Value and Returns: Time Value of Money, Valuation of Bonds and Shares, Risk and Return, Capital Budgeting and Dividend Theories

Return over a holding period is (income + price change) ÷ beginning price; expected return is the probability-weighted average of possible returns, Σ p_i R_i; risk is the dispersion of returns around the expectation, measured by variance Σ p_i (R_i − E(R))^2 and its square root the standard deviation, and — to compare investments of different size — the coefficient of variation, SD ÷ mean. Risk divides into systematic (market, non-diversifiable — interest rates, inflation, recession, war — measured by beta) and unsystematic (specific, diversifiable — a strike, a product failure, a lawsuit); a portfolio of about fifteen to twenty uncorrelated stocks removes most unsystematic risk, so the market rewards only systematic risk. Markowitz's portfolio theory (1952) shows that the risk of a two-asset portfolio, σp^2 = w1^2 σ1^2 + w2^2 σ2^2 + 2 w1 w2 ρ12 σ1 σ2, is below the weighted average of the individual risks whenever the correlation ρ is less than +1, and can be eliminated entirely at ρ = −1; the efficient frontier is the set of portfolios with the highest return for each level of risk, and the investor chooses on it by their utility. Adding a risk-free asset gives the capital market line, and the tangency portfolio is the market portfolio.

Capital budgeting is the process of evaluating and selecting long-term investments whose benefits extend beyond a year — expansion, replacement and modernisation, diversification, research and development, and statutory or strategic projects. Investment decisions are large, largely irreversible, long-lived and risky, and they shape the firm's cost structure and competitive position, which is why they are taken at the top. Proposals are independent, mutually exclusive (accepting one rejects the others) or contingent. The cash flows relevant to appraisal are incremental, after tax, and ignore sunk costs and allocated overheads but include opportunity costs and working-capital changes: initial outlay (cost plus installation plus working capital less proceeds and tax effects of the old asset), annual operating cash flows (EBIT(1 − t) + depreciation, or PAT + depreciation + interest(1 − t) when financing charges are kept out), and terminal flows (salvage after tax and recovery of working capital). Financing costs are excluded because they are in the discount rate.

Risk in capital budgeting is the variability of a project's returns; uncertainty is the case where even the probabilities are unknown. The techniques divide into those that adjust the discount rate or the cash flows and those that describe the distribution. The risk-adjusted discount rate adds a premium to the cost of capital for riskier projects — simple, but it compounds the penalty over time and treats risk as growing with time. The certainty-equivalent approach multiplies each risky cash flow by a coefficient between 0 and 1 and discounts at the risk-free rate — theoretically cleaner because it separates time from risk. Sensitivity analysis changes one variable at a time — price, volume, cost, life — to find which the NPV is most sensitive to; scenario analysis changes several together in optimistic, most-likely and pessimistic cases; break-even analysis finds the sales at which NPV is zero. Probability analysis assigns probabilities and computes the expected NPV and its standard deviation, from which the probability of a negative NPV can be read; Hillier's model handles correlated flows over time. Simulation (Monte Carlo, Hertz 1964) draws thousands of combinations from the input distributions to build the NPV distribution. Decision-tree analysis lays out sequential decisions and chance events, values from the end backward by expected NPV, and prices the option to abandon or expand — the root of real options analysis, which values flexibility (defer, expand, contract, abandon, switch) with option-pricing methods. Shorter payback and conservative forecasts are the informal methods.

Determination of dividend policy weighs the determinants: legal rules (under the Companies Act 2013, s. 123, dividend is paid only out of current or past profits after depreciation, or out of free reserves within limits; the Companies (Declaration and Payment of Dividend) Rules cap dividend from reserves; it must be paid within 30 days of declaration, unpaid amounts go to the Unpaid Dividend Account and after seven years to the Investor Education and Protection Fund; interim dividend is declared by the board, final dividend by shareholders in general meeting on the board's recommendation and cannot exceed it), liquidity (profit is not cash), the investment opportunities and growth stage of the firm, the stability of earnings, access to capital markets, cost of external finance, control considerations (new equity dilutes promoters), the tax position of shareholders (dividend has been taxed in shareholders' hands since dividend distribution tax was abolished in 2020, with TDS at 10% above 10,000 rupees), contractual restrictions in loan covenants, inflation and shareholder expectations. Policies are stable dividend per share (the most common — Lintner's finding), constant payout ratio (dividend varies with earnings), stable rupee dividend plus extra, and residual. Forms: cash dividend, stock dividend (bonus shares — capitalisation of reserves, no cash leaves, share price falls proportionately), stock split (more shares of lower face value, no accounting entry beyond face value), reverse split, share buy-back (s. 68 — up to 25% of paid-up capital and free reserves, taxed since October 2024 as dividend in the shareholder's hands), and dividend reinvestment plans. Stability of dividends is valued because it resolves uncertainty, meets the income needs of some investors and satisfies institutional investment rules.