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3.5. Capital Budgeting and Taxation

Another incremental cash flow, which we haven't touched on, that may involve timing discrepancies affecting project selection and shareholder wealth, is corporate taxation.

We know that in the absence of tax, depreciation should be added back to accounting profits for DCF appraisal. It is a non-cash expense and not an incremental outflow. But if depreciation is a capital allowance that reduces taxable profits and because tax represents a cash outflow, we must include both in our calculation of net tax cash inflows.

Consider a project with an annual £100k cash return on a five year investment costing £300k with a 100 per cent straight-line capital allowance and a corporate tax rate of 25 per cent. We can compare the project's annual post-tax profits with its true cash position as follows:

Annual Data(£k)

Taxable Income

Taxable Income (without any capital allowance)

Cash flow

Profit before depreciation

100

100

100

Capital allowance (20%)

60

Pre-tax profit

40

100

Corporation tax (25%)

10

25

(10)

Post-tax profit

30

75

90

If we do not deduct a capital allowance from the profit before depreciation (Column 2) the tax liability would be £25k (i.e. 25 per cent of £100k). And post-tax profit and net cash inflow would both equal £75k. However, with the capital allowance, an extra £15k cash flow is retained because the 25 per cent tax rate is applied to a profit figure of £40k adjusted for the annual capital allowance (£60k / 5). Consequently, the true annual cash flow is £90k.

Depreciation therefore acts as a tax shield if it is a capital allowance because it reduces a company's net tax liability and increases its net cash inflow.

Of course, we have still not considered the timing discrepancy associated with deferred tax payments. These too, exert a positive bias on our DCF calculations. For example, assuming a twelve month delay, an accurate picture of the cash flow pattern for our five year project adjusted for relief, prior to any periodic net working capital adjustments, would be:

Cash Flows (£k)

Year 0

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Inflow

-

100

100

100

100

100

-

Outflow

(300)

-

(10)

(10)

(10)

(10)

(10)

Net Flow

(300)

100

90

90

90

90

(10)

Once we incorporate working capital (if any) into the schedule, all that is required is to discount the net cash flows at the project's opportunity cost of capital adjusted for inflation.

3.6. NPV and Purchasing Power Risk

If a firm seeks to maximise shareholder wealth and their consumption-investment preferences, its capital budgeting decisions must be inoculated from two types of purchasing power risk.

- Specific price rises that erode the real value of a project's future net cash flows and diminish a firm's operating capability and share value. Management must uplift current (real) cash flows by specific price adjustments if necessary, to produce a project's forecast money flows.

- Inflation, that erodes consumption of goods and services generally, which must be reinstated by an upward revision of project discount rates if they ignore purchasing power losses. Nominal (real) interest rates that reflect zero inflation must be adjusted to money rates which reflect the expectations of investors who determine the market rate to compensate for this.

Irving Fisher (1930 op cit) defined the relationship between a market (money) interest rate (m) and a nominal (real) rate(r) given an annual compound inflation rate (i) as follows:

(4) (1 + m) = (1 + r) (1 + i) So, that re-arranging terms:

(5) m = (1 +r)(1 + i) - 1 = the money rate,

(6) r = [(1 + m) / (1 + i)] - 1 = the real rate.

For example, if a project's real (nominal) discount rate is 7.5 per cent and the annual rate of inflation is 7 per cent, the money (market) rate of interest used to discount a project's money cash flows to determine a project's NPV is given by Equation (5): m = (1.075) (1.07) - 1 = 15%

Activity 4

Armed with this information, use Equation (6) to reverse the Fisher effect on the money rate (m = 15%) with an inflation rate (i= 7%) and prove that the real rate (r) equals 7.5 percent.

Review Activity

Your University intends to market a financial text priced at £60 over four years with the following demand pattern, forecast money flows and a 15 percent money cost of capital.

Year 1 Year 2 Year 3 Year 4 Annual Demand 6,200 7,200 4,000 2,800

- Capital set-up investment of £100k with a residual value of £20k in year 4

- Variable production costs of £40 per text

- Royalty costs of £20k in year one, £15k in year two and £10k in years three and four

- Working capital investment of £80k recoverable in year 4

- Fixed cost recovery of £60,000 per annum that includes depreciation

Using NPV and NTV criteria, establish whether the University should proceed with the project.

First, the data needs to be reformulated in terms of relevant cash flows.

- Depreciation must be removed from fixed costs because it is not a cash flow.

- Fixed costs should only be included if relevant i.e. incurred only if the project is undertaken.

- Residual asset values including working capital are always relevant because they defray the final project cost through their future opportunity value to the company, or sale on the market.

- Because universities (at least in the UK) are charities that do not pay tax, we can ignore it. Second, let us assume fixed cost relevancy (the worst case scenario) whereby:

Fixed costs minus depreciation = £60k - £20k = £40k per annum

[Annual depreciation = capital cost less residual value / project life = £100k-£20k / 4 = £20k] Finally, we can tabulate the data to calculate NPV and NTV.

The table overleaf reveals the project is profitable, even if burdened with fixed costs. The NTV confirms an NPV surplus in terms of economic value added four years from now. Obviously, if fixed costs are genuinely "fixed" (incurred irrespective of project acceptance) they should be ignored. And in this case the NPV and NTV would be higher still (£137.57k and £240.6k respectively).

Perhaps you can confirm this?

3.7. Summary and Conclusions

Unless management is confronted by a single project with one initial outflow followed by subsequent net inflows, the IRR may produce sub-optimal investment decisions, whereas the NPV maximisation of all a firm's projects, which discounts relevant incremental money cash flows at the money (market) rate of interest, should maximise wealth. Differences arise because the latter is a measure of absolute wealth, whilst the former is a relative measure. The validity of the two models also hinges upon their respective assumptions concerning borrowing and reinvestment rates. NPV calculations use the opportunity cost of capital, whilst IRR assumes that capital cost and re-investment rates equal a project's IRR, usually without any economic foundation whatsoever.

Of course, we must remember that even if NPV incorporates relevant cash flows, taxation and price changes it is still only a model that simplifies a complex world of risk and uncertainty. So, how do management deal with these phenomena to maximise shareholder wealth?

 
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