real rates from nominal rate

CFA Level II
#1

If a question requires us to use the real rate but provides nominal rate and inflation do we use:

real = nominal - expected inflation

or

real = [(1+nominal)/(1+expected inflatin)] - 1

They provide very different answers when discounting and i’ve seen both being used…

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#2

The different result of the two formulas is around or less than 0.1%. So, you can use both.

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#3

So youre saying that if you have $144 real FCFF(t-1) and your real wacc is 8%, nominal growth is 12% and real inflation is 8% then these should be th same?

real growth = 12-8 = 4%: Value = 144*1.04/0.04 = 3744 real growth = 1.12/1.08 - 1 = 3.7%: Value = 144*1.037/0.043 = 3472

These answers are almost 10% different…

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#4

Compound.

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#5

please expand?

I’ve seen something similar with the uncovered IR parity, where we should use (1+id)/(1+if)-1 instead of (id - if).

Why bother putting the approximation in the syllubus if we’re meant to use the actual formula?

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#6

Compund formula is the accurate one. Sum formula is an approximation.

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#7

For small inflation rate and nominal rate, the real rate is

Formula 1: real = nominal - expected inflation

Formula 2; real =~= [(1+nominal)/(1-expected inflation)] - 1 =~= nominal - expected inflation- nominal*inflation

The formula 1 is an approximation of the formula 2. The different value is nominal*inflation.

For example, If nominal = 2%, inflation = 1%, the difference is just 0.01% in absolute value or 1% in relative value.

In this case, inflation rate and nominal rate are quite high, the error nominal*inflation is high. So, it’s better to use the exact formula (formula 2)

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#8

Thanks for the help everyone. I’m going to wipe the formula to approximate nominal rates and changes in spot rate due to uncovered IR parity from my memory.

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