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Proof that the PV of nominal CFs at a nominal rate of interest is equal to...

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Accounting

Proof that the PV of nominal CFs at a nominal rate of interestis equal to PV of the parallel real CFs at a equivalent real rateof interest.

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3.6 Ratings (632 Votes)

Let,
Real rate of interest at period t r.rt
Nominal rate of interest at period t n.rt
inflation rate i
Nominal Cash flow at period t n.CFt
Real Cash flow at period t r.CFt
For example
You will receive $10,000 in 3 years ( n.CF3 = $10,000)
The inflation rate is 3%
nominal discount rate for valuing the $10,000 is 8%
n.rt 10%
i 2%
n.CF3 $10,000
Real cash flow that will be received in 3 years = n.CF3/(1+ i)3
= 10000/((1+0.02)3)
= $                                      9,423
PV of nominal cash flows at nominal rate= n.CF3/(1+n.r3)3
= $10000/(1.10)3
= $7,513
Calculation of real time discount rate= (n.r3-i)/1+i
= (0.10-0.02)/(1+0.02)
= 7.843%
PV of real cash flows at real rate            = r.CF3/(1+n.r3)3
= $9423/(1+0.07843)3
= $7,513
Therefore,
PV of nominal cash flows at nominal rate= PV of real cash flows at real rate

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