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I am trying to understand illustration 2 on page 144 of the BPP P&R – looking at the deflated cashflows. In summary:
The cost of purchasing a machine is $10m, running costs are $1.2m/yr and the savings in rental costs are $6.6m
Running costs increase at a general inflation rate of 5.26% and rental costs being saved are expected to increase at 2%/yr. The real cost of capital is 14%.Where the example says “Deflated / 1.0526)^n” What exactly is the “Deflated” figure that is being divided by 1.0526 to get 0.95 in year 1?
Earlier in the chapter, it states that the deflated rate is (1+r)=(1+i)/(1+h)^n, therefore 1+r = (1+0.2)/(1.0526) = 1.14
Then discount the real cashflows at the real cost of capital – so 14% at time 1 = 0.877 not 0.95.The deflated figure in the example refers to the nominal cash flow divided by the deflation factor. The deflation factor is calculated as (1 + r) = (1 + i) / (1 + h)^n, where r is the real rate of interest, i is the nominal rate of interest, and h is the rate of inflation. In this case, the deflated figure is obtained by dividing the nominal cash flow by (1.0526)^n
In the example you mentioned, the deflated figure in year 1 is obtained by dividing the nominal cash flow by (1 + 5.26%)^1, which gives 0.95.
This adjustment accounts for the increase in general inflation over time. The deflated figure refers to the nominal cash flow adjusted for inflation.
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