Question

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

Answer 1

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