CPA(U) FM Exam 1

Relevant cash flows: the Shs 45m market survey is a sunk cost and is excluded. The Shs 60m rent given up is an opportunity cost and is deducted each year (it is taxable, so it reduces taxable cash flow).

Net present value (Shs'000)

NPV = +768893 (about 768900 in Shs'000, roughly Shs 769 million).

W1 Capital allowances (25% reducing balance): year 1 = 25% × 2560000 = 640000; year 2 = 480000; year 3 = 360000; year 4 = 270000. Tax written-down value at the end of year 4 = 810000, so the balancing allowance in year 5 = 810000 − 250000 = 560000. Tax saved at 30% = 192000, 144000, 108000, 81000 and 168000.

W2 Working capital: revenue = litres × 2200, giving 4400000, 5720000, 6600000, 6600000 and 5280000. Requirement at 10% = 440000, 572000, 660000, 660000, 528000. Increments: 440000 at year 0, 132000 at year 1, 88000 at year 2, nil at year 3, a release of 132000 at year 4 and the remaining 528000 recovered at the end of year 5. Working capital flows are not taxed.

Advice: the NPV is positive at the 15% cost of capital, so the UHT line adds about Shs 769m to shareholder value and should be accepted, subject to the risks discussed in part (d).

📋 Objective: 4.6 (Impact of taxation and working capital on appraisal)

Present values at 25% (Shs'000): year 1 683000 × 0.800 = 546400; year 2 973000 × 0.640 = 622720; year 3 1221000 × 0.512 = 625152; year 4 1326000 × 0.410 = 543660; year 5 1765000 × 0.328 = 578920. Total present value 2916852, so the NPV at 25% = 2916852 − 3000000 = −83148.

By linear interpolation: IRR = 15% + [768893 / (768893 + 83148)] × 10% = 15% + 9.02% = 24.02%, about 24.0%.

Evaluation: the IRR of about 24.0% exceeds the 15% cost of capital, which is consistent with the positive NPV. The margin of safety is about 9 percentage points, so the discount rate could rise substantially before the project stopped adding value. Interpolation over a 10-point range gives an approximation only.

📋 Objective: 4.5 (Investment appraisal techniques)

Simple payback (Shs'000): cumulative net cash flow: year 0 −3000000; year 1 −2317000; year 2 −1344000; year 3 −123000; year 4 +1203000. Payback = 3 + 123000 / 1326000 = 3.09 years, about 3 years 1 month. This fails the 3-year target, but only marginally (by about one month).

Discounted payback: cumulative present values at 15%: year 1 −2405790; year 2 −1670202; year 3 −866784; year 4 −108312; year 5 +768893. Discounted payback = 4 + 108312 / 877205 = 4.12 years, about 4 years 1.5 months. This is within the 5-year life, so the second target is met.

Advice: the line fails marginally on simple payback yet recovers its outlay in present value terms within its life and has a large positive NPV. The board should not reject it on the 3-year rule alone; payback should be used as a liquidity screen alongside NPV.

📋 Objective: 4.5 (Investment appraisal techniques)

Net present value: NPV is the most reliable method because it uses relevant cash flows, allows for the time value of money and measures the absolute increase in shareholder wealth (about Shs 769m here). Its weaknesses are that the 15% cost of capital is hard to estimate and the answer depends on volume and price forecasts five years ahead.

Internal rate of return: the director's wish for a single percentage is met by the IRR of about 24%, which managers and bankers understand easily. However, the IRR assumes cash flows are reinvested at the IRR itself, it can rank mutually exclusive projects of different size wrongly, and non-conventional cash flows can give multiple IRRs. Where NPV and IRR conflict, NPV should prevail.

Payback and discounted payback: the chairman's concern about liquidity is valid, and payback is simple and favours early cash recovery, which reduces risk. But it ignores cash flows after the payback point (the large year 5 flow and the released working capital) and the simple version ignores timing. Discounted payback corrects timing but still ignores later flows, so neither measures value.

Recommendation and other factors: the board should accept the line on its positive NPV and use payback only as a secondary screen. Before committing it should consider (1) milk volumes in dry seasons, securing supply contracts with farmer groups; (2) sensitivity analysis on price, volume and the variable cost per litre; (3) competition from established long-life milk brands in Kampala; and (4) the exchange rate risk on export sales to South Sudan and on imported carton materials, together with how the Shs 3 billion outlay will be financed.

📋 Objective: 4.7 (Merits and demerits of each appraisal method)

Cash budget, January to March (GHS)

Purchases paid in January relate to December purchases, which were 65% of January sales (65% × 380000 = 247000); February and March follow the same pattern. The 2% irrecoverable debts are never received.

Advice: the January balance is comfortable, but the February balance of 17560 is 32440 below the GHS 50,000 minimum and March is still 2200 short. The shortfall is caused mainly by paying for the equipment in one sum. The treasurer should arrange a short overdraft facility in advance, negotiate instalment terms or a lease for the equipment, or sell some treasury bills in February, and then rebuild the balance in March.

📋 Objective: 7.10 (Cash flow planning and cash management)

Baumol optimal conversion amount: Q = √(2 × 5400000 × 160 / 0.12) = √14400000000 = GHS 120000.

Number of sales a year = 5400000 / 120000 = 45 sales. Transaction cost = 45 × 160 = 7200. Holding (interest forgone) cost = (120000 / 2) × 12% = 7200. Total cost = GHS 14400.

Present policy: 5400000 / 300000 = 18 sales, costing 18 × 160 = 2880; average cash 150000 × 12% = 18000 interest forgone; total GHS 20880.

Evaluation: moving to conversions of GHS 120000 saves 20880 − 14400 = GHS 6480 a year. The saving is real but modest relative to the group's cash flows, so it is worth adopting provided the extra transactions are easy to administer.

📋 Objective: 7.10 (Cash flow planning and cash management)

Limitations: the model assumes payments are certain and occur at a steady rate, but pharmacy payments are lumpy (equipment and tax instalments) and receipts are uncertain, so a buffer is still needed. It also assumes a fixed fee per sale and a constant bill yield.

Recommendation for February: negotiate to defer or spread the equipment payment, or arrange short-term borrowing such as an agreed overdraft for the few weeks needed, rather than disposing of a large block of bills at an unplanned time.

📋 Objective: 7.10 (Cash flow planning and cash management)

Growth rate from past dividends: g = (4.20 / 3.10)^(1/4) − 1 = 1.0789 − 1 = 7.89% (about 7.9%).

Next year's dividend D1 = 4.20 × 1.0789 = KES 4.53.

Cost of equity by the dividend growth model: Ke = D1 / P0 + g = 4.53 / 52.00 + 0.0789 = 0.0871 + 0.0789 = 16.60%, about 16.6%.

The ex-dividend price is used because the dividend just paid will not be received by a new investor.

📋 Objective: 10.7 (Cost of capital and its relevance to investment decisions)

Cost of irredeemable debentures: Kd = I(1 − T) / P0 = 12 × 0.70 / 96 = 8.75%.

Cost of the bank loan: 11% × (1 − 0.30) = 7.70%.

Market values (KES million): equity 40 × 52 = 2080; debentures 600 × 0.96 = 576 million; bank loan 250. Total 2906.

WACC = (2080 × 16.60% + 576 × 8.75% + 250 × 7.7%) / 2906 = 14.28%, about 14.3%. Market value weights are used because they reflect the current opportunity cost of each investor group.

📋 Objective: 10.7 (Cost of capital and its relevance to investment decisions)

Dividend growth model: it assumes constant growth in perpetuity, but the 7.89% is extrapolated from historical dividends over only four years and may not continue. The model is very sensitive to g, ignores changes in dividend policy and cannot be used if growth exceeds the cost of equity.

Using the WACC for the Juja warehouse: 14.28% is appropriate only if the project has the same business risk as existing warehousing and the capital structure (gearing) does not change. A cold-chain facility may be riskier, and KES 300 million is about 10% of the company's market value, so the marginal cost of new finance might differ. The directors should adjust the rate or use a risk-adjusted rate if these conditions fail.

📋 Objective: 10.7 (Cost of capital and its relevance to investment decisions)

Prohibition of riba: money must not earn a predetermined return simply for being lent, so the fixed interest and penalty charges on the current loans are not permitted.

Avoidance of gharar: contracts must avoid excessive uncertainty, so the price, asset and terms must be clearly specified.

No maisir or haram activity: speculation and gambling are forbidden, and funds may not go to unlawful sectors such as alcohol; leather processing is acceptable.

Asset-backed transactions: every financing must relate to an underlying asset or real trade, with proper contract documentation.

Profit and loss sharing: the provider of funds earns a return by sharing the risk of the venture rather than by guaranteed interest.

📋 Objective: 6.7 (Principles of Islamic finance)

Need 1, skins and chemicals: murabahah. The bank buys the skins and chemicals, takes title, and resells them to the company at cost plus the disclosed mark-up, payable in six months. This is a cost-plus sale, not a loan. Deferred price = 80000000 × 1.09 = NGN 87200000, a profit to the bank of 7200000. The price is fixed at the outset and cannot be increased if the company pays late.

Need 2, drums and wastewater unit: ijarah. The bank buys the equipment and leases it to the company for agreed rentals. The bank, as lessor, keeps ownership and bears the risks of ownership (major repairs, insurance), while the company bears day-to-day maintenance. An ijarah wa iqtina form can transfer the equipment to Sokoto at the end of ten years.

Need 3, new division: musharakah. The bank and the company form a partnership with a capital contribution of 60% and 40%. Profits are shared in an agreed ratio, which may differ from the capital shares, but losses must be borne in proportion to capital. A diminishing musharakah would let the company buy out the bank's units over time.

📋 Objective: 6.10 (Modes of Islamic finance)

Under the conventional loans the bank is a creditor and the company a debtor: the bank earns fixed interest whatever the tannery's results, takes security, and charges compound penalties on late payment.

Under Islamic finance the bank acts as trader, lessor or partner. In murabahah and ijarah it owns the asset for a time and bears asset risk; in musharakah it is an investor and shares the risk of loss. A debtor in genuine hardship must be given time to pay rather than charged extra, and any late-payment charge goes to charity. So the arrangements are not simply relabelled loans, although the cost may look similar.

📋 Objective: 6.5 (Islamic versus conventional modes of finance)