Chapter 4 DCF with Inflation and Taxation



ACCA F9

Financial Management

Premium Class

Session 3 and 4

Patrick Lui

hklui2007@.hk

| |

Chapter 5 DCF with Inflation and Taxation

|SYLLABUS |

| |

|1. Apply and discuss the real-terms and nominal-terms approaches to investment appraisal. |

|2. Calculate the taxation effects of relevant cash flows, including the tax benefits of capital allowances and the tax liabilities of |

|taxable profit. |

|3. Calculate and apply before- and after-tax discount rates. |

[pic]

1. Inflation

(Pilot, Jun 08, Jun 09, Dec 10, Jun 11, Jun 12, Dec 12, Jun 13, Dec 13, Jun 14, Dec 14, Jun 15)

1.1 Specific and general inflation

1.1.1 It is important to adapt investment appraisal methods to cope with the phenomenon of price movement. Future rates of inflation are unlikely to be precisely forecasted; nevertheless, we will assume in the analysis that follows that we can anticipate inflation with reasonable accuracy.

1.1.2 Two types of inflation can be distinguished.

(a) Specific inflation refers to the price changes of an individual good or service.

(b) General inflation is the reduced purchasing power of money and is measured by an overall price index which follows the price changes of a ‘basket’ of goods and services through time.

Even if there was no general inflation, specific items and sectors might experience price rises.

[pic]

1.1.3 Inflation creates two problems for project appraisal.

(a) The estimation of future cash flows is made more troublesome. The project appraiser will have to estimate the degree to which future cash flows will be inflated.

(b) The rate of return required by the firm’s security holders, such as shareholders, will rise if inflation rises. Thus, inflation has an impact on the discount rate used in investment evaluation.

1.2 Real and money interest rate

(Pilot, Jun 10, Dec 13)

1.2.1 The money (nominal or market) interest rate incorporates inflation. When the nominal rate of interest is higher than the rate of inflation, there is a positive real rate. When the rate of inflation is higher than the nominal rate of interest, the real rate of interest will be negative.

|1.2.2 |Fisher’s (1930) Equation |

| |The generalized relationship between real rates of interest and nominal rate of interest is expressed as follow under |

| |Fisher’s equation: |

| | |

| |(1 + i) = (1 + r) (1 + h) |

| | |

| |Where h = inflation rate |

| |r = real interest rate |

| |i = nominal interest rate |

|1.2.3 |EXAMPLE 1 |

| |$1,000 is invested in an account that pays 10% interest pa. Inflation is currently 7% pa. Find the real return on the |

| |investment. |

| | |

| |Solution: |

| | |

| |Real return = $1,000 × 1.1/1.07 = $1.028. A return of 2.8%. |

|1.2.4 |Test your understanding 1 |

| |If the real rate of interest is 8% and the rate of inflation is 5%, what should the money rate of interest be? |

|Solution: |

| |

| |

1.3 Money cash flows and real cash flows

(Jun 13, Dec 13)

1.3.1 We have now established two possible discount rates, the money discount rate and the real discount rate. There are two alternative ways of adjusting for the effect of future inflation on cash flows.

(a) The first is to estimate the likely specific inflation rates for each of the inflows and outflows of cash and calculate the actual monetary amount paid or received in the year that the flow occurs. This is the money (nominal) cash flow.

(b) The other possibility is to measure the cash flows in terms of real prices. That is, all future cash flows are expected in terms of, say, Time 0’s prices. With real cash flows, future cash flows are expressed in terms of constant purchasing power.

|1.3.2 |EXAMPLE 2 |

| |Storm Co is evaluating Project X, which requires an initial investment of $50,000. Expected net cash flows are $20,000 pa |

| |for four years at today’s prices. However these are expected to rise by 5.5% pa because of inflation. The firm’s cost of |

| |capital is 15%. Find the NPV by: |

| | |

| |(a) discounting money cash flows |

| |(b) discounting real cash flows. |

| | |

| |Solution: |

| | |

| |(a) Discounting money cash flow at the money rate: The cash flows at today’s prices are inflated by 5.5% for every year to |

| |take account of inflation and convert them into money flows. They are then discounted using the money cost of capital. |

| |[pic] |

| | |

| |Note: The question simply refers to the ‘firm’s cost of capital’. You can assume this is the money rate – if you are given |

| |a real rate the examiner will always specify. |

| | |

| |Time |

| |Money cash flow ($) |

| |Discount rate |

| |@ 15% |

| |PV ($) |

| | |

| |0 |

| |(50,000) |

| |1 |

| |(50,000) |

| | |

| |1 |

| |21,100 |

| |0.870 |

| |18,357 |

| | |

| |2 |

| |22,261 |

| |0.756 |

| |16,829 |

| | |

| |3 |

| |23,485 |

| |0.658 |

| |15,453 |

| | |

| |4 |

| |24,776 |

| |0.572 |

| |14,172 |

| | |

| | |

| | |

| |NPV = |

| |14,811 |

| | |

| | |

| |(b) |

| |Calculate the real rate by removing the general inflation from the money cost of capital: |

| |(1 + r) = (1 + i) / (1 + h) |

| |= (1 + 15%) / (1 + 5.5%) |

| |= 1.09 |

| |r = 9% |

| | |

| |The real rate can now be applied to the real flows without any further adjustments. |

| |Time |

| |Real cash flow ($) |

| |Discount rate |

| |@ 9% |

| |PV ($) |

| | |

| |0 |

| |(50,000) |

| |1.000 |

| |(50,000) |

| | |

| |1 – 4 |

| |20,000 |

| |3.240 |

| |64,800 |

| | |

| | |

| | |

| |NPV = |

| |14,800 |

| | |

| | |

| |Note: Differences due to rounding. |

1.3.3 In situations where you are given a number of specific inflation rates, the real method outlined above cannot be used.

1.3.4 The following gives a useful summary of how to approach examination questions.

[pic]

1.3.5 If a question contains both tax and inflation, it is advisable to use the money method.

|Multiple Choice Questions |

| |

|I. Inflation |

| |

|1. When appraising investment projects using discounted cash flow methods, two approaches to dealing with inflation could be used. |

|These are: |

| |

|1. to exclude inflation from the estimated future cash flows and to apply a discount rate based on the money cost of capital. |

|2. to include inflation in the estimated future cash flows and to apply a discount based on the real cost of capital. |

| |

|Which ONE of the following combinations (true/false) concerning the above statements is correct? |

| |

| |

|Statement 1 |

|Statement 2 |

| |

|A |

|True |

|True |

| |

|B |

|True |

|False |

| |

|C |

|False |

|True |

| |

|D |

|False |

|False |

| |

| |

|2. To deal with the effect of inflation when appraising investment projects, two possible approaches can be used. These are: |

| |

|1. To exclude inflation from the estimated future cash flows and to apply a discount rate expressed in real terms. |

|2. To adjust the estimated future cash flows by the relevant rates of inflation and to adjust the discount rate to reflect current |

|market rates. |

| |

|Which one of the following combinations is correct? |

| |

| |

|Statement 1 |

|Statement 2 |

| |

|A |

|True |

|True |

| |

|B |

|True |

|False |

| |

|C |

|False |

|True |

| |

|D |

|False |

|False |

| |

| |

| |

|3. The one year rate of inflation is expected to be 3·0%. The one year money rate of interest is 6·3%. |

| |

|The one year real rate of interest is: |

| |

|A 3·30% |

|B 3·20% |

|C 9·30% |

|D 9·49%. |

| |

|4. Dunlin plc is examining an investment opportunity that will lead to savings in staff costs. The company uses the net present value |

|method of investment appraisal based on cash flows expressed in real terms. Staff costs are expected to rise at a rate of 5% each year,|

|whereas the general rate of inflation is expected to rise at a rate of 3% each year. The company has a required rate of return of 10%, |

|assuming no inflation. |

| |

|What is the appropriate discount rate to use when evaluating the investment opportunity? |

| |

|A 10% |

|B 13% |

|C 13·3% |

|D 15·5%. |

| |

|5. Consider the following statements. |

| |

|When using the net present value method of investment appraisal, the required rate of return from investors is used as the appropriate |

|discount factor. This rate of return should be: |

| |

|(1) calculated on an after-tax basis |

|(2) expressed in real terms if the cash flows are expressed in terms of the actual number of dollars to be received. |

| |

|Which one of the following combinations (true/false) concerning the above statements is correct? |

| |

| |

| |

|Statement 1 |

|Statement 2 |

| |

|A |

|True |

|True |

| |

|B |

|True |

|False |

| |

|C |

|False |

|True |

| |

|D |

|False |

|False |

| |

| |

|6. A project consists of a series of cash outflows in the first few years followed by a series of positive cash inflows. The total cash|

|inflows exceed the total cash outflows. The project was originally evaluated assuming a zero rate of inflation. |

| |

|If the project were re-evaluated on the assumption that the cash flows were subject to a positive rate of inflation, what would be the |

|effect on the payback period and the internal rate of return? |

| |

| |

|Payback |

|IRR |

| |

|A |

|Increase |

|Increase |

| |

|B |

|Decrease |

|Decrease |

| |

|C |

|Decrease |

|Increase |

| |

|D |

|Increase |

|Decrease |

| |

| |

|7. Spotty Ltd plans to purchase a machine costing $18,000 to save labour costs. Labour savings would be $10,000 in the first year and |

|labour rates in the second year will increase by 10%. The estimated average annual rate of inflation is 9% and the company’s real cost |

|of capital is estimated at 11%. The machine has a two year life with an estimated actual salvage value of $5,000 receivable at the end |

|of year 2. All cash flows occur at the year end. |

| |

|What is the NPV (to the nearest $10) of the proposed investment? |

| |

|A $50 |

|B $270 |

|C $370 |

|D $1,430 |

| |

| |

| |

| |

| |

|8. A project has an initial outflow at year 0 when an asset is bought, then a series of revenue inflows at the end of each year, and |

|then finally sales proceeds from the sale of the asset. Its NPV is $12,000 when general inflation is zero % per year. |

| |

|If general inflation were to be rise to 7% per year, and all revenue inflows were subject to this rate of inflation but the initial |

|expenditure and resale value of the asset were not subject to inflation, what would happen to the NPV? |

| |

|A The NPV would remain the same |

|B The NPV would rise |

|C The NPV would fall |

|D The NPV could rise or fall |

| |

|9. Data of relevance to the evaluation of a particular project is given below. |

| |

|Cost of capital in real terms 10% per annum |

|Expected inflation 5% per annum |

|Expected increase in the project's annual cash inflow 6% per annum |

|Expected increase in the project's annual cash outflow 4% per annum |

| |

|Which one of the following sets of adjustments will lead to the correct NPV being calculated? |

| |

| |

|Cash inflow |

|Cash outflow |

|Discount % |

| |

|A |

|Unadjusted |

|Unadjusted |

|10.0% |

| |

|B |

|5% pa increase |

|5% pa increase |

|15.5% |

| |

|C |

|6% pa increase |

|4% pa increase |

|15.0% |

| |

|D |

|6% pa increase |

|4% pa increase |

|15.5% |

| |

2. Taxation and Investment Appraisal

(Pilot, Jun 07, Dec 07, Jun 08, Dec 08, Jun 10, Dec 10, Jun 11, Dec 11, Jun 12, Dec 12, Jun 13, Dec 13, Jun 14, Dec 14, Jun 15)

2.1 Tax payable

2.1.1 Taxation can have an important impact on project viability. If management are implementing decisions that are shareholder wealth enhancing, they will focus on the cash flows generated which are available for shareholders. Therefore, they will evaluate the after-tax cash flows of a project.

2.1.2 Payments of tax, or reductions of tax payments, are cash flows and ought to be considered in DCF analysis. Assumptions which may be stated in questions are as follows.

(a) Tax is payable in the year following the one in which the taxable profits are made. Thus, if a project increases taxable profits by $10,000 in year 2, there will be a tax payment, assuming tax at 30%, of $3,000 in year 3.

(b) Net cash flows from a project should be considered as the taxable profits (not just the taxable revenues) arising from the project.

2.2 Capital allowances (tax-allowable depreciation, or writing down allowances (WDAs) or depreciation allowances)

2.2.1 Writing down allowance is used to reduce taxable profits, and the consequent reduction in a tax payment should be treated as a cash saving from the acceptance of a project.

|2.2.2 |EXAMPLE 3 |

| |ABC Ltd is considering a project which will require the purchase of a machine for $1,000,000 at time zero. This machine |

| |will have a scrap value at the end of its four-year life: this will be equal to its written-down value. Inland Revenue |

| |Department (IRD) permits a 25% declining balance writing-down allowance on the machine each year. Corporation tax, at a |

| |rate of 30% of taxable income, is payable. ABC Ltd’s required rate of return is 12%. Operating cash flows, excluding |

| |depreciation, and before taxation, are forecast to be: |

| | |

| | |

| | |

| | |

| |Time (year) |

| |1 |

| |2 |

| |3 |

| |4 |

| | |

| | |

| |$ |

| |$ |

| |$ |

| |$ |

| | |

| |Cash flows before tax |

| |400,000 |

| |400,000 |

| |220,000 |

| |240,000 |

| | |

| |Note: All cash flows occur at year ends. |

| | |

| |In order to calculate the NPV, first calculate the annual WDA. Note that each year the WDA is equal to 25% of the asset |

| |value at the start of the year. |

| | |

| |Years |

| |Annual WDA ($) |

| |Written-down value ($) |

| | |

| |0 |

| |0 |

| |1,000,000 |

| | |

| |1 |

| |1,000,000 × 25% = 250,000 |

| |750,000 |

| | |

| |2 |

| |750,000 × 25% = 187,500 |

| |562,500 |

| | |

| |3 |

| |562,500 × 25% = 140,625 |

| |421,875 |

| | |

| |4 |

| |421,875 × 25% = 105,469 |

| |316,406 |

| | |

| | |

| |The next step is to derive the project’s incremental taxable income and to calculate the tax payments. |

| | |

| |Time (year) |

| |1 |

| |2 |

| |3 |

| |4 |

| | |

| | |

| |$ |

| |$ |

| |$ |

| |$ |

| | |

| |Net income before WDA and tax |

| |400,000 |

| |400,000 |

| |220,000 |

| |240,000 |

| | |

| |Less: WDA |

| |250,000 |

| |187,500 |

| |140,625 |

| |105,469 |

| | |

| |Taxable profit |

| |150,000 |

| |212,500 |

| |79,375 |

| |134,531 |

| | |

| |Tax payable at 30% |

| |45,000 |

| |63,750 |

| |23,813 |

| |40,359 |

| | |

| | |

| |Finally, the total cash flows and NPV are calculated. |

| | |

| |Time (year) |

| |0 |

| |1 |

| |2 |

| |3 |

| |4 |

| | |

| | |

| |$ |

| |$ |

| |$ |

| |$ |

| |$ |

| | |

| |Incremental cash flow before tax |

| | |

| |(1,000,000) |

| | |

| |400,000 |

| | |

| |400,000 |

| | |

| |220,000 |

| | |

| |240,000 |

| | |

| |Sale of machine |

| | |

| | |

| | |

| | |

| |316,406 |

| | |

| |Tax payable |

| |0 |

| |(45,000) |

| |(63,750) |

| |(23,813) |

| |(40,359) |

| | |

| |Net cash flows |

| |(1,000,000) |

| |355,000 |

| |336,250 |

| |196,187 |

| |516,047 |

| | |

| |Discount factor @12% |

| |1.0000 |

| |0.8929 |

| |0.7972 |

| |0.7118 |

| |0.6355 |

| | |

| |Discounted cash flow |

| |(1,000,000) |

| |316,980 |

| |268,059 |

| |139,646 |

| |327,948 |

| | |

| | |

| |NPV = $52,633 |

| | |

| |The assumption that machine can be sold at the end of the fourth year, for an amount equal to the written-down value, may |

| |be unrealistic. It may turn out that the machine is sold for the larger sum of $440,000. If this is the case, a balancing |

| |charge will need to be made, because by the end of the third year IRD have already permitted write-offs against taxable |

| |profit such that the machine is shown as having a written-down value of $421,875. A year later its market value is found to|

| |be $440,000. The balancing charge is equal to the sale value at Time 4 minus the written-down value at Time 3, viz: |

| | |

| |$440,000 – $421,875 = $18,125 |

| | |

| |Taxable profits for year 4 are now: |

| | |

| |$ |

| | |

| |Pre-tax cash flows |

| |240,000 |

| | |

| |Plus balancing charge |

| |18,125 |

| | |

| | |

| |258,125 |

| | |

| | |

| |This result in a tax payment of $258,125 × 0.3 = $77,438 rather than $40,359. |

| | |

| |Of course, the analyst does not have to wait until the actual sale of the asset to make these modifications to a proposed |

| |project’s projected cash flows. It may be possible to estimate a realistic scrap value at the outset. |

| | |

| |An alternative scenario, where the scrap value is less than the Year 4 written-down value, will require a balancing |

| |allowance. If the disposal value is $300,000 then the machine cost the firm $700,000 ($1,000,000 – $300,000) but the tax |

| |written-down allowances amount to only $683,594 ($1,000,000 – $316,406). The firm will effectively be overcharged by IRD. |

| |In this case a balancing adjustment, amount to $16,406 ($700,000 – $683,594), is made to reduce the tax payable. |

| | |

| | |

| |$ |

| | |

| |Pre-tax cash flows |

| |240,000 |

| | |

| |Less: Annual writing-down allowance |

| |(105,469) |

| | |

| |Less: Balancing allowance |

| |(16,406) |

| | |

| |Taxable profits |

| |118,125 |

| | |

| |Tax payable @ 30% |

| |35,438 |

| | |

|Multiple Choice Questions |

| |

|II. Taxation |

| |

|10. A company has 31 December as its accounting year end. On 1 January 2014 a new machine costing $2,000,000 is purchased. The company |

|expects to sell the machine on 31 December 2015 for $350,000. |

| |

|The rate of corporation tax for the company is 30%. Tax-allowable depreciation is obtained at 25% on the reducing balance basis, and a |

|balancing allowance is available on disposal of the asset. The company makes sufficient profits to obtain relief for capital allowances|

|as soon as they arise. |

| |

|If the company’s cost of capital is 15% per annum, what is the present value of the tax-allowable depreciation at 1 January 2014 (to |

|the nearest thousand dollars)? |

| |

|A $391,000 |

|B $248,000 |

|C $263,000 |

|D $719,000 |

| |

|11. Jones Ltd plans to spend $90,000 on an item of capital equipment on 1 January 2012. The expenditure is eligible for 25% |

|tax-allowable depreciation, and Jones pays corporation tax at 30%. Tax is paid at the end of the accounting period concerned. The |

|equipment will produce savings of $30,000 per annum for its expected useful life deemed to be receivable every 31 December. The |

|equipment will be sold for $25,000 on 31 December 2015. Jones has a 31 December year end and has a 10% post-tax cost of capital. |

| |

|What is the present value at 1 January 2012 of the tax savings that result from the capital allowances? |

| |

|A $13,170 |

|B $15,826 |

|C $16,018 |

|D $19,827 |

| |

| |

|12. A company receives a perpetuity of $20,000 per annum in arrears, and pays 30% corporation tax 12 months after the end of the year |

|to which the cash flows relate. |

| |

|At a cost of capital of 10%, what is the after tax present value? |

| |

|A $140,000 |

|B $145,460 |

|C $144,000 |

|D $127,274 |

| |

|13. A project has an annual net cash inflow (in current terms) of $3 million, occurring at the end of each year of the project's two |

|year life. An investment of $3.5 million is made at the outset. All cash inflows are subject to corporation tax of 30%, payable when |

|the cash is received. There is no tax allowable depreciation on the initial investment. An average inflation rate of 5% per annum is |

|expected to affect the inflows of the project. |

| |

|The cost of capital in money terms is 15.5% |

| |

|What is the expected net present value of the project (to the nearest $100)? |

| |

|A $92,600 |

|B $145,970 |

|C $286,600 |

|D $367,400 |

| |

|14. An asset costing $40,000 is expected to last for three years, after which is can be sold for $16,000. The corporation tax rate is |

|30%, tax allowable depreciation at 25% is available, and the cost of capital is 10%. Tax is payable at the end of each financial year. |

| |

|Capital expenditure occurs on the last day of a financial year, and the tax allowable depreciation is claimed as early as possible. |

| |

|What is the cash flow in respect of tax allowable depreciation that will be used at time 2 of the net present value calculation? |

| |

| |

|A $1,688 |

|B $2,250 |

|C $5,624 |

|D $7,500 |

| |

|15. The details of an investment project are as follows. |

| |

|Life of the project |

|10 years |

| |

|Cost of asset bought at the start of the project |

|$100,000 |

| |

|Annual cash inflow |

|$20,000 |

| |

|Cost of capital, after tax |

|8% each year |

| |

| |

|Corporation tax is 30% and is paid half in the year and half in the following year, in equal quarterly instalments. The instalments are|

|in the 7th and 10th months of the year in which the profit was earned and in the 1st and 4th months of the following year. |

| |

|Tax allowable depreciation of 25% reducing balance will be claimed each year. |

|(Assume the asset is bought on the first day of the tax year and that the company's other projects generate healthy profits.) |

|(Round all cash flows to the nearest $ and discount end of year cash flows.) |

| |

|What is the present value of the cash flows that occur in the second year of the project? |

| |

|A 17,622 |

|B 18,426 |

|C 20,193 |

|D 22,764 |

|Question 1 – NPV with inflation and tax allowable depreciation |

| |

|Uftin Co is a large company which is listed on a major stock market. The company has been evaluating an investment proposal to |

|manufacture Product K3J. The initial investment of $1,800,000 will be payable at the start of the first year of operation. The |

|following draft evaluation has been prepared by a junior employee. |

| |

|Year |

|1 |

|2 |

|3 |

|4 |

| |

|Sales (units/year) |

|95,000 |

|100,000 |

|150,000 |

|150,000 |

| |

|Selling price ($/unit) |

|25 |

|25 |

|26 |

|27 |

| |

|Variable costs ($/unit) |

|11 |

|12 |

|12 |

|13 |

| |

| |

|(Note: The above selling prices and variable costs per unit have not been inflated.) |

| |

|Year |

|$000 |

|$000 |

|$000 |

|$000 |

| |

|Sales revenue |

|2,475 |

|2,605 |

|4,064 |

|4,220 |

| |

|Variable costs |

|(1,097) |

|(1,260) |

|(1,890) |

|(2,048) |

| |

|Fixed costs |

|(155) |

|(155) |

|(155) |

|(155) |

| |

|Interest payments |

|(150) |

|(150) |

|(150) |

|(150) |

| |

|Cash flow before tax |

|1,073 |

|1,040 |

|1,869 |

|1,867 |

| |

|Tax allowable depreciation |

|(450) |

|(450) |

|(450) |

|(450) |

| |

|Taxable profit |

|623 |

|590 |

|1,419 |

|1,417 |

| |

|Taxation |

| |

|(137) |

|(130) |

|(312) |

| |

|Net cash flow |

|623 |

|453 |

|1,289 |

|1,105 |

| |

|Discount at 12% |

|0.893 |

|0.797 |

|0.712 |

|0.636 |

| |

|Present values |

|556 |

|361 |

|918 |

|703 |

| |

| |

| |

| |

| |

| |

| |

|Present value of cash inflows |

|2,538 |

| |

| |

| |

| |

|Cost of machine |

|(1,800) |

| |

| |

| |

| |

|NPV |

|738 |

| |

| |

| |

| |

| |

|The junior employee also provided the following information: |

|1. Relevant fixed costs are forecast to be $150,000 per year. |

|2. Sales and production volumes are the same and no finished goods inventory is held. |

|3. The corporation tax rate is 22% per year and tax liabilities are payable one year in arrears. |

|4. Uftin Co can claim tax allowable depreciation of 25% per year on a reducing balance basis on the initial investment. |

|5. A balancing charge or allowance can be claimed at the end of the fourth year. |

|6. It is expected that selling price inflation will be 4·2% per year, variable cost inflation will be 5% per year and fixed cost |

|inflation will be 3% per year. |

|7. The investment has no scrap value. |

|8. The investment will be partly financed by a $1,500,000 loan at 10% per year. |

|9. Uftin Co has a weighted average cost of capital of 12% per year. |

| |

|Required: |

| |

|(a) Prepare a revised draft evaluation of the investment proposal and comment on its financial acceptability. (11 marks) |

|(b) Explain any TWO revisions you have made to the draft evaluation in part (a) above. |

|(4 marks) |

|(15 marks) |

|(ACCA F9 Financial Management December 2014 Q4) |

|Question 2 – NPV with tax allowance |

|Hendil plc plans to invest £1 million in a new product range and has forecast the following financial information: |

| |

|Year |

|1 |

|2 |

|3 |

|4 |

| |

|Sales volume (units) |

|70,000 |

|90,000 |

|100,000 |

|75,000 |

| |

|Average selling price (£/unit) |

|40 |

|45 |

|51 |

|51 |

| |

|Average variable costs (£/unit) |

|30 |

|28 |

|27 |

|27 |

| |

|Incremental cash fixed costs (£/year) |

|500,000 |

|500,000 |

|500,000 |

|500,000 |

| |

| |

|The above cost forecasts have been prepared on the basis of current prices and no account has been taken of inflation of 4% per year on|

|variable costs and 3% per year on fixed costs. Working capital investment accounts for £200,000 of the proposed £1 million investment |

|and machinery for £800,000. |

| |

|Hendil uses a four-year evaluation period for capital investment purposes, but expects the new product range to continue to sell for |

|several years after the end of this period. Capital investments are expected to pay back within two years on an undiscounted basis, and|

|within three years on a discounted basis. |

| |

|The company pays tax on profits in the year in which liabilities arise at an annual rate of 30% and claims capital allowances on |

|machinery on a 25% reducing balance basis. Balancing allowances or charges are claimed only on the disposal of assets. |

| |

|Required: |

| |

|(a) Using Hendil plc’s current average cost of capital of 11%, calculate the net present value of the proposed investment. (15 marks) |

|(b) Calculate, to the nearest month, the payback period and the discounted payback period of the proposed investment. (4 marks) |

|(c) Discuss the acceptability of the proposed investment and explain ways in which your net present value calculation could be |

|improved. (6 marks) |

|(Total 25 marks) |

|(Amended ACCA Paper 2.4 Financial Management and Control December 2006 Q1) |

3. Incorporating Working Capital

(Jun 08, Dec 08, Jun 11, Dec 11, Jun13, Dec 13)

3.1 Investment in a new project often requires an additional investment in working capital, i.e. the difference between short-term assets and liabilities.

3.2 The treatment of working capital is as follows:

(a) Initial investment is a cost at the start of the project.

(b) If the investment is increased during the project, the increase is a relevant cash outflow.

(c) At the end of the project all the working capital is released and treated as cash inflow.

|3.3 |EXAMPLE 4 |

| |A company expects sales for a new project to be $225,000 in the first year growing at 5% pa. The project is expected to |

| |last for 4 years. Working capital equal to 10% of annual sales is required and needs to be in place at the start of each |

| |year. Calculate the working capital flows for incorporation into the NPV calculation. |

| | |

| |Solution: |

| | |

| |Calculate the absolute amounts of working capital needed over the project: |

| |Year |

| |0 |

| |1 |

| |2 |

| |3 |

| |4 |

| | |

| | |

| |$ |

| |$ |

| |$ |

| |$ |

| |$ |

| | |

| |Sales |

| | |

| |225,000 |

| |236,250 |

| |248,063 |

| |260,466 |

| | |

| |Working capital (10% sales) |

| |22,500 |

| |23,625 |

| |24,806 |

| |26,047 |

| | |

| | |

| | |

| |Work out the incremental investment required each year (remember that the full investment is released at the end of the |

| |project): |

| |Year |

| |0 |

| |1 |

| |2 |

| |3 |

| |4 |

| | |

| | |

| |$ |

| |$ |

| |$ |

| |$ |

| |$ |

| | |

| |Working |

| | |

| |23,625 – 22,500 |

| |24,806 – 23,625 |

| |26,047 – 24,806 |

| | |

| | |

| |Working capital investment |

| |(22,500) |

| |(1,125) |

| |(1,181) |

| |(1,241) |

| |26,047 |

| | |

|Multiple Choice Questions |

| |

|III. Incorporating working Capital |

| |

|16. A project has the following projected cash inflows. |

| |

|Year 1 100,000 |

|Year 2 125,000 |

|Year 3 105,000 |

| |

|Working capital is required to be in place at the start of each year equal to 10% of the cash inflow for that year. The cost of capital|

|is 10%. |

| |

|What is the present value of the working capital? |

| |

|A $ Nil |

|B $(30,036) |

|C $(2,735) |

|D $33,000 |

| |

|17. AW Co needs to have $100,000 working capital in place immediately for the start of a 2 year project. The amount will stay constant |

|in real terms. Inflation is running at 10% per annum, and AW Co’s money cost of capital is 12%. |

| |

|What is the present value of the cash flows relating to working capital? |

| |

|A $(21,260) |

|B $(20,300) |

|C $(108,730) |

|D $(4,090) |

| |

|18. A new project is expected to generate sales of 55,000 units per year. The selling price is expected to be $3.50 per unit in the |

|first year, growing at 6% pa. The project is expected to last for three years. Working capital equal to 12% of annual sales is required|

|and needs to be in place at the start of each year. |

| |

|What is the cash flow in respect of working capital that will be used at time 2 of the net present value calculation? |

| |

|A $(25,955) |

|B $(24,486) |

|C $(1,386) |

|D $(1,469) |

4. General layout of cash flow preparation

4.1 The general layout can be shown as follows:

|Year |0 |1 |2 |3 |4 |

| |$000 |$000 |$000 |$000 |$000 |

|Sales | |X |X |X | |

|Costs | |(X) |(X) |(X) | |

|Operating cash flows | |X |X |X | |

|Taxation | | |(X) |(X) |(X) |

|Tax benefit of CAs | | |X |X |X |

|Capital expenditure and scrap value |(X) | | |X | |

|Working capital changes |(X) |(X) |(X) |(X) |X |

|Net cash flows |(X) |X |X |X |X |

|Discount factor |X |X |X |X |X |

|Present value |(X) |X |X |X |X |

|Question 3 – NPV with inflation, capital allowances and working capital |

|SC Co is evaluating the purchase of a new machine to produce product P, which has a short product life-cycle due to rapidly changing |

|technology. The machine is expected to cost $1 million. Production and sales of product P are forecast to be as follows: |

| |

|Year |

|1 |

|2 |

|3 |

|4 |

| |

|Production and sales (units/year) |

|35,000 |

|53,000 |

|75,000 |

|36,000 |

| |

| |

|The selling price of product P (in current price terms) will be $20 per unit, while the variable cost of the product (in current price |

|terms) will be $12 per unit. Selling price inflation is expected to be 4% per year and variable cost inflation is expected to be 5% per|

|year. No increase in existing fixed costs is expected since SC Co has spare capacity in both space and labour terms. |

| |

|Producing and selling product P will call for increased investment in working capital. Analysis of historical levels of working capital|

|within SC Co indicates that at the start of each year, investment in working capital for product P will need to be 7% of sales revenue |

|for that year. |

| |

|SC Co pays tax of 30% per year in the year in which the taxable profit occurs. Liability to tax is reduced by capital allowances on |

|machinery (tax-allowable depreciation), which SC Co can claim on a straight-line basis over the four-year life of the proposed |

|investment. The new machine is expected to have no scrap value at the end of the four-year period. |

| |

|SC Co uses a nominal (money terms) after-tax cost of capital of 12% for investment appraisal purposes. |

| |

|Required: |

|(a) Calculate the net present value of the proposed investment in product P. (12 marks) |

|(b) Calculate the internal rate of return of the proposed investment in product P. |

|(3 marks) |

|(c) Advise on the acceptability of the proposed investment in product P and discuss the limitations of the evaluations you have carried|

|out. (5 marks) |

|(d) Discuss how the net present value method of investment appraisal contributes towards the objective of maximising the wealth of |

|shareholders. (5 marks) |

|(Total 25 marks) |

|(ACCA F9 Financial Management June 2008 Q4) |

Additional Examination Style Questions

Question 4 – NPV and IRR

Charm plc, a software company, has developed a new game, ‘Fingo’, which it plans to launch in the near future. Sales of the new game are expected to be very strong, following a favourable review by a popular PC magazine. Charm plc has been informed that the review will give the game a ‘Best Buy’ recommendation. Sales volumes, production volumes and selling prices for ‘Fingo’ over its four-year life are expected to be as follows.

|Year |1 |2 |3 |4 |

|Sales and production (units) |150,000 |70,000 |60,000 |60,000 |

|Selling price (£ per game) |£25 |£24 |£23 |£22 |

Financial information on ‘Fingo’ for the first year of production is as follows:

|Direct material cost |£5.40 per game |

|Other variable production cost |£6.00 per game |

|Fixed costs |£4.00 per game |

Advertising costs to stimulate demand are expected to be £650,000 in the first year of production and £100,000 in the second year of production. No advertising costs are expected in the third and fourth years of production. Fixed costs represent incremental cash fixed production overheads. ‘Fingo’ will be produced on a new production machine costing £800,000. Although this production machine is expected to have a useful life of up to ten years, government legislation allows Charm plc to claim the capital cost of the machine against the manufacture of a single product. Capital allowances will therefore be claimed on a straight-line basis over four years.

Charm plc pays tax on profit at a rate of 30% per year and tax liabilities are settled in the year in which they arise. Charm plc uses an after-tax discount rate of 10% when appraising new capital investments. Ignore inflation.

Required:

(a) Calculate the net present value of the proposed investment and comment on your findings. (11 marks)

(b) Calculate the internal rate of return of the proposed investment and comment on your findings. (5 marks)

(c) Discuss the reasons why the net present value investment appraisal method is preferred to other investment appraisal methods such as payback, return on capital employed and internal rate of return. (9 marks)

(Total 25 marks)

(ACCA Paper 2.4 Financial Management and Control June 2006 Q5)

Question 5 – NPV with inflation

Trecor Co plans to buy a new machine to meet expected demand for a new product, Product T. This machine will cost $250,000 and last for four years, at the end of which time it will be sold for $5,000. Trecor Co expects demand for Product T to be as follows:

|Year |1 |2 |3 |4 |

|Demand (units) |35,000 |40,000 |50,000 |25,000 |

The selling price for Product T is expected to be $12.00 per unit and the variable cost of production is expected to be $7.80 per unit. Incremental annual fixed production overheads of $25,000 per year will be incurred. Selling price and costs are all in current price terms.

Selling price and costs are expected to increase as follows:

| |Increase |

|Selling price of Product T: |3% per year |

|Variable cost of production: |4% per year |

|Fixed production overheads: |6% per year |

Other information:

Trecor Co has a real cost of capital of 5.7% and pays tax at an annual rate of 30% one year in arrears. It can claim capital allowances on a 25% reducing balance basis. General inflation is expected to be 5% per year.

Trecor Co has a target return on capital employed of 20%. Depreciation is charged on a straight-line basis over the life of an asset.

Required:

(a) Calculate the net present value of buying the new machine and comment on your findings (work to the nearest $1,000). (13 marks)

(b) Calculate the before-tax return on capital employed (accounting rate of return) based on the average investment and comment on your findings. (5 marks)

(c) Discuss the strengths and weaknesses of internal rate of return in appraising capital investments. (7 marks)

(ACCA F9 Financial Management Pilot Paper Q4)

Question 6 – NPV with tax allowance and IRR

Duo Co needs to increase production capacity to meet increasing demand for an existing product, ‘Quago’, which is used in food processing. A new machine, with a useful life of four years and a maximum output of 600,000 kg of Quago per year, could be bought for $800,000, payable immediately. The scrap value of the machine after four years would be $30,000. Forecast demand and production of Quago over the next four years is as follows:

|Year |1 |2 |3 |4 |

|Demand (units) |1.4 million |1.5 million |1.6 million |1.7 million |

Existing production capacity for Quago is limited to one million kilograms per year and the new machine would only be used for demand additional to this.

The current selling price of Quago is $8.00 per kilogram and the variable cost of materials is $5.00 per kilogram. Other variable costs of production are $1.90 per kilogram. Fixed costs of production associated with the new machine would be $240,000 in the first year of production, increasing by $20,000 per year in each subsequent year of operation.

Duo Co pays tax one year in arrears at an annual rate of 30% and can claim capital allowances (tax-allowable depreciation) on a 25% reducing balance basis. A balancing allowance is claimed in the final year of operation.

Duo Co uses its after-tax weighted average cost of capital when appraising investment projects. It has a cost of equity of 11% and a before-tax cost of debt of 8·6%. The long-term finance of the company, on a market-value basis, consists of 80% equity and 20% debt.

Required:

(a) Calculate the net present value of buying the new machine and advise on the acceptability of the proposed purchase (work to the nearest $1,000). (13 marks)

(b) Calculate the internal rate of return of buying the new machine and advise on the acceptability of the proposed purchase (work to the nearest $1,000).

(4 marks)

(c) Explain the difference between risk and uncertainty in the context of investment appraisal, and describe how sensitivity analysis and probability analysis can be used to incorporate risk into the investment appraisal process. (8 marks)

(Total 25 marks)

(ACCA F9 Financial Management December 2007 Q2)

Question 7 – NPV with inflation and Discounted Payback

PV Co is evaluating an investment proposal to manufacture Product W33, which has performed well in test marketing trials conducted recently by the company’s research and development division. The following information relating to this investment proposal has now been prepared.

|Initial investment |$2 million |

|Selling price (current price terms) |$20 per unit |

|Expected selling price inflation |3% per year |

|Variable operating costs (current price terms) |$8 per unit |

|Fixed operating costs (current price terms) |$170,000 per year |

|Expected operating cost inflation |4% per year |

The research and development division has prepared the following demand forecast as a result of its test marketing trials. The forecast reflects expected technological change and its effect on the anticipated life-cycle of Product W33.

|Year |1 |2 |3 |4 |

|Demand (units) |60,000 |70,000 |120,000 |45,000 |

It is expected that all units of Product W33 produced will be sold, in line with the company’s policy of keeping no inventory of finished goods. No terminal value or machinery scrap value is expected at the end of four years, when production of Product W33 is planned to end. For investment appraisal purposes, PV Co uses a nominal (money) discount rate of 10% per year and a target return on capital employed of 30% per year. Ignore taxation.

Required:

(a) Identify and explain the key stages in the capital investment decision-making process, and the role of investment appraisal in this process. (7 marks)

(b) Calculate the following values for the investment proposal:

(i) net present value;

(ii) internal rate of return;

(iii) return on capital employed (accounting rate of return) based on average investment; and

(iv) discounted payback period.

(13 marks)

(c) Discuss your findings in each section of (b) above and advise whether the investment proposal is financially acceptable. (5 marks)

(Total 25 marks)

(ACCA F9 Financial Management June 2009 Q2)

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ACCA Dec 2015 Dec 2014

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