DCF with Inflation and Taxation

Chapter 5 DCF with Inflation and Taxation

1.       Objectives

1.1       Explain the impact of inflation on interest rates and define and distinguish between real and nominal (money) interest rates.
1.2       Explain the difference between the real terms and nominal terms approaches to investment appraisal.
1.3       Explain the impact of tax on DCF appraisals.
1.4       Calculate the tax cash flows associated with capital allowances and incorporate them into NPV calculations.
1.5       Calculate the tax cash flows associated with taxable profits and incorporate them into NPV calculations.
1.5       Explain the impact of working capital on an NPV calculation and incorporate working capital flows into NPV calculations.

2.       Inflation
(Pilot, Jun 08, Jun 09, Dec 10, Jun 11, Jun 12, Dec 12, Jun 13)
2.1       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.
2.2       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.

2.3       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.

2.4       Real and money interest rate
(Pilot, Jun 10)
2.4.1    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.

2.4.2	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

2.4.3	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%.

2.4.4	EXERCISE 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:

 

2.5       Money cash flows and real cash flows
(Jun 13)
2.5.1    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.

2.5.2

EXAMPLE 2

Storm Co is evaluating Project X, which requires an initial investment of $50,000. Expected net cash flows are $20,000 pa for four years at today’s prices. However these are expected to rise by 5.5% pa because of inflation. The firm’s cost of capital is 15%. Find the NPV by: (a)      discounting money cash flows (b)      discounting real cash flows. Solution: (a)      Discounting money cash flow at the money rate: The cash flows at today’s prices are inflated by 5.5% for every year to take account of inflation and convert them into money flows. They are then discounted using the money cost of capital. Note: The question simply refers to the ‘firm’s cost of capital’. You can assume this is the money rate – if you are given a real rate the examiner will always specify. Time Money cash flow ($) Discount rate @15% PV ($) 0 (50,000) 1 (50,000) 1 21,100 0.870 18,357 2 22,261 0.756 16,829 3 23,485 0.658 15,453 4 24,776 0.572 14,172     NPV = 14,811 (b) Calculate the real rate by removing the general inflation from the money cost of capital: (1 + r) = (1 + i) / (1 + h) = (1 + 15%) / (1 + 5.5%) = 1.09 r = 9% The real rate can now be applied to the real flows without any further adjustments. Time Money cash flow ($) Discount rate @9% PV ($) 0 (50,000) 1 (50,000) 1 – 4 20,000 3.240 64,800     NPV = 14,800 Note: Differences due to rounding.

3.       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)
3.1       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.
3.2       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.

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

3.3.1    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.

3.3.2

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   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

 

4.       Incorporating Working Capital
(Jun 08, Dec 08, Jun 11, Dec 11, Jun13)
4.1       Investment in a new project often requires an additional investment in working capital, i.e. the difference between short-term assets and liabilities.
4.2       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.

4.3

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

 

Examination Style Questions

Question 1 – 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.

The ordinary shareholders of Hendil plc require an annual return of 12%. Its ordinary shares are currently trading on the stock market at £1·80 per share. The dividend paid by the company has increased at a constant rate of 5% per year in recent years and, in the absence of further investment, the directors expect this dividend growth rate to continue for the foreseeable future.

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)

Question 2 – 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 3 – 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 4 – 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 5 – NPV
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)

Question 6 – 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)