of debt = 8% × (1 − 0.30) = 5.6%.
• WACC = (E/V)×Ke + (D/V)×Kd×(1 − T) = 0.6×12% + 0.4×5.6% = 7.2% + 2.24% = 9.44%.

Implications: As a firm uses more debt, the after‑tax cost of debt may be lower than equity, which can lower WACC up to a point. Beyond that point, higher financial risk raises the required return on equity and debt, increasing WACC. The optimal mix is where WACC is minimum.

Practical considerations for choosing capital structure:

• Nature and stability of earnings (stable earnings can support more debt).
• Cost and availability of different finance sources.
• Management preference (risk aversion) and control (equity dilution).
• Tax position (tax shields from debt).
• Market conditions and lender covenants.

Fig 8 — Educational Diagram: Financial Markets and Institutions

Definition: Financial markets are venues (physical or electronic) where financial instruments such as shares, bonds, bills and currencies are issued, bought and sold. Financial institutions are intermediaries (banks, insurance companies, mutual funds, NBFCs, etc.) that channel funds between savers and users of capital.

Key functions of financial markets and institutions:

• Mobilisation of savings: Collect savings from households and channel them to businesses and government.
• Price discovery: Determine prices of financial instruments (e.g., share prices) through demand and supply.
• Liquidity provision: Allow investors to convert assets into cash quickly (secondary markets).
• Risk management and transfer: Provide insurance, derivatives and diversification (mutual funds) to manage risk.
• Maturity transformation: Institutions (especially banks) convert short-term deposits into longer-term loans.
• Information and monitoring: Help evaluate creditworthiness and monitor borrowers (reducing information asymmetry).

Types of financial markets:

• Money market: Deals in short-term instruments (maturity < 1 year) such as treasury bills, commercial paper, call money. Used for liquidity management.
• Capital market: Deals in long-term instruments (equity and debt). Includes primary market (new issues, IPOs) and secondary market (trading of existing securities on stock exchanges).
• Foreign exchange market: Trading of currencies (e.g., rupee/dollar) for trade, investment and hedging.
• Derivatives market: Trading of futures, options and swaps used for hedging or speculation.
• Commodity market: Trading of agricultural, metal and energy products; price discovery for commodities.

Major financial institutions and their roles:

• Commercial banks: Accept deposits, provide loans, enable payments, and offer basic investment products.
• Non-Banking Financial Companies (NBFCs): Provide credit, leasing, hire-purchase and other services where banks may have limited reach.
• Development banks and investment banks: Support long-term project finance, underwriting, and advisory for corporations.
• Mutual funds: Pool small investors' savings to invest in diversified portfolios managed by professionals.
• Insurance companies: Provide risk cover and mobilise long-term savings through policy premiums.
• Stock exchanges and clearing houses: Provide organised platforms for secondary trading and settlement.
• Regulators (e.g., RBI, SEBI, IRDAI): Ensure stability, protect investors and enforce rules.

Importance for entrepreneurs:

• Access to finance: Loans, venture capital, IPOs and bond issues help fund business growth.
• Cost of capital and investment decisions: Market rates and investor expectations influence pricing and expansion choices.
• Risk management: Insurance and derivatives reduce business risk (e.g., currency or interest-rate risk).
• Valuation and exit routes: Secondary markets enable founders and investors to value and sell stakes.

Common financial instruments: Equity shares, preference shares, debentures/bonds, commercial paper, treasury bills, certificates of deposit, mutual fund units, derivatives (futures/options), insurance policies.

Regulation and safety: Regulators set disclosure norms, trading rules and prudential standards to ensure market integrity, protect retail investors, and maintain systemic stability.

Summary: Financial markets and institutions together form the financial system that mobilises savings, allocates capital efficiently, enables risk-sharing and supports economic growth — all essential for entrepreneurship and business finance.

Fig 9 — Educational Diagram: Financial Statements and Basic Analysis

What are Financial Statements?

Financial statements are formal records summarizing the financial activities and position of a business. The three primary statements are:

• Balance Sheet (Statement of Financial Position): Shows assets, liabilities and owner’s equity at a specific date. Equation: Assets = Liabilities + Equity.
• Income Statement (Profit & Loss Account): Shows revenue, expenses and profit or loss over a period (e.g., one year).
• Cash Flow Statement: Shows cash inflows and outflows classified into operating, investing and financing activities.

Purpose: To inform stakeholders (owners, lenders, managers) about profitability, liquidity, solvency and cash position for decision-making.

Main components explained:

• Assets: Current (cash, receivables, inventory) and non-current (machinery, buildings).
• Liabilities: Current (payables, short-term borrowings) and long-term (loans).
• Equity: Owner's capital, retained earnings.
• Revenue & Expenses: Sales, cost of goods sold, operating expenses, taxes.
• Cash flows: Operating (from core business), Investing (buy/sell assets), Financing (loans, owner’s capital).

Basic Analysis Techniques

• Horizontal (Trend) Analysis: Compares financial data over two or more periods to see growth or decline (e.g., sales trend over 3 years).
• Vertical (Common-size) Analysis: Expresses each item as a percentage of a base (e.g., each income statement item as % of sales; each balance sheet item as % of total assets) to compare firms of different sizes.
• Ratio Analysis: Uses relationships between numbers to measure performance. Main categories:
  • Liquidity ratios (ability to meet short-term obligations)
  • Solvency/debt ratios (long-term financial stability)
  • Profitability ratios (ability to earn returns)
  • Turnover/efficiency ratios (how well assets are used)
• Cash Flow Analysis: Checks whether profits are backed by cash — important for survival of small businesses.

How to perform a simple analysis (steps):

1. Collect last 3–5 years of financial statements.
2. Prepare common-size statements (vertical analysis) for easier comparison.
3. Compute key ratios (liquidity, profitability, leverage, turnover).
4. Plot trends for sales, profit, key ratios to spot improvements or deterioration.
5. Interpret results and compare with industry norms or competitors.

Limitations: Financial statements are historical, based on accounting policies and estimates, and may not show seasonal or non-financial factors (brand value, market conditions).

Practical tip: Always look at both profit and cash flow. A business can show accounting profit but run out of cash.

Fig 10 — Educational Diagram: Bills of Exchange, Promissory Notes and Cheques

Overview

These three instruments are negotiable instruments used to make, accept or transfer a promise to pay money. They are governed in India by the Negotiable Instruments Act, 1881. They differ in form, parties involved and when payment is due.

1. Promissory Note

• Definition: A written, signed unconditional promise by one person (the maker) to pay a certain sum of money to another (the payee) or to the bearer, either on demand or at a fixed future date.
• Parties: Maker (promisor) and payee (promisee). Two-party instrument.
• Key features: written, signed, unconditional, contains amount, payee name (or bearer), date and term (on demand or time).
• Example use: A borrower signs a promissory note promising to pay a lender Rs. 50,000 after 6 months.

2. Bill of Exchange

• Definition: A written order from one person (drawer) directing another person (drawee) to pay a certain sum to a specified person (payee) or to the bearer, on demand or at a future date.
• Parties: Drawer, Drawee, Payee. Three-party instrument (though drawer and payee can be same person).
• Key features: Must be an order (not a promise), signed by drawer, specifies amount, drawee and payee, dated and payable on demand or after a certain period (time/Usance bill).
• Acceptance: The drawee accepts by signing the bill, becoming primarily liable to pay on maturity.
• Use: Common in trade—seller draws a bill on buyer for goods supplied; buyer accepts and the bill may be held till maturity or discounted at a bank.

3. Cheque

• Definition: A bill of exchange drawn on a banker, payable on demand (i.e., it is always a demand instrument).
• Parties: Drawer (account holder), Drawee (bank), Payee. In practice, payment is made by the drawee bank from the drawer's account.
• Key features: Drawn on a bank, always payable on demand, may be crossed, endorsed, or bearer/order. Types include bearer cheque, order cheque, crossed cheque, post-dated cheque, stale cheque (after 3 months in India).
• Use: Everyday payments—salaries, rent, purchases, etc. Dishonour of cheque (bounce) can have legal consequences under the Negotiable Instruments Act.

Common processes and terms

• Negotiation/Transfer: Instruments can be transferred by delivery (bearer) or by endorsement and delivery (order instrument).
• Endorsement: Signing on the back to transfer rights; may be blank (to bearer) or special (naming the new payee).
• Discounting: A bill or promissory note payable in future may be presented to a bank to receive present cash less a discount (bank charges interest for the period).
• Dishonour: Failure to pay on maturity (for cheques, when presented) — leads to noting/protest and legal remedies.

Differences (brief)

• Promissory note = promise; Bill of exchange = order; Cheque = bill on banker payable on demand.
• Promissory note involves two parties; bill and cheque normally involve three.
• Cheque is always payable on demand; bills/notes can be demand or time instruments.

Accounting/Banking aspect — Discounting

When a bill or promissory note is discounted at a bank before maturity the bank deducts a discount (simple interest) for the remaining period. The proceeds received = Face value − Banker's discount.

Note on Legal position

These instruments are negotiable and transferable (subject to endorsements and crossings). Cheques dishonoured for insufficiency of funds can attract criminal action under Section 138 of the Negotiable Instruments Act (subject to procedure and defences).

Fig 11 — Educational Diagram: Interest: Simple Interest

Definition: Simple Interest (SI) is interest calculated only on the original principal amount (the sum borrowed or invested), for the actual time the money is lent or invested. It does not take into account interest on previously earned interest.

Key idea: SI is directly proportional to the principal (P), the rate of interest per annum (R), and the time period in years (T). That is, if any one of P, R or T doubles, the simple interest doubles.

When used: Simple interest is typically used for short-term loans, trade credit, some bank deposits, and quick business loans—situations common in entrepreneurship and small business finance.

How to calculate (step-by-step):

• Make sure the rate R is an annual rate (per cent per annum).
• Express time T in years. If given months, T = months/12. If given days, T = days/365 (or days/360 if that convention is specified).
• Apply the SI formula to get interest for the given period, then add to principal to get the total amount payable.

Worked mini-example: If a trader borrows Rs. 10,000 at 5% p.a. for 3 years, the simple interest = (10000 × 5 × 3) / 100 = Rs. 1,500. The amount to repay = 10000 + 1500 = Rs. 11,500.

Difference from compound interest: In compound interest, interest is calculated on principal plus previously accumulated interest. In simple interest, interest is always on the original principal, so interest grows linearly with time, not exponentially.

Practical tips for students:

• Always convert time to years before using the main formula.
• For part-year periods, use fractional years (6 months = 0.5 year).
• When solving for P, R, or T, rearrange the basic formula (see formulas list).

Fig 12 — Educational Diagram: Compound Interest and Time Value of Money

Overview
Time Value of Money (TVM) is the principle that a sum of money available today is worth more than the same sum in the future because of its potential earning capacity. Compound Interest is the mechanism by which money grows over time when interest is added to the principal and future interest is earned on previously accumulated interest.

Compound interest — concept
When interest is added to the principal at the end of each compounding period, the new amount becomes the principal for the next period. This causes exponential growth. The more frequent the compounding (annually, semiannually, quarterly, monthly, daily, or continuously), the greater the accumulated amount for the same nominal rate.

Time Value of Money — two directions
- Future value (FV): How much a current sum will grow to at a given rate and time.
- Present value (PV) or discounting: How much a future sum is worth today given a discount rate. Discounting reverses compounding.

Why it matters in business and everyday life
TVM is used to evaluate investments, savings, loans, pricing, project appraisal (NPV), EMIs, retirement planning, and any decision that involves cash flows at different times.

Important ideas to remember
- Compound interest leads to faster growth than simple interest because interest earns interest.
- Present value decreases as the discount rate or time increases.
- Frequency of compounding affects the effective annual rate.

Fig 13 — Educational Diagram: Annuities, Equated Installments and Amortization

What is an annuity?
An annuity is a series of equal payments made at regular intervals. Payments can be at the end of each period (ordinary annuity) or at the beginning of each period (annuity due).

Common types and real-life occurrences

• Ordinary annuity: monthly EMI paid at month-end, periodic rent paid at month-end.
• Annuity due: rent or salary paid at the beginning of a period, some insurance premiums.
• Perpetuity: an infinite annuity (e.g., some fixed perpetual dividends).

Key ideas — Time value of money
Because of interest, a rupee today is worth more than a rupee in the future. Annuity formulas give the present value (PV) or future value (FV) of a stream of equal payments A, using the periodic interest rate r and number of periods n.

Primary formulas (conceptual)

• Present value of an ordinary annuity (payments at period end): PV = A * (1 - (1 + r)^{-n}) / r
• Future value of an ordinary annuity (value at time n): FV = A * ((1 + r)^{n} - 1) / r
• Annuity due values = ordinary annuity values × (1 + r) (because every payment is shifted one period earlier).
• Perpetuity (infinite payments): PV = A / r (only if n → ∞ and r > 0).

Equated Installments (EMI)
When a borrower repays a loan by equal periodic payments (EMIs), each payment covers interest on the outstanding balance and repays some principal. The standard EMI formula for a loan principal P, periodic rate r and n payments:

EMI = P * r * (1 + r)^{n} / ((1 + r)^{n} - 1)

Why this formula works (intuitive)
The lender discounts all future equal payments at rate r to find their present value; that PV must equal the loan amount P. Solving PV = EMI * (1 - (1+r)^{-n}) / r gives the EMI formula above.

Amortization
Amortization is the process of paying off a loan over time by installments. Each installment = interest on opening balance + principal repaid. Over time interest portion falls and principal portion rises (for fixed EMI).

Amortization schedule (what it shows)

• Period number
• Opening balance
• Interest for the period = opening balance × r
• Installment (EMI) — fixed
• Principal repaid = EMI − interest
• Closing balance = opening balance − principal repaid

Outstanding balance after k payments
Two equivalent forms:

• OB_k = P*(1 + r)^{k} − EMI * (( (1 + r)^{k} − 1 ) / r)
• Or OB_k = EMI * (1 − (1 + r)^{-(n − k)}) / r (PV of remaining payments)

Worked (compact) numeric example
Loan P = ₹100,000, annual interest 10% compounded monthly → r = 0.10/12 = 0.008333333, n = 5 years × 12 = 60 months. Compute (1 + r)^{n} ≈ 1.647. Then EMI ≈ 100000 × 0.0083333 × 1.647 / (1.647 − 1) ≈ ₹2,121 per month.

Month 1: interest = 100,000 × 0.0083333 = ₹833.33; principal repaid = 2,121 − 833.33 = ₹1,287.67; closing balance ≈ ₹98,712.33. Month 2 interest = 98,712.33 × 0.0083333 ≈ ₹822.60, principal ≈ ₹1,298.40, closing ≈ ₹97,413.93. Continue until balance is zero at month 60.

Practical points for students

• Check whether payments are at period start (annuity due) or end (ordinary annuity) — this multiplies PV by (1 + r) when moving to annuity due.
• For monthly EMI problems, convert annual rate to monthly by dividing by 12 and use n in months.
• Total interest paid = (EMI × n) − P.
• Amortization tables help show how much interest vs principal you pay each period — useful for budgeting and tax planning.

Connections to entrepreneurship & business finance
Businesses use annuities and amortization when taking loans, leasing equipment, evaluating recurring cash flows (rent, subscriptions), and calculating project cash flows (NPV of equal periodic benefits or costs).

Fig 14 — Educational Diagram: Discounting of Bills and Related Calculations

What is a bill and discounting? A bill of exchange (or bill) is a written, dated and signed instrument containing an unconditional order to pay a certain sum of money on a specified future date (maturity). When a holder of a bill needs cash before maturity, they can take it to a bank. The bank buys the bill by deducting an interest-like amount called the banker's discount and any service charges, and pays the balance (the proceeds).

Key concepts

• Face value (F): The amount payable on maturity.
• Discounting date: The date when the bill is sold to the bank (before maturity).
• Time (t): Remaining time to maturity measured in years (for months use months/12).
• Rate (r): Discount rate per annum (expressed as a decimal, e.g., 12% = 0.12).
• Banker's Discount (BD): Interest computed on the face value for the remaining period using simple interest. It is deducted up front by the bank.
• Proceeds (P): Amount the holder receives from the bank = Face value − Banker's discount − any bank charges.
• True Discount (TD): The difference between the face value and the present worth (PV) of that face value, where PV = F / (1 + r t). TD = F − PV. TD is the actual interest corresponding to bringing a future sum to present at rate r for time t.

How banks calculate discount

Most banks use simple interest on the face value for the remaining period. Thus banker's discount is proportional to the face amount and time. This method means the bank effectively charges interest on the whole future sum even though it pays only the reduced amount now.

Difference between Banker's Discount and True Discount

• Banker's discount (BD) = F × r × t (simple linear formula).
• True discount (TD) = F − PV = F × (r t) / (1 + r t) (smaller than BD for positive r and t).
• The banker's discount is usually larger than the true discount; the difference is the bank's implicit gain for discounting.

Practical steps to discount a bill at a bank

1. Find the remaining time to maturity in years (t).
2. Convert annual rate into decimal (r).
3. Calculate BD = F × r × t.
4. Subtract BD (and any commission/charges) from F to get proceeds.

Common variations: Banks may (a) charge a commission (flat or percentage of face value or proceeds), (b) compute discount on actual/360 or actual/365 basis for time, or (c) quote discount rates differently—always read bank terms.

Fig 15 — Educational Diagram: Practical Business Arithmetic (Basics)

Practical Business Arithmetic covers the basic arithmetic operations and percentage-based calculations that every entrepreneur and small-business operator must know. It helps in pricing, discounting, calculating interest, estimating profit/loss, analysing costs, and making quick financial decisions.

Core concepts

• Cost Price (CP) and Selling Price (SP) – CP is what you pay to acquire a good or produce a service; SP is what you charge the customer.
• Profit and Loss – Profit = SP − CP (if SP > CP). Loss = CP − SP (if SP < CP). Profit and loss are often expressed as percentages of cost or selling price.
• Percentages – Used for discounts, taxes, margins, rates of return. Converting rates into absolute amounts is routine in business.
• Markup vs Margin – Markup is the amount added to cost to get selling price. Margin (gross profit margin) is profit expressed as a percentage of selling price or revenue.
• Discounts – Reductions from the listed price; often expressed in percentage terms.
• Simple Interest and Compound Interest – Used for loans, deposits and investments. Simple interest is linear; compound interest grows exponentially when interest is reinvested.
• Ratio and Proportion – Useful for splitting costs/profits, scaling recipes, or allocating resources.
• Averages – Useful for per-unit cost, average sales, average price etc.

Practical uses and approach

• Estimate the selling price by adding a planned markup on cost and adjusting for expected discount and taxes.
• Compute the effective interest on loans or returns on savings to compare financing options.
• Use ratio/proportion to divide partnership profits or allocate shared expenses.
• Apply quick percentage techniques (like 10%, 5%, 1%) for fast mental calculations while buying or negotiating.

Tips for quick calculations

• Convert percentage changes to multipliers: a 10% increase = multiply by 1.10; a 10% decrease = multiply by 0.90.
• For successive percentage changes, multiply the successive multipliers (e.g., after 10% increase then 20% decrease multiply by 1.10 × 0.80).
• For compound growth visualize as repeated multiplication; for frequent compounding keep the compounding period correct.