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**Project Appraisal, Capital Rationing, Taxation and Inflation**

Corporate Finance 8

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**Project appraisal: capital rationing, taxation and inflation**

Coping with investment appraisal in an environment of capital rationing, taxation and inflation More specifically: Explain why capital rationing exists and be able to use the profitability ratio in one-period rationing situations Show awareness of the influence of taxation on cash flows Discount money cash flows with a money discount rate, and real cash flows with a real discount rate

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Capital rationing Capital rationing occurs when funds are not available to finance all wealth-enhancing projects Soft rationing Hard rationing One-period capital rationing 1 Divisible projects 2 Indivisible projects

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**One-period capital rationing with divisible projects**

Capital at time zero has been rationed to £4.5m

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**Bigtasks plc (continued)**

Ranking according to absolute NPV Gross present value Profitability index = –––––––––––––––– Initial outlay Net present value Benefit–cost ratio = –––––––––––––– Initial outlay

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**Bigtasks plc: Profitability indices and benefit–cost ratios**

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**Bigtasks plc: Ranking according to the highest profitability index**

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Indivisible projects Multi-period capital rationing

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**Taxation and investment appraisal**

Rule 1: If acceptance of a project changes the tax liabilities of the firm then incremental tax effects need to be accommodated in the analysis Rule 2: Get the timing right. Incorporate the cash outflow of tax into the analysis at the correct time Specific projects are not taxed separately, but if a project produces additional profits in a year, then this will generally increase the tax bill The Inland Revenue permit a ‘writing-down’ allowance rather than depreciation

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**Snaffle plc Purchase of a machine for £1,000,000 at time zero**

Scrap value at the end of its four-year life: this will be equal to its written-down value The Inland Revenue permit a 25 per cent declining balance writing- down allowance on the machine each year Corporation tax, at a rate of 30 per cent of taxable income, is payable Snaffle’s required rate of return is 12 per cent Operating cash flows, excluding depreciation, and before taxation, are forecast to be:

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Snaffle (continued)

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**Snaffle: Calculation of corporation tax**

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**Snaffle: Calculation of flows**

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Inflation Specific inflation refers to the price changes of an individual good or service 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 Inflation creates two problems for project appraisal 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. The rate of return required by the firm’s security holders will rise if inflation rises.

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**‘Real’ and ‘money’ rates of return**

Discount rate takes account of three types of compensation: The pure time value of money, or impatience to consume Risk Inflation Real rate of return: that which is required in the absence of inflation, say 8 per cent If we change the assumption so that prices do rise then investors will demand compensation for general inflation If inflation is 4 per cent then the money value of one basket of commodities at Time 1 which would leave the investor indifferent when comparing it with one basket at Time 0, is: 1.08 × 1.04 = Since the money cash flow of £1, at Time 1 is financially equivalent to £1,000 now, the money rate of return is per cent

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Fisher’s equation The generalised relationship between real rates of return and money (or market, or nominal) rates of return and inflation is expressed in Fisher’s (1930) equation: (1 + money rate of return) = (1 + real rate of return) × (1 + anticipated rate of inflation) (1 + m) = (1 + h) × (1 + i) ( ) = ( ) × ( )

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**‘Money’ cash flows and ‘real’ cash flows**

Two possible discount rates: Money discount rate Real discount rate Two alternative ways of adjusting for the effect of future inflation on cash flows: 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 cash flow or the nominal cash flow Measure the cash flows in terms of real prices. That is, all future cash flows are expressed in terms of, say, Time 0’s prices

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**Amplify plc A project requires an outlay of £2.4m at the outset**

Money cash flows receivable from sales will depend on the specific inflation rate for Amplify’s product–anticipated to be 6 per cent per annum Labour costs are expected to increase at 9 per cent per year, materials by 12 per cent and overheads by 8 per cent The discount rate of per cent that Amplify uses is a money discount rate, including an allowance for inflation M1 M Mn NPV = M0 + –––––– + –––––––– ... –––––––– m (1 + m) (1 + m)n M = actual or money cash flow m = actual or money rate of return

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**Amplify plc (continued)**

Annual cash flows in present (Time 0) prices are as follows: All cash flows occur at year ends except for the initial outflow

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**Amplify plc: Money cash flow**

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**Amplify plc: Money cash flows discounted at the money discount rate**

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**Amplify: Cash flow in real terms and real discount rate**

Discounting real cash flow by the real discount rate A real cash flow is obtainable by discounting the money cash flow by the general rate of inflation, thereby converting it to its current purchasing power equivalent The general inflation rate is derived from Fisher’s equation: (1 + m) = (1 + h) × (1 + i), m is given as , h as 0.08, i as 0.04 (1 + m) i = ––––––– – 1 = –––––––––– – 1 = (1 + h)

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Real cash flows Under this method net present value becomes: The net present value is equal to the sum of the real cash flows Rt discounted at a real rate of interest, h R1 R R NPV = R0 + –––––– + ––––––– + ––––––– +… h (1 + h) (1 + h)3

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**Amplify plc: Discounting money cash flows by the general inflation rate**

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**Amplify plc: Real cash flows discounted at the real discount rate**

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**A warning 1 Discount money cash flows with the real discount rate**

Never do either of the following: 1 Discount money cash flows with the real discount rate 2 Discount real cash flows with the money discount rate Source: Arnold and Harzopoulos (2000).

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**Lecture review Soft capital rationing Hard capital rationing**

Profitability index Benefit–cost ratio Two rules for allowing for taxation in project appraisal: Include incremental tax effects of a project as a cash outflow Get the timing right Specific inflation General inflation Adjusting for inflation in project appraisal: Approach 1 – Estimate the cash flows in money terms and use a money discount rate Approach 2 – Estimate the cash flows in real terms and use a real discount rate

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