Institute of Chartered Accountants in England and Wales (ICAEW) ACA Professional Level: Business Strategy, Finance and Management Syllabus

What four perspectives make up Kaplan and Norton's Balanced Scorecard?

Financial, Customer, Internal business process, and Learning and growth (innovation) perspectives — linking performance measures to strategy beyond purely financial measures.

Define Net Present Value (NPV) and give its formula.

NPV is the sum of the present values of all project cash flows discounted at the cost of capital, less the initial investment. $$NPV = \sum_{t=0}^{n} \frac{C_t}{(1+r)^{t}}$$ where $C_t$ is the cash flow at time $t$ and $r$ is the discount rate.

State the NPV decision rule for investment appraisal.

Accept a project if its $NPV > 0$ (it increases shareholder wealth); reject if $NPV < 0$. For mutually exclusive projects, choose the one with the highest positive NPV.

Define the Internal Rate of Return (IRR).

The IRR is the discount rate at which a project's NPV equals zero, i.e. the value of $r$ satisfying $$\sum_{t=0}^{n} \frac{C_t}{(1+r)^{t}} = 0.$$ A project is accepted if its IRR exceeds the cost of capital.

What is the formula for IRR using linear interpolation between two trial discount rates?

$$IRR \approx L + \left( \frac{NPV_L}{NPV_L - NPV_H} \right)(H - L)$$ where $L$ and $H$ are the lower and higher discount rates, and $NPV_L$, $NPV_H$ are the corresponding NPVs.

Give two limitations of IRR compared with NPV.

(1) IRR can give multiple values when cash flows change sign more than once, and (2) it can rank mutually exclusive projects incorrectly because it assumes reinvestment at the IRR and ignores the scale of investment. NPV is theoretically superior.

What is the discounted payback period and how does it differ from simple payback?

The discounted payback period is the time taken for the cumulative discounted cash flows to recover the initial investment. Unlike simple payback, it accounts for the time value of money, though both ignore cash flows after the payback point.

How is a real (inflation-adjusted) discount rate converted to a nominal (money) rate?

Using the Fisher equation: $$(1 + i) = (1 + r)(1 + h)$$ where $i$ is the nominal/money rate, $r$ is the real rate and $h$ is the expected inflation rate. Discount money cash flows at the money rate and real cash flows at the real rate.

What is the formula for the Weighted Average Cost of Capital (WACC) with debt and equity?

$$WACC = \frac{E}{E+D}\,k_e + \frac{D}{E+D}\,k_d(1-T)$$ where $k_e$ is the cost of equity, $k_d$ is the pre-tax cost of debt, $T$ is the corporation tax rate, and $E$, $D$ are the market values of equity and debt.

State the Capital Asset Pricing Model (CAPM) formula for the required return on equity.

$$k_e = R_f + \beta\,(E(R_m) - R_f)$$ where $R_f$ is the risk-free rate, $\beta$ is the equity beta (systematic risk), and $(E(R_m) - R_f)$ is the equity market risk premium.

What is the dividend growth model (Gordon growth) formula for the cost of equity?

$$k_e = \frac{D_1}{P_0} + g = \frac{D_0(1+g)}{P_0} + g$$ where $D_0$ is the current dividend, $D_1$ the next expected dividend, $P_0$ the ex-dividend share price, and $g$ the constant dividend growth rate.

Distinguish systematic from unsystematic risk in the context of CAPM.

Systematic (market) risk affects all securities and cannot be diversified away; it is measured by beta and is the only risk rewarded with return. Unsystematic (specific) risk is firm-specific and can be eliminated through diversification, so it is not rewarded.

What does an equity (asset) beta of 1.0 indicate, and what does a beta greater than 1 indicate?

A beta of 1.0 means the share moves in line with the market (same systematic risk as the market portfolio). A beta greater than 1 means the share is more volatile than the market (more systematic risk), so it carries a higher required return.

State the Modigliani–Miller (MM) Proposition I without taxes.

In a perfect capital market with no taxes, a firm's total market value is independent of its capital structure; the WACC remains constant regardless of the debt-equity mix because the benefit of cheaper debt is exactly offset by the rising cost of equity.

Under MM with corporate taxes, what is the value of a geared (levered) firm?

$$V_g = V_u + T \cdot D$$ where $V_u$ is the value of the equivalent ungeared firm, $T$ is the corporation tax rate and $D$ is the market value of debt. The term $TD$ is the present value of the debt tax shield.

What is the traditional view of capital structure regarding an optimal gearing level?

The traditional view holds that WACC initially falls as cheap debt is introduced, reaches a minimum at an optimal level of gearing (maximising firm value), and then rises as financial risk increases the cost of equity and eventually the cost of debt.

Give the asset beta (degearing) formula linking equity beta and asset beta with debt.

$$\beta_a = \beta_e \cdot \frac{V_e}{V_e + V_d(1-T)} + \beta_d \cdot \frac{V_d(1-T)}{V_e + V_d(1-T)}$$ Assuming debt is risk-free ($\beta_d = 0$) it simplifies to $\beta_a = \beta_e \cdot \frac{V_e}{V_e + V_d(1-T)}$.

In business valuation, give the formula for the net asset (assets-based) valuation of equity.

Net asset value of equity = total assets (at chosen basis — book, replacement or realisable value) less total liabilities and any preference capital. It typically ignores intangibles and is often used as a minimum/floor valuation.

State the dividend valuation model (Gordon growth) for the value of a share with constant growth.

$$P_0 = \frac{D_1}{k_e - g} = \frac{D_0(1+g)}{k_e - g}$$ valid where the required return $k_e$ exceeds the constant dividend growth rate $g$.

What is the P/E ratio method of valuing a company's equity?

Equity value = earnings (profit after tax attributable to ordinary shareholders) × an appropriate P/E ratio. The P/E is usually taken from a comparable quoted company, then discounted for an unquoted target to reflect lower marketability and risk.

How is the value of equity derived under a discounted free cash flow (DCF) valuation?

Discount the firm's free cash flows to firm at the WACC to obtain enterprise value, then subtract the market value of debt: $$V_e = \sum_{t=1}^{n} \frac{FCF_t}{(1+WACC)^{t}} + \frac{TV}{(1+WACC)^{n}} - V_d$$ where $TV$ is the terminal value.

Give the formula for terminal (continuing) value using a perpetuity with constant growth.

$$TV = \frac{FCF_{n+1}}{WACC - g}$$ i.e. the free cash flow in the first year beyond the forecast horizon, capitalised at WACC less the long-run growth rate $g$, then discounted back to present value.

What are the three forms of the efficient market hypothesis (EMH)?

Weak form (prices reflect all past price/volume information), Semi-strong form (prices reflect all publicly available information), and Strong form (prices reflect all information, public and private/insider).

What does the pecking order theory predict about how firms prefer to finance investment?

Firms prefer internal finance (retained earnings) first, then debt, and issue new equity only as a last resort. This ordering arises from asymmetric information and the signalling/cost effects of issuing securities, rather than targeting an optimal gearing ratio.

State the dividend irrelevancy argument of Modigliani and Miller.

In a perfect capital market, dividend policy does not affect shareholder wealth or firm value; what matters is the firm's investment/earning power. Shareholders can create 'home-made dividends' by selling shares, so the split between dividends and retentions is irrelevant.

What is the 'signalling' effect of dividends?

Because of information asymmetry, a change in dividend conveys information to the market: an unexpected dividend increase signals management confidence in future cash flows (raising the share price), while a cut signals trouble. This explains why firms are reluctant to cut dividends.

Distinguish transaction, translation and economic exposure to foreign currency risk.

Transaction exposure: risk on settling specific future foreign-currency cash flows from existing contracts. Translation exposure: accounting risk on retranslating foreign assets/liabilities into the reporting currency. Economic exposure: long-term effect of exchange-rate movements on the present value of future cash flows and competitiveness.

State interest rate parity (IRP) and what it predicts about forward exchange rates.

$$F_0 = S_0 \times \frac{1 + i_c}{1 + i_b}$$ where $F_0$ is the forward rate, $S_0$ the spot rate, and $i_c$, $i_b$ the interest rates of the counter (variable) and base currencies. The currency with the higher interest rate trades at a forward discount.

State purchasing power parity (PPP) for forecasting the expected future spot rate.

$$S_1 = S_0 \times \frac{1 + h_c}{1 + h_b}$$ where $h_c$ and $h_b$ are the expected inflation rates in the counter and base currency countries. The currency of the higher-inflation country is expected to depreciate.

Name three internal (non-derivative) techniques for managing foreign currency transaction risk.

Matching (offsetting receipts and payments in the same currency), Netting (settling only net intra-group balances), Leading and lagging (accelerating or delaying payments), and invoicing in the home currency. (Any three.)

How does a money market hedge work for a future foreign currency payment?

Borrow domestic currency now, convert to the foreign currency at spot, and deposit it so that with interest it grows to the exact amount needed to make the future payment. This fixes the cost today, replicating a forward rate using current spot and money-market interest rates.

Compare forward contracts with currency futures as hedging instruments.

Forwards are OTC, tailored in amount and date, settled at maturity with no margin, but carry counterparty risk. Futures are exchange-traded, standardised in size and date, marked to market daily with margin requirements, and largely free of counterparty risk but may leave basis risk and require an imperfect match.

What is the key difference between hedging with options and with forwards/futures?

A currency or interest-rate option gives the holder the right but not the obligation to transact at the strike, allowing the holder to benefit from favourable movements while capping downside, in exchange for a non-refundable premium. Forwards/futures lock in a rate with no flexibility and (usually) no upfront premium.

What is a Forward Rate Agreement (FRA) and how does it manage interest rate risk?

An FRA is an OTC agreement fixing the interest rate on a notional principal for a future period. The parties exchange the difference between the agreed (fixed) rate and the reference market rate at settlement, so a borrower is compensated if rates rise — locking in borrowing cost without exchanging principal.

Explain how an interest rate swap can reduce financing costs.

Two parties exchange interest payment streams (typically fixed for floating) on a notional principal. By exploiting comparative advantage in different markets (the difference in credit spreads between fixed and floating rates), both parties can achieve cheaper financing or convert exposure between fixed and floating to match their risk preference.

What is the role of a corporate treasury function?

Treasury manages the firm's liquidity, funding and financial risk: cash and working-capital management, raising and managing debt/equity finance, banking relationships, foreign exchange and interest-rate risk management, and investment of surplus funds. It may operate as a cost centre or a profit centre.

What is an interest rate collar and why is it used?

A collar combines buying a cap (option setting a maximum rate for a borrower) and selling a floor (setting a minimum rate). The premium received from selling the floor reduces the net cost of the cap, but the borrower gives up the benefit of rate falls below the floor — limiting both cost and benefit within a band.

Define value at risk (VaR) as a measure of financial risk.

VaR estimates the maximum loss expected over a given time horizon at a stated confidence level under normal market conditions — e.g. a one-day 95% VaR of £1m means there is a 5% chance of losing more than £1m in a day. For a normal distribution, $VaR = \text{value} \times z \times \sigma \times \sqrt{t}$.