8.
inflation & its impact on project cash flows
8.1. concept of inflation
Inflation is an increase in amount of money necessary to
obtain the same amount of product or service before the
inflated price was present.
In other words,
It is the state in which market prices are rapidly raising i.e.
value of money is falling.
Causes of inflation
Due to increase in production cost of various service and
goods.
When business industries increases price of their service
or goods to amplify their profit margins.
When specific section of mass industry increases the
price of its service or goods; it will affect other sections.
E.g.increase in price of crude oil will spontaneously
increase in bus fares and air fares.
Terminologies in the inflation:
Following indices are used in inflation:
A) Consumer price index (CPI)
It measures the change in price of consumer’s goods
like: food, shelter, medical care, transportation etc.
B) Producer price index (PPI)/ wholesale price index
(WPI)
It measures the changes in price charged by
manufacturers or wholesalers.
( ) ( )
(CPI or PPI annual change rate,%)k = *100
( )
For example, the end-of-year CPI for 2006 was 201.6, and the
estimated end-of-year CPI for 2007 is 208.0. The CPI annual change
rate for 2007 is then estimated to be
( ) ( )
= *100%
( )
. .
*100%
.
=3.17%
C) GDP Deflector
It is a measure of level of prices of all new
domestically produced final goods and services in an
economy.
( )
GDP Deflector= ( )
Interest Rates:
a) Market interest rate (i)= interest rate quoted by
financial institutions that takes account for both
earning & purchasing power i.e. it takes account of
earning value of capital (earning power) & any
anticipated inflation (purchasing power).
- Also called inflation-adjusted MARR.
b) Inflation free interest rate (i’)=this rate is an estimate
of the true earning power of money when inflation
effects have been removed.(real-interest rate).
c) Inflation rate(f)= this is measure of the rate of change
in value of money.
Relation between 3 interest rates:
( 1 + i ) = ( 1 + f ) + ( 1 + i’)
i = ( 1 + f ) + ( 1 + i’) -1
i = i’ + f + i’f
Question
Calculate the inflation free rate when inflation rate is 5% &
market interest rate is 13% per year.
Solution:
Given,
f= 5% i=13% i’=?
We know,
i = i’ + f + i’f
0.13= i’ + 0.05+ i’*0.05
0.13= i’ (1+ 0.05)+ 0.05
i’ =0.07619
=7.619%
Actual(Current) dollars (An)=Actual dollars are estimates of
future cash flows for year n that take into account any
anticipated changes in amounts caused by inflationary or
deflationary effects.
Constant (real) dollars(An’)= it represents constant
purchasing power that is independent of passage of time.
Conversion from constant dollar to Actual dollars:
An= An’(1+ f)^n = An’(F/P, f, n)
Conversion from Actual dollar to constant dollar
𝑨𝒏
An’ = =An (P/F, f, n)
(𝟏 )^
Equivalence calculation under inflation:
Case I: All cash flows are estimated in constant dollars i.e.
constant dollar analysis.
Suppose that all cash flow elements are already given in
constant dollars and you want to compute the equivalent
present worth of constant dollars(An’) occurring in year n.
(𝑨𝒏’)
Pn= ′
( )^
Question
Consider the cash flows in constant dollar for the company as
follows. Managers want to earn 12% inflation free rate of
return(i’) before tax on investment, what would be present
worth of this project?
Period Net cash flow in constant
dollar
0 -2,50,000
1 1,00,000
2 1,10,000
3 1,20,000
4 1,30,000
5 1,20,000
Since all values are in constant dollars, we use the inflation-
free interest rate. We simply discount all dollar inflows at
12%
PW(12%)=-2,50,000+1,00,000
(P/A,12%,5)+10,000(P/G,12%,4)+20,000(P/F,12%,5)
=-
( . ) ( . ) . ∗
2,50,000+1,00,000* +10,000 +2
. ( . )^ . ( . )^
0,000(1+0.12)^-5
=1,63,010
Since the equivalent net receipts exceed the investment, the
project can be justified before considering tax effects.
Case 2: All cash elements are estimated in actual dollars i.e.
Actual dollar analysis.
To find the equivalent present worth of the actual dollar
amount (An) in year n, we may either use deflation method
or adjusted-discount method.
a) Deflation Method:
Question 2:
The project is expected to generate the following cash flows
in actual dollars.
Year Net cash flow in Actual
Dollars
0 -75,000
1 32,000
2 35,700
3 32,800
4 29,000
5 58,000
a) What are the equivalent year-0 dollars (constant
dollars) if the general inflation rate (f) is 5% per year?
b) Compute the present worth of these cash flows in
constant dollars at i’=10%.
Solution:
The net cash flows in actual dollars can be converted
to constant dollars by deflating them again assuming
5% yearly deflation factor. The deflated (or constant-
dollar) cash flows then can be used to determine
NPW at i’.
Converting Actual dollars into Constant dollars.
Year(n) Cash flows Deflating Cash flow
in actual factors in constant
dollar (1+f)^-n dollar
0 -75,000 1 -75,000
1 32,000 (1+0.05)^- 30,464
1=0.952
2 35,700 (1+0.05)^- 32,380
2=0.9070
3 32,800 (1+0.05)^- 28,340
3=0.864
4 29,000 (1+0.05)^- 23,867
4=0.823
5 58,000 (1+0.05)^- 45,472
5=0.784
Calculating equivalent present worth:
-75,000+30,464(1+0.1)^-1+32,380(1+0.1)^-
2+28,340(1+0.1)^-3+23,867(1+0.1)^-
4+45,472(1+0.1)^-5
=45,283.15
b) Adjusted-Discount Method:
the two step process shown above can be streamlined
by the efficiency of the adjusted-discount method
which performs the deflation and discounting in one
step.
pn=
( )^
where, i = i’ + f + i’f
Question:
Considering cash flow same as Q2, compute the
equivalent present worth of these cash flows.
Solution:
We have,
f=5% i’=10%
i = i’ + f + i’f
=0.1+0.05+0.1*0.05
=0.155
=15.5%
So,
PW=-75,000+32,000(1+0.155)^-1+35,700(1+0.155)^-
2+32,800(1+0.155)^-3+29,000(1+0.155)^-
4+58,000(1+0.155)^-5
=45,268
Case3: some of the cash flow elements are estimated in
constant dollars & others are estimated in actual dollars i.e.
mix dollar analysis.
In this situation we can convert all cash flow elements into
same dollars (either constant or actual). If the cash flow is
converted into actual dollars, the market rate i should be used
in calculating the equivalence value. If cash flow is converted
into constant dollars, inflation-free interest rate (i’) should be
used.
