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The more specific a particular cost or revenue assumption may be, the

greater the potential for its own inflation rate to diverge from the general rate

of inflation. Individual commodity prices have changed by huge amounts

over recent years while the overall level of inflation has, the politicians assure

us, hardly changed. So a good financial model will make several different

assumptions about how costs and/or prices are changing for different items.

Modelling when inflation is high

When the general level of inflation is high (say 10% or more) and we want

to be able to model the effect of changes in inflation rates over the period

covered by the model we are forced to adopt an alternative approach. The

approach I recommend is to adopt a so-called â€˜real termsâ€™ convention.

The expression â€˜real termsâ€™ refers to sums of money that have been con-

verted into equivalent purchasing power terms. So if inflation is 20%, some-

thing that costs 1 unit today will cost 1.2 units in a yearâ€™s time and 1.44 units

in two yearsâ€™ time and so on. So if all sums of money in the second year are

divided by 1.2 and all sums in year 3 are divided by 1.44 they would then be

said to be stated in real (year 1) terms. These so-called real cash flows would

then be converted into present values by discounting at the real CoC.

220 The three pillars of financial analysis

We will now study how inflation might impact on one of the earlier cases

that we studied during the first building block. This is the paving slabs exam-

ple that was considered on pages 24â€“26. In the initial analysis of this case the

inflation assumption was set to zero and the project had an NPV of $6.9m

and a reported IRR of 18%.16 We will now study the effect of changing the

assumed rate of inflation to 10% while holding all other assumptions (includ-

ing the 10% CoC) unchanged.

The numbers with no inflation are shown in table 7.1. If inflation is set at

10% the numbers change as shown in table 7.2. All of the cash flows are sim-

ply 10% higher for each year. This is because I chose a particularly simple set

of assumptions with no tax or working capital effects to model. We will study

what might happen to tax and working capital later but for the present, focus

please on the economic indicators.

The project appears to have got a lot better. The NPV and IRR are higher.

Note in particular how the IRR change can be explained through the

formula:

(1 + inflation ) Ã— (1 + real IRR ) = (1 + nominal IRR )

In this case:

1.1 Ã— 1.177 = 1.295

The increase in IRR is purely due to the effect of inflation because all future

cash flow numbers have been increased by the same percentage figure each

year. The increase in NPV is simply a reflection of the fact that we left the

CoC unchanged when we changed the inflation rate. It is not realistic to

assume 10% inflation and at the same time assume a 10% CoC. We should

convert the cash flows into real terms and then apply a real CoC. In this case

the real CoC to apply is 10% because this was the CoC that we assumed when

the inflation rate was zero.

We can now illustrate the methodology that should be used when

inflation is high. We need to insert an additional line into our spread-

sheet that converts the forecast money-of-the-day cash flow into real

terms.17 The sheet becomes as shown in table 7.3 (the key lines are shown

in bold).

The exact number was 17.7%.

16

The real cash flow is equal to the money-of-the-day cash flow divided by an inflation index. The index

17

starts at 1 in the first year and then increases by the rate of inflation each year.

221

Table 7.1 The numbers with no inflation.

Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13

Sales 5.3 5.6 6.0 6.4 6.8 6.8 6.8 6.8 6.8 6.8 0.0

Fixed costs 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.0

Variable costs 0.8 0.8 0.9 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.0

Capex 10.0 8.0

Close-down cost 2.0

Cash flow âˆ’10.0 âˆ’8.0 3.7 4.0 4.3 4.6 4.9 4.9 4.9 4.9 4.9 4.9 âˆ’2.0

Discount factor 1 0.953 0.867 0.788 0.716 0.651 0.592 0.538 0.489 0.445 0.404 0.368 0.334 0.304

Present value âˆ’9.5 âˆ’6.9 2.9 2.9 2.8 2.7 2.7 2.4 2.2 2.0 1.8 1.7 âˆ’0.6

cash flow

Cumulative

present value 0.0 âˆ’9.5 âˆ’16.5 âˆ’13.6 âˆ’10.7 âˆ’7.9 âˆ’5.2 âˆ’2.5 âˆ’0.1 2.1 4.1 5.9 7.5 6.9

NPV 6.9

IRR 17.7%

Discounted

payback year 9

Efficiency 38%

222

Table 7.2 The numbers with inflation set at 10%.

Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13

Sales 6.4 7.5 8.8 10.3 12.0 13.2 14.5 15.9 17.5 19.3 0.0

Fixed costs 1.0 1.1 1.2 1.3 1.4 1.6 1.7 1.9 2.1 2.3 0.0

Variable costs 1.0 1.1 1.3 1.5 1.8 2.0 2.2 2.4 2.6 2.9 0.0

Capex 10.0 8.8

Close-down cost 6.3

Cash flow âˆ’10.0 âˆ’8.8 4.4 5.3 6.3 7.4 8.7 9.6 10.6 11.6 12.8 14.1 âˆ’6.3

Discount factor 1 0.953 0.867 0.788 0.716 0.651 0.592 0.538 0.489 0.445 0.404 0.368 0.334 0.304

Present value

cash flow âˆ’9.5 âˆ’7.6 3.5 3.8 4.1 4.4 4.7 4.7 4.7 4.7 4.7 4.7 âˆ’1.9

Cumulative

present value 0.0 âˆ’9.5 âˆ’17.2 âˆ’13.7 âˆ’9.9 âˆ’5.8 âˆ’1.4 3.3 8.0 12.8 17.5 22.2 26.9 25.0

NPV 25.0

IRR 29.5

Discounted

payback year 7

Efficiency 133%

223

Table 7.3 The numbers when inflation is high.

Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13

Sales 0.0 0.0 6.4 7.5 8.8 10.3 12.0 13.2 14.5 15.9 17.5 19.3 0.0

Fixed costs 0.0 0.0 1.0 1.1 1.2 1.3 1.4 1.6 1.7 1.9 2.1 2.3 0.0

Variable costs 0.0 0.0 1.0 1.1 1.3 1.5 1.8 2.0 2.2 2.4 2.6 2.9 0.0

Capex 10.0 8.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Close-down cost 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 6.3

Cash flow âˆ’10.0 âˆ’8.8 4.4 5.3 6.3 7.4 8.7 9.6 10.6 11.6 12.8 14.1 âˆ’6.3

Real cash flow âˆ’10.0 âˆ’8.0 3.7 4.0 4.3 4.6 4.9 4.9 4.9 4.9 4.9 4.9 âˆ’2.0

Discount factor 1.000 0.953 0.867 0.788 0.716 0.651 0.592 0.538 0.489 0.445 0.404 0.368 0.334 0.304

Present value

cash flow 0.0 âˆ’9.5 âˆ’6.9 2.9 2.9 2.8 2.7 2.7 2.4 2.2 2.0 1.8 1.7 âˆ’0.6

Cumulative

present value 0.0 âˆ’9.5 âˆ’16.5 âˆ’13.6 âˆ’10.7 âˆ’7.9 âˆ’5.2 âˆ’2.5 âˆ’0.1 2.1 4.1 5.9 7.5 6.9

NPV 6.9

IRR 17.7%

Discounted

payback year 9

Efficiency 37%

224 The three pillars of financial analysis

NPV, IRR and discounted payback have now all returned to exactly what

they were before inflation was increased to 10%. The only change is the small

decrease in the efficiency number. This has reduced because it is calculated

by dividing NPV by capex and not the inflation-adjusted capex.

How tax and working capital make inflation â€˜hurtâ€™

There are two more or less unavoidable facts of business life that make infla-

tion â€˜hurtâ€™. That is to say that inflation lowers NPV, unlike the calculation

above where we saw that NPV was unchanged.

The first effect to allow for is that of taxation. The tax rules usually work

in such a way that the tax offset for capital costs is spread over a number

of years but is set based on the original capital spend. This means that

the purchasing power of the tax offsets is reduced as inflation rises. The

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