Discounting Inflation - A Note

The .hn of tt14paperL to clarify the conLmed h e ofthe dectof idation on the dhcountingprocahm for investment 8 p p d me atandud npprod b coaddered, together with the bp8ct d h&tioa, 8nd the problem of how to adjust the s t m d d 8pprO8ch to take 8ccount of inlhtion. 'Lbe point b nude th8t it b usually enieat to estimate expected rrtmar in emrrnt plea, in which are the d h m n t n t e dmoldreket

to the mjectbn of wonihwMe projacIa. An example L &em dhow the d rate of Interest CUI be eopnpnted

sanple project. 'Ibe paper then flusbatem how d ratem of interest have freqocntly beea neg8Iive over the pnt decade and how thb b p h th8t projecia nuy be ampt.ble even if the sum of f o h a tudmmnnted re- L less timu the initinl onthy. Ibt eondnsion dram is that investors s h o d maddza economic pm6t dehed as the surplus over opporldly coat, Whkh redam the detemcnt of nomianoy high inter& mtea, for t h e . * tfoo of slupb over opportnnity coot hu the corollary of * * . tion of opportmity 10~3.

the d Op- CC& of

hI0 the O O d d Of 8Od the mtC of -0,80d thc -m &La t0 dk000- 8

t0 8 V d d *d Md 0- h e fn 8 llllpDcT W h k h k8&

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INTRODUCllON

The purpose of this note is to clarify a confused issue - the effect of inflation on the discounting procedure for investment appraisal. While this has been discussed briefly elsewhere,'-3 nowhere is there a clear explanation of an issue that has con- siderable relevance to contemporary decision mak- ers. It is our contention that the failure to correct discounting to take account of inflation leads to a significant undervaluation of the benefits of a given investment project, and hence to the rejection of projects that ought to have been accepted and ultimately to underinvestment.

Consider a capital project with an initial cost Co, generating net cash flows Al * . * A,, over the next n periods. If the discount factor is d, the project will be accepted if the net discounted present value ( N D P V ) is greater than zero, where

A A N D p v = 2 + ~ + . . .+A,- ( l+d)" CO l + d ( l+d)*

Table 1 illustrates an example. A project costs f 1000 and returns a net profit of f300 per year for the next five years. Discounted at 15% the project has a present value of approximately zero and the

Table 1. An Example of the st.ndud Approach Y..r R m m Dlvoum t.nn: 16% w,*- Dirmm hcmr: fi Pv.

0 -lo00 1 -lm 1 -lo00 1 300 0.870 281 0.943 2829 2 300 0.756 226.8 0.890 261 3 300 0.658 191.4 0.840 252 4 300 0.571 171.3 0.792 237.6 5 300 0.497 149.1 0.747 224.1

'W, is the present value of some future return at the discount rate x, i.e. W, =A, times discount factor x in year i.

investor attempting to maximize present value will be indifferent between investing or not.

THE IMPACT OF INFLATION

In the standard approach inflation is not specifically considered. The general price level is assumed not to change over the project life, and the rate of interest which obtains adjusts to the environment of stable prices. However, in reality, prices are chang- ing and the problem arises of how to accommodate this within the discounting framework.

To examine the effect of inflation it is necessary to be more specific about what the values mean. The anticipated future returns are necessarily esti- mated, and it is inevitably easier to make estimates based on current prices (for example the enquiry 'what would be costs and revenues if the projected capital equipment were in use now?' implies meas- urement in terms of the current value of money).

c c c - o 1 ~ ~ - 6 ~ 7 o / ~ i ~ o n o 2 ~ 1 z 1 s o 1 .so @ Heyden & Son Ltd. 1981 MANAGERIAL AND DECISION ECONOMICS, VOL 2, NO. 2. 1981 121

The discount rate used for investment appraisal should reflect the investors opportunity cost of capi- tal but in most cases the current market rate of interest is used as an approximation. If in our example prices were changing in year 0. then the standard procedure would lead to a mixture of real values (future returns in current prices) and nomi- nal values (the market money rate of interest). This mixture of future returns in current prices and nominal interest rates leads to the adoption of discount factors which overestimate the real oppor- tunity cost of capital and hence lead to the rejection of worthwhile projects.

The solution is to be consistent. If future returns are in real @rms then the project should be dis- counted at the real rate of interest as an approxima- tion to the real opportuniry cost. If x is the money rate of interest, and y is the current rate of infiation (both expressed as decimals), then the real rate of interest r can be represented as:

l+x x-y l + y l + y

r =-- 1 =-

This can be illustrated by our example. Suppose the market rate of interest is 15% while the rate of inflation is 8%. Then the real rate of interest

0.15-0.08 r = = 0.0609 1.15

If the project is discounted at 6 X its net dis- counted present value becomes f236.6 (last col- umn, Table 1) and the project is clearly acceptable.

Alternatively, there may be some circumstances where it is easier to estimate returns in terms of future prices (although given the uncertainty of future price changes this is difficult to envisage). The solution is then to discount these money values by the money (or nominal) rate of interest. In terms of our example, the cash flows could be inflated by a price index. If the expected inflation rate was 8% the year 1 value would be multiplied by 1.08, year 2 by (1.08)’ etc. If the resulting cash flows are then discounted at 15% (the money rate of interest). the result is again a positive net discounted present value of f236.6. Consequently it does not matter

which method is chosen, as long as the investment appraisal is consistent.

NEGATlVJ3 REAL RATES

It is a feature of British experience over the past decade that the real rate of interest has frequently been negative (i.e. when the money rate of interest is less than the rate of inflation). This is illustrated in Table 2. using the retail price index as the rate of inflation, and approximating the rate companies are likely to pay for borrowed money by 2% above the Bank of England minimum lending rate4 (averaged over the year on a rime basis). The figures show that the real borrowing rate has frequently been negative, with peak inflation in 1975 meaning a record negative real rate of almost 10%. Inflation again recently accelerated, but real rates have not been reduced as much because interest rates have risen to record levels.

The problem arises of adjusting the discounting procedure to take account of negative real rates. The effect of the negative rate is that inflation partly pays for the cost of the investment, because monetary debt is repaid in depreciating currency. If cash flows are expressed in current prices the dis- counting formula with negative real opportunity cost of capital implies that the denominator (by which each cash flow should be divided to calculate present value) should be less than one, so that in effect the cash flows are multiplied up.

Table

V n r

1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979

2. Neptlve Real Ratg of Interest, 1969- 1979

RmsdIniuth N~mirulbonarlram Rrlbwro*ringnp

5.38 9.84 4.23 6.38 . 9.23 268 9.40 7.92 -1.35 7.13 7.91 0.07 9.22 11.91 2.46

16.02 13.60 -1.83 24.09 1280 -9.68 15.07 13.81 -1.09 12.14 10.25 -1.69 9.91 11.25 1.22

18.39 16.93 -208

STEPHEN HLL obtained a B.Sc. Econ. degree In Economics and Statistics from U.C.W. Aberyrtwyth, and en M.Sc. Econ. in Economics from University College, Cardiff. Since 1977 he has been lecturer in Managerial Economics in the Department of Applied Economics, UWIST. His main research interests are in decision making and oligopoly behaviour under uncertainty. Joint author with Julian Gough of Fundamentals of Mana- gerial Economics (Macmillan, 1979).

JUlAN OOUGH graduated at University College, Cardiff, in 1967, and then studied at the University of East Anglia, Norwich, and obtained degrees of M.A. and M.Phil. He was appointed Lecturer in the Department of Applied Economics, UWIST, in 1970 to specialize in teaching of Managerial Economics and microeconomic theory. His main research is in the economics of housing, housing finance and the economics of building societies. Address: Department of Applied Economics, UWIST, King Edward VII Avenue, Cardiff CFl 3NU, UK.

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Returning to our example, suppose that the rate of inflation is 20% while the investing firm pays interest of 15% for borrowed money. Then, using the earlier formula, the real rate of interest is -4.2%. The net discounted present value of the project is then:

5 fL- 300 -1000 ,-, (1 + d)' ''= (1 -0.042)' = 709.29

In fact the existence of negative real rates implies that a project may be acceptable even if the sum of future undiscounted cash flows is less than the initial outlay.

The situation is unchanged if the firm is an initial net lender of cash. The only difference is that the real opportunity cost of capital is then the real lending rate (which may be negative) rather than the real borrowing rate. Of course if the capital market was perfect these two would be equal.

CONCLUSIONS

The objective of an investor should be to maximize economic profit defined as the surplus over oppor- tunity cost. The existence of inflation reduces that opportunity cost, and may even make it negative. The conclusion to be drawn is that decision makers should not be deterred by nominally high interest charges. It may appear paradoxical to suggest that a project may be worthwhile even if the sum of cash flows (undiscounted and in current prices) is less than the initial outlay. The paradox is resolved by the realisation that the maximization of surplus over opportunity cost has the corollary of the minimizing of opportunity loss (defined as the benefit foregone by not making the best decision). For if all investments fail to keep pace with infla- tion, the best the decision maker can do is to try to minimize the gap.

NOTESANDREFERENCES

1. M. Bromwich. Inflation and the capitel budgeting prw cesl. Journal of Business Finance, 3946. (Autumn lW1.

2 8. Carsberg, Analysis for Investment Decisions, pp. 101- 106. Accounting Age Book., London (1974).

3. J. Gough and S. Hill, Fundamentals of Managwial Economics, pp. 208-209. Mamillan, London (19791.

4. The minimum lending rate is the rate at which the Bank of EnOland is prepared to lend at last resort to authorised participants in the discount market and is closely related to the base rate of the commercial bank..

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