ACCA FM Exam 1

✅ Correct answer: Efficiency of staff use

📌 Explanation: Value for money is judged by economy (the cost of inputs), efficiency (the output achieved from the inputs used) and effectiveness (whether the objectives are met). Treating 30% more patients with the same staff and budget raises output per unit of input, which is an efficiency gain.

❌ Why the other options are wrong: Economy would mean buying the same staff time or supplies more cheaply, but input costs have not changed; effectiveness would need evidence that health outcomes or waiting-time targets improved; equity of access is a fairness measure and not one of the three measures of value for money.

📋 Objective: 1.4 (Objectives in not-for-profit organisations (A4))

✅ Correct answer: 3.5 years

📌 Explanation: Present values are $100,870, $92,620, $84,920 and $77,880 for years 1 to 4, so the cumulative present value after three years is $278,410 and $41,590 of the investment is still unrecovered. Discounted payback = 3 + 41,590 / 77,880 = 3.53, or 3.5 years, assuming the year 4 cash flow arises evenly.

❌ Why the other options are wrong: 2.9 years is the simple payback (320,000 / 110,000), which ignores the time value of money; 3.4 years divides the year 3 shortfall by the undiscounted inflow of $110,000 instead of the year 4 present value; 4.0 years rounds up to the whole year in which the cumulative present value turns positive.

📋 Objective: 4.1 (Investment appraisal techniques (D1))

✅ Correct answer: $4.64

📌 Explanation: A 1 for 4 issue means one new share is offered for every four held. Four shares at $4.80 are worth $19.20 and one new share costs $4.00, so the theoretical ex-rights price is (19.20 + 4.00) / 5 = $4.64. The price falls because new shares are issued at a discount to the market price.

❌ Why the other options are wrong: $4.40 takes a simple average of the market price and the issue price and ignores the number of shares of each; $4.16 attaches the weights the wrong way round (one share at $4.80 and four at $4.00); $4.80 assumes the market price is unchanged by the issue, which ignores the dilution.

📋 Objective: 5.1 (Sources of, and raising, business finance (E1))

✅ Correct answer: $3.78

📌 Explanation: The P/E method values a share as earnings per share multiplied by a comparable P/E ratio: 0.42 x 12 = $5.04. Unlisted shares are harder to sell than listed ones, so a marketability discount of 25% is deducted: 5.04 x 0.75 = $3.78 per share.

❌ Why the other options are wrong: $5.04 is the value before the marketability discount; $3.50 treats the P/E ratio of 12 as an earnings yield of 12% (0.42 / 0.12) and also omits the discount; $6.30 adds 25% to $5.04 instead of deducting it.

📋 Objective: 6.2 (Models for the valuation of shares (F2))

✅ Correct answer: $42,308

📌 Explanation: Present value of costs = 85,000 + (12,000 x 0.909) + (14,000 x 0.826) + (17,000 x 0.751) - (20,000 x 0.751) = 85,000 + 10,908 + 11,564 + 12,767 - 15,020 = $105,219. Equivalent annual cost = 105,219 / 2.487 = $42,308, which can be compared with other replacement cycles.

❌ Why the other options are wrong: $35,073 divides the present value by three years instead of the annuity factor; $48,347 leaves out the resale value; $43,426 adds the costs without discounting (108,000) before dividing by the annuity factor.

📋 Objective: 4.4 (Specific investment decisions (D4))

✅ Correct answer: Employees who work at the old mill; The local community that depends on mill wages

📌 Explanation: Stakeholders have different objectives, and these can conflict with the shareholders' wish for profit. Employees lose their jobs and income, and the local community loses spending power and local employment, so both would oppose closure even though it raises profit.

❌ Why the other options are wrong: Shareholders and institutional investors benefit from higher profit and dividend growth, so they would support the closure; lenders gain stronger interest cover from higher profit and lower costs, so they would also support it.

📋 Objective: 1.3 (Stakeholders and corporate objectives (A3))

✅ Correct answer: $108,000

📌 Explanation: With one limiting resource, rank divisible projects by profitability index (NPV per $ invested): Q 0.26, P 0.24, R 0.20 and S 0.17. Take Q ($200,000) and P ($150,000), then the remaining $100,000 buys 40% of R: 52,000 + 36,000 + (0.4 x 50,000) = $108,000.

❌ Why the other options are wrong: $102,000 ranks projects by absolute NPV and funds Q and R; $105,000 is the best whole-project combination (Q, P and S) and ignores that projects can be part-funded; $155,000 adds the NPVs of all four projects and ignores the $450,000 limit.

📋 Objective: 4.4 (Specific investment decisions (D4))

✅ Correct answer: $94.86

📌 Explanation: The floor value of a convertible is the value it would have as straight debt: the present value of the interest and the redemption proceeds at the return investors require on similar debt. (6 x 2.577) + (100 x 0.794) = 15.46 + 79.40 = $94.86 per $100 nominal.

❌ Why the other options are wrong: $75.00 values the interest as a perpetuity (6 / 0.08) and ignores redemption; $100.00 would only apply if investors required the 6% coupon rate; $79.40 counts the discounted redemption payment and leaves out the interest.

📋 Objective: 6.3 (Valuation of debt and other financial assets (F3))

✅ Correct answer: 7.1%

📌 Explanation: Cash flows in current prices are real cash flows, so they must be discounted at a real rate. From the Fisher relationship (1 + nominal) = (1 + real) x (1 + inflation), the real rate = 1.114 / 1.04 - 1 = 7.1%.

❌ Why the other options are wrong: 7.4% subtracts inflation from the nominal rate, which is only an approximation; 15.9% multiplies the two rates instead of dividing; 11.4% is the nominal rate and would mix real cash flows with a money discount rate.

📋 Objective: 4.2 (Inflation and taxation in DCF (D2))

✅ Correct answer: Tax relief on interest lowers its cost of capital

📌 Explanation: With corporation tax, Modigliani and Miller showed that interest is tax-deductible, so debt carries a tax shield. The cost of equity rises with gearing but by less than the benefit of the cheaper after-tax debt, so the weighted average cost of capital falls as gearing rises and company value increases.

❌ Why the other options are wrong: A cost of capital unaffected by gearing is Modigliani and Miller's result without tax; the cost of equity rises, not falls, as gearing increases because shareholders bear more financial risk; a steadily rising cost of capital is not the Modigliani and Miller result and conflicts with the tax shield.

📋 Objective: 5.4 (Capital structure theories and practical considerations (E4))

✅ Correct answer: 41.9%

📌 Explanation: Total depreciation = 560,000 - 80,000 = $480,000, so average annual accounting profit = (1,150,000 - 480,000) / 5 = $134,000. Average capital employed = (560,000 + 80,000) / 2 = $320,000. ROCE = 134,000 / 320,000 = 41.9%.

❌ Why the other options are wrong: 23.9% divides average profit by the initial investment of $560,000; 36.9% ignores the scrap value when calculating depreciation (profit $118,000); 47.9% halves the initial cost only ($280,000) and ignores the scrap value in average capital employed.

📋 Objective: 4.1 (Investment appraisal techniques (D1))

✅ Correct answer: Semi-strong form but not strong form

📌 Explanation: In a semi-strong form efficient market the price reflects the publicly available information, so it adjusts quickly to announcements. Insiders can still profit from unpublished information, which shows that the market is not strong form efficient.

❌ Why the other options are wrong: Weak form efficiency concerns past price movements only and does not explain the quick reaction to public news; a strong form market would prevent insiders from making abnormal gains; the fast reaction to announcements shows that the market is at least weak and semi-strong form efficient.

📋 Objective: 6.4 (Efficient market hypothesis and practical considerations (F4))

✅ Correct answer: $66,250

📌 Explanation: Expected NPV = (0.25 x 310,000) + (0.45 x 95,000) + (0.30 x -180,000) = 77,500 + 42,750 - 54,000 = $66,250. It is a probability-weighted average, and the board should also note the 30% chance of a negative NPV, which means the project involves risk and not only expected gain.

❌ Why the other options are wrong: $75,000 is the simple average of the three NPVs, which ignores the probabilities; $120,250 leaves out the negative outcome; $174,250 treats the negative outcome as if it were a gain.

📋 Objective: 4.3 (Risk and uncertainty in investment appraisal (D3))

✅ Correct answer: Banks refuse further loans because security is inadequate; Investors decline a new share issue at an acceptable price

📌 Explanation: Hard capital rationing is imposed by the external capital market: lenders will not provide more debt and investors will not subscribe to new equity on acceptable terms. Both correct answers describe funds that are unavailable to the company from outside sources.

❌ Why the other options are wrong: A fixed divisional budget, a board limit on borrowing and a management preference for steady growth are internal decisions, which is soft capital rationing, because the company could raise more funds if it chose to.

📋 Objective: 4.4 (Specific investment decisions (D4))

✅ Correct answer: 16.2%

📌 Explanation: IRR = lower rate + [NPV at lower rate / (NPV at lower rate - NPV at higher rate)] x (higher rate - lower rate) = 12% + [48,000 / (48,000 + 21,000)] x 6% = 12% + 4.17% = 16.2%. The IRR is the rate at which the NPV is zero, so it lies between the two rates tested.

❌ Why the other options are wrong: 15.0% is the midpoint of the two rates and ignores the sizes of the two NPVs; 13.8% uses the NPV at the higher rate as the numerator and so sits too near 12%; 22.7% subtracts the negative NPV the wrong way and extrapolates beyond 18%.

📋 Objective: 4.1 (Investment appraisal techniques (D1))

✅ Correct answer: 15.9%

📌 Explanation: Customers who take the discount pay 50 days earlier (60 - 10) and the company gives up 2 of every 100 invoiced. Effective annual cost = (100 / 98)^(365 / 50) - 1 = 1.0204^7.3 - 1 = 15.9%, which exceeds the 8% overdraft rate, so the discount is an expensive way to raise cash.

❌ Why the other options are wrong: 14.9% is the simple-interest approximation (2 / 98 x 365 / 50), which ignores compounding; 13.1% uses the full 60-day credit period instead of the 50 days saved; 14.6% divides the discount by the invoice value instead of the amount received (0.02 x 365 / 50).

📋 Objective: 3.2 (Managing inventories, receivables, payables and cash (C2))

✅ Correct answer: Net benefit of $36,904

📌 Explanation: Receivables fall from 18m x 60 / 365 = $2,958,904 to 18m x 40 / 365 = $1,972,603, releasing $986,301 that saves overdraft interest of 8% = $78,904. Adding the credit control saving of $120,000 and bad debts of $108,000, and deducting the fee of $270,000, gives a net benefit of $36,904.

❌ Why the other options are wrong: A net benefit of $306,904 leaves out the factor's fee; a net cost of $71,096 ignores the bad debts that the factor would bear; a net cost of $42,000 ignores the overdraft interest saved from the faster collection.

📋 Objective: 3.2 (Managing inventories, receivables, payables and cash (C2))

✅ Correct answer: 1.05%

📌 Explanation: The discount is worth offering only if its effective annual cost does not exceed 8%. Setting (1 / (1 - d))^(365 / 50) = 1.08 gives 1 - d = 1.08^(-50 / 365) = 0.98951, so d = 1.05%.

❌ Why the other options are wrong: 1.10% is the simple-interest estimate (8% x 50 / 365) that ignores compounding; 1.26% uses the full 60-day period instead of the 50 days saved; 0.21% uses the 10-day discount period instead of the 50 days saved.

📋 Objective: 3.2 (Managing inventories, receivables, payables and cash (C2))

✅ Correct answer: Confidential invoice discounting

📌 Explanation: Invoice discounting advances cash against invoices while the company keeps its own sales ledger and collects the debts. It can be confidential, so customers are unaware of the arrangement, which meets both aims and protects the customer relationship.

❌ Why the other options are wrong: Non-recourse and recourse factoring both transfer the sales ledger and collection to the factor, so the company loses credit control; supply chain finance is arranged by the customer's own bank and depends on the buyer's approval of invoices, so it does not suit the company's aim.

📋 Objective: 3.2 (Managing inventories, receivables, payables and cash (C2))

✅ Correct answer: Higher liquidity, but some sales may be lost to rivals

📌 Explanation: Working capital policy balances liquidity against profitability. A shorter credit period collects cash sooner and reduces receivables and financing costs, but customers may buy from rivals who offer longer credit, so sales and profit could fall.

❌ Why the other options are wrong: A shorter credit period does not make customers pay less punctually and would raise liquidity; receivables do carry a financing cost, so it cannot be said to be nil; sales are likely to change if terms become less attractive, so liquidity would not simply stay the same.

📋 Objective: 3.1 (Nature, elements and importance of working capital (C1))

✅ Correct answer: 13.4%

📌 Explanation: Ke = D0(1 + g) / P0 + g = (0.24 x 1.055) / 3.20 + 0.055 = 0.2532 / 3.20 + 0.055 = 0.0791 + 0.055 = 13.4%. The next dividend D1, not the dividend just paid, is the cash flow investors will receive.

❌ Why the other options are wrong: 13.0% uses the dividend just paid (D0) instead of D1; 7.9% is the dividend yield only and omits the growth rate; 10.4% is the answer from the capital asset pricing model, which is a different method.

📋 Objective: 5.2 (Estimating the cost of capital (E2))

✅ Correct answer: 10.4%

📌 Explanation: Ke = Rf + beta x (Rm - Rf) = 3.5% + 1.15 x (9.5% - 3.5%) = 3.5% + 6.9% = 10.4%. The premium for systematic risk is the equity beta multiplied by the market risk premium of 6.0%.

❌ Why the other options are wrong: 14.4% multiplies the beta by the full market return instead of the market risk premium; 6.9% is the risk premium alone and omits the risk-free rate; 8.7% divides the market risk premium by the beta instead of multiplying.

📋 Objective: 5.2 (Estimating the cost of capital (E2))

✅ Correct answer: 12.1%

📌 Explanation: After-tax cost of irredeemable debt = 6 x (1 - 0.25) / 92 = 4.89%. Market values: equity 80m x $3.20 = $256m and debt $50m x 0.92 = $46m, total $302m. WACC = (256 x 13.4% + 46 x 4.89%) / 302 = 12.1%.

❌ Why the other options are wrong: 9.6% uses the capital asset pricing model cost of equity instead of the dividend growth model figure; 12.4% uses the pre-tax cost of debt of 6.5% (6 / 92); 10.1% weights the costs by the number of shares and the nominal value of the loan notes (80m and 50m) instead of market values.

📋 Objective: 5.2 (Estimating the cost of capital (E2))

✅ Correct answer: It has more systematic risk than the market

📌 Explanation: Beta measures systematic risk, which is the sensitivity of a share's returns to movements in the market and cannot be diversified away. A beta of 1.15 means the share's returns are expected to move by more than the market's, so it carries more systematic risk than the average share.

❌ Why the other options are wrong: Unsystematic risk can be removed by diversification and is not measured by beta; a beta above 1 means more risky than the market, not less; beta measures the volatility of returns relative to the market and says nothing about the rate of earnings growth.

📋 Objective: 5.2 (Estimating the cost of capital (E2))

✅ Correct answer: Lenders rank ahead of shareholders, so bear less risk

📌 Explanation: Lenders have a prior claim on profit through interest and on assets if the company fails, and their return is contractual. Shareholders receive what remains, so they bear more risk and require a higher return, which is why the cost of equity exceeds the cost of debt.

❌ Why the other options are wrong: Fixed interest means lenders do not share in growth, so this does not explain the lower return; irredeemable notes are held for an indefinite period, not a shorter one; lenders rank ahead of shareholders and so are less, not more, exposed to business risk.

📋 Objective: 5.3 (Sources of finance and their relative costs (E3))

✅ Correct answer: £0.7541 per $1

📌 Explanation: PPP: expected spot = S0 x (1 + h sterling) / (1 + h dollar) = 0.7800 x 1.02 / 1.055 = £0.7541 per $1. Dollar inflation is higher than sterling inflation, so the dollar is expected to weaken and buy fewer pounds.

❌ Why the other options are wrong: £0.8068 applies the inflation rates the wrong way round; £0.7800 assumes the spot rate stays unchanged despite the inflation differential; £0.7527 deducts the 3.5% inflation difference from the spot rate instead of using the PPP ratio.

📋 Objective: 7.2 (Causes of exchange rate and interest rate movements (G2))

✅ Correct answer: Forward contract, by $32,955

📌 Explanation: Forward: 2,400,000 / 0.7740 = $3,100,775. Money market hedge: borrow sterling now, 2,400,000 / 1.014 = £2,366,864; convert at spot, / 0.7800 = $3,034,441; deposit dollars for three months at 4.4% / 4, x 1.011 = $3,067,820. The forward contract gives $32,955 more.

❌ Why the other options are wrong: The money market hedge is not better, so choosing it by $32,955 reverses the comparison; a forward advantage of $58,817 comes from using the annual interest rates instead of three-month rates in the money market hedge; a forward advantage of $19,280 comes from wrongly using the sterling deposit rate instead of the sterling borrowing rate.

📋 Objective: 7.3 (Hedging foreign currency risk (G3))

✅ Correct answer: It falls because the home currency strengthens

📌 Explanation: Higher interest rates attract foreign capital, which raises demand for the home currency and strengthens it. A stronger home currency buys more pounds, so each pound received is worth fewer units of home currency, and the value of the sterling receipts falls.

❌ Why the other options are wrong: Higher rates strengthen, not weaken, the home currency; the receipts are fixed in sterling but their home-currency value changes with the exchange rate; more attractive sterling deposits would only follow if UK rates rose relative to home rates.

📋 Objective: 2.1 (The economic environment for business (B1))

✅ Correct answer: A short-term treasury bill

📌 Explanation: Treasury bills are discount instruments: they are issued below their face value and redeemed at face value, so the investor's return is the difference. They are short-term, low-risk securities that suit temporary cash surpluses.

❌ Why the other options are wrong: A certificate of deposit is an interest-bearing instrument that pays interest on the amount deposited; an interest rate swap is a derivative used to manage interest rate risk, not a security bought for a surplus; a fixed-rate government bond pays coupons and has a long maturity.

📋 Objective: 2.3 (Money markets (B3))

✅ Correct answer: Take out export credit insurance on the debt

📌 Explanation: Non-payment is a credit risk on a foreign receivable. Export credit insurance pays the exporter if the customer defaults, so it directly addresses the risk, while the other choices deal with exchange rates or the timing of payment.

❌ Why the other options are wrong: Invoicing in dollars moves the exchange rate risk to the customer but does not protect against default; a settlement discount speeds up payment but does not remove default risk; buying sterling forward is the wrong way round for a sterling receipt and hedges exchange rate risk only.

📋 Objective: 3.2 (Managing inventories, receivables, payables and cash (C2))

Net present value of Product M4 (nominal terms, $)

NPV = $234,198 (about $234,200; 234,199 if the lines are not rounded) (the sum of the present values less the initial investment).

W1 Sales revenue: year 1 = 9,000 panels x $356 x 1.03 = $3,300,120; year 2 = 12,000 x $356 x 1.03² = $4,532,165; year 3 = 14,000 x $356 x 1.03³ = $5,446,151; year 4 = 10,000 x $356 x 1.03⁴ = $4,006,811.

W2 Variable costs: year 1 = 9,000 x $230 x 1.045 = $2,163,150, then $3,013,989, $3,674,555 and $2,742,793 using 1.045 raised to the power of the year.

W3 Fixed costs: $400,000 x 1.05 = $420,000 in year 1, then $441,000, $463,050 and $486,203.

W4 Tax-allowable depreciation: year 1 claim 20% x $2,600,000 = $520,000, a tax benefit of $130,000; year 2 claim $416,000, benefit $104,000; year 3 claim $332,800, benefit $83,200. The tax written-down value at the end of year 3 is $1,331,200, so the balancing allowance in year 4 is $1,331,200 - $500,000 = $831,200, a tax benefit of $207,800. Tax in year 1 = 25% x $716,970 = $179,243 (179,242.5 before rounding, so 179,242 if rounded down).

Advice: the project has a positive NPV of $234,198, so it earns more than the 13% cost of capital and the company should accept it, because it is expected to increase shareholder wealth. The NPV is only about 9% of the investment, so the board should test the forecasts of price and demand before it commits.

📋 Objective: 4.2 (Inflation and taxation in DCF (D2))

The sensitivity of the NPV to the selling price is the NPV divided by the present value of the after-tax sales revenue. The present value of the after-tax sales revenue is 2,190,455 + 2,661,514 + 2,830,637 + 1,842,131 = $9,524,737, because each year's revenue is multiplied by (1 - 0.25) and discounted at 13%.

Sensitivity = 234,198 / 9,524,737 = 0.0246, so the selling price could fall by 2.5% (2.46% before rounding), that is, 2.5 per cent, in every year before the NPV becomes zero.

This is a very small margin of safety. The NPV is very sensitive (highly sensitive) to price, and the selling price is a critical variable, and the sales director's concern is serious: a price cut of only a few per cent would make the project unattractive, so the board should look closely at the competition from importers.

📋 Objective: 4.3 (Risk and uncertainty in investment appraisal (D3))

Probability analysis would give the board a range of outcomes instead of one forecast. Management would estimate probabilities for different selling prices and demand levels, for example a high, expected and low case for the irrigation tender, and calculate an expected NPV, the probability-weighted average. It would also show the chance of a negative NPV, which speaks directly to the operations director's concern about volumes. Its weakness is that the probabilities are usually subjective, and the expected value is an average that may never occur for a one-off investment.

Simulation, often called Monte Carlo analysis, would go further. A computer model would draw random values for price, volume and costs from their probability ranges, calculate the NPV each time and repeat this many times. The result is a distribution of NPV, showing the range of outcomes and the chance of a negative NPV, and it allows for price and demand moving together, which sensitivity analysis on one variable cannot do. Its drawbacks are the cost of building the model and its reliance on the quality of the assumptions.

📋 Objective: 4.3 (Risk and uncertainty in investment appraisal (D3))

Economic order quantity: EOQ = square root of (2 x 60 x 48,000 / 1.80) = square root of 3,200,000 = 1,789 packs (1,788.9 before rounding). This means 48,000 / 1,789 = 26.8 orders a year.

Annual cost at the EOQ: ordering cost = 26.8 orders x $60 = $1,610; holding cost = (1,789 / 2) x $1.80 = $1,610; relevant costs = $3,220. Purchases = 48,000 x $9.00 = $432,000, so the total annual cost = $435,220.

Annual cost with the discount, ordering 3,000 packs at a time: purchases = 48,000 x $9.00 x 0.98 = $423,360; ordering cost = (48,000 / 3,000) x $60 = $960; holding cost = (3,000 / 2) x $1.80 = $2,700; total annual cost = $427,020.

Advice: the discount saves $8,200 a year ($435,220 less $427,020), because the saving on purchases far outweighs the extra holding cost. The company should accept the discount and order 3,000 packs at a time (take the discount), provided the packs do not reach their expiry date before they are sold and the stores can hold the larger quantity.

📋 Objective: 3.2 (Managing inventories, receivables, payables and cash (C2))

Inventory days = 6,900,000 / 38,000,000 x 365 = 66.3 days (66.28, about 66 days).

Receivables days = 3,900,000 / 24,000,000 x 365 = 59.3 days (59.31, about 59 days).

Payables days = 4,400,000 / 38,000,000 x 365 = 42.3 days (42.26, about 42 days).

Cash operating cycle = 66.3 + 59.3 - 42.3 = 83.3 days (83.33), about 83 days.

📋 Objective: 3.2 (Managing inventories, receivables, payables and cash (C2))

Paying suppliers 15 days later. Extra credit from suppliers is an interest-free source of finance, so it lengthens the payables period, shortens the cash operating cycle by 15 days and reduces the need for borrowing. However, paying late can damage supplier goodwill, and the company might lose any settlement discount it now receives. Suppliers might restrict or stop supply of medicines, and the company's credit rating could suffer, which are serious risks for a business that depends on reliable stock.

Deliveries twice a week. Cutting inventory to 45 days reduces the cash tied up in stock, lowers holding costs and reduces the risk that medicines pass their expiry date. However, more frequent deliveries raise delivery costs and ordering costs, and a supplier failure or a late delivery would cause stock shortages in a pharmacy, leading to lost sales and unhappy patients. The proposal is safer than paying suppliers late, provided the supplier is reliable, but the company should compare the extra delivery costs with the interest saved on the cash released.

📋 Objective: 3.3 (Working capital needs and funding strategies (C3))