Transcript Inflation and Price Changes - Industrial Engineering and

Inflation and Price Changes
Annual Benefits
Flood reduction
Irrigation
Recreation
Total Benefits
I.
Improve
Channel
$200,000
0
0
$200,000
Annual Costs
Depreciation
CR 2,500,000(A/F,10%,20)
Interest at 10%
O&M
Total Costs
Benefit - Cost Ratio
II.
Dam
$550,000
175,000
45,000
$770,000
I.
Improve
Channel
$ 43,750
250,000
80,000
$373,750
0.54
III.
Dam and
Channel
$650,000
175,000
45,000
$870,000
IL
Dam
$850,000
50,000
$900,000
0.85
III.
Dam and
Channel
$ 43,750
1,100,000
130,000
$1,273,750
0.68
Although all three values are less than one, assume that
one of the alternatives has to be chosen (i.e. doing nothing
is not an acceptable alternative).
Use II as basis of comparison because it has the least
negative PW of the three.
II - I: ($770,000 - $200,000 ) / ($900,000 - $373,750) = 1.08.
Accept I.
III - I: ($870,000 - $200,000)/($1,273,750 $373,750) = 0.74
Keep I
Therefore, choose Alternative I.
Note that this project also minimizes the costs to the
taxpayer.
General Price
Inflation & Deflation



Inflation - An increase in the prices paid for goods
and services bringing about a reduction in the
purchasing power of the monetary unit, is a
business reality that can affect the economic
comparison of alternatives.
Deflation - a decrease in prices with an increase in
the purchasing power of the monetary unit.
The concepts and methodology discussed in this
chapter apply to any price changes.
Dr. C.J. Su, IEEM Dept. HKUST
Consumer Price Index (CPI)


The CPI is a composite price index that measures
price changes in food, shelter, medical care,
transportation, apparel, and other selected goods and
services used by individuals and families.
(CPI annual inflation rate)k = (CPI)k - (CPI)k-1
(CPI)k-1
Dr. C.J. Su, IEEM Dept. HKUST
Annual Inflation Rate
Dr. C.J. Su, IEEM Dept. HKUST
Terminology

Actual dollars (A$): The number of dollars
associated with a cash flow as of the time it
occurs.
– A$ = current dollars, then-current dollars, and inflated
dollars, and their relative purchasing power is affected
by general price inflation.

Real dollars (R$): Dollars expressed in terms of
the same purchasing power relative to a
particular time.
– provide a consistent means of comparison. Sometimes
R$ are termed constant dollars.
Dr. C.J. Su, IEEM Dept. HKUST
Terminology


General price inflation rate ( f ): A measure of the
change in the purchasing power of a dollar during a
specified period of time. Many large organizations
have their own selected index that reflects the
particular business environment in which they
operate.
Combined (nominal) interest rate ( ic ): A nominal rate
that includes a market adjustment for the anticipated
general price inflation rate in the economy.
– market interest rate that takes into account both the
potential real earning power of money and the
estimated general price inflation in the economy.
Dr. C.J. Su, IEEM Dept. HKUST
Terminology

Real interest rate ( ir ) A nominal rate (%) that does
not include a market adjustment for the anticipated
general price inflation rate in the economy.
– It represents the time value change in future cash flows
based only on the potential real earning power of
money. It is sometimes called the inflation-free interest
rate.

Base time period ( b ): The reference or base time
period used to define the purchasing power of real
(constant) dollars.
Dr. C.J. Su, IEEM Dept. HKUST
Relationship Between
Actual Dollars and Real Dollars

Actual dollars as of any point in time, k, can be
converted into real dollars as of any base time
period, b
(R$)k = (A$)k [1/(1 + f)]k - b = (A$)k (P/F, f%, k - b)

In the case of deflation, i.e., f% < 0
(R$)k = (A$)k [1/(1 + f)]k - b
Dr. C.J. Su, IEEM Dept. HKUST

Suppose that your salary is $35,000 in year one, will increase
at 6% per year through year four, and is expressed in actual
dollars as follows:
End of Year, k Salary (A$)
1
$35,000
2
37,100 = 35,000 * (1 + 006)
3
39,326 = 35,000 * (1 + 006)2
4
41,685 = 35,000 * (1 + 006)3
If the general price inflation rate (f ) is expected to average 8%
per year, what is the real dollar equivalent of these actual
dollar salary amounts? Assume that the base time period is
year one (k = 1).
Year
Salary (R$ in Year 1)
1
$35,000(P/F, 8%, 0) = $35,000
2
37,100(P/F, 8%, 1) = 34,351
3
39,326(P/F, 8%, 2) = 33,714
4
41,685(P/F, 8%, 3) = 33,090
Example

An engineering project team is analyzing the
potential expansion of an existing production
facility. Different design alternatives are being
considered. The estimated after-tax cash flow
(ATCF) in actual dollars. If the general price
inflation rate ( f ) is estimated to be 5.2% per year
during the eight-year analysis period, what is the
real dollar ATCF equivalent to the actual dollar
ATCF? The base time period is year zero (b = 0).
Dr. C.J. Su, IEEM Dept. HKUST
Dr. C.J. Su, IEEM Dept. HKUST
Using Correct Interest Rate


Economic analyses can be made in either the
actual or real dollar domains with equal validity,
provided that the appropriate interest rate is used
for equivalence calculations.
If Cash flows are in terms of A$
then use Combined Interest Rate, ic
If Cash flows are in terms of R$
then use Real Interest Rate, ir
Dr. C.J. Su, IEEM Dept. HKUST
Relationship Among ic, ir, and f
Consider a future cash flow in actual dollars at time k,
(A$)k. The equivalent worth (EW) of this amount in the
base time period (b),
(EW)b = (A$)k [ 1/(1 + ic) ] k - b
From the relationship of R$ & A$
(R$)k = (A$)k [1/(1 + f)]k - b
Calculate EW using Real Dollar R$
(EW)b = (R$)k [ 1/(1 + ir) ] k - b = (A$)k [1/(1 + ic)] k - b
(A$)k[1/(1 + f)]k - b[1/(1 + ir)] k - b = (A$)k[1/(1 + ic)] k - b
[1/(1 + f)]k - b[1/(1 + ir)] k - b = [1/(1 + ic)] k - b
=> (1
+ f)(1 + ir) = (1 + ic)
Dr. C.J. Su, IEEM Dept. HKUST
Relationship Among IRRr, IRRc, and f
(1 + f)(1 + ir) = (1 + ic) or
ir = ( ic - f ) / ( 1 + f )
Similarly,
(1 + f)(1 + IRRr) = (1 + IRRc)
When IRRr = IRRc ?
And when A$ = R$ ?
f = 0, i.e., at base year ( b = 0)
Dr. C.J. Su, IEEM Dept. HKUST
If a company borrowed $100,000 today to be repaid at
the end of three years at a combined interest rate of
11%, what is the actual dollar amount owed at the
end of three years, the real rate of return to the
lender, and the real dollar amount equivalent in
purchasing power to the actual dollar amount at the
end of the third year? Assume that the base or
reference year is now (b = 0), and the general price
inflation rate ( f ) is 5% per year.
(A$)3 = (A$)o(F/P, ic%, 3) = 100,000(F/P,11%,3) = 136,763
ir = (ic - f) / (1+f) = (0.11 - 0.05) / 1.05 = 0.05714,
(R$)3 = (R$)o(F/P,ir%,3) = 100,000(F/P,5.714%,3)
= 118,140
(R$)3 = (A$)3 (P/F,f%,3) = 136,763(P/F,5%,3) = 118,140
Fixed and Responsive Cash
Flow

If future cash flows are predetermined by
contract, e.g., bond or a fixed annuity (rent,
interest, etc.), these amounts do not respond to
general price inflation (fixed cash flow).

If future amounts are not predetermined, they
may respond to general price inflation.
Dr. C.J. Su, IEEM Dept. HKUST

If f = 6% per year
The Impact of General Price
Inflation on After-Tax Analysis

The cost of some newly installed and more efficient electrical
circuit switching equipment is $180,000. It is estimated (in
base year dollars, b = 0) that the equipment will reduce
current net operating expenses by $36,000 per year for 10
years and will have a $30,000 market value at the end of the
tenth year. These cash flows are estimated to increase at the
general price inflation rate. Due to new computer control
features on the equipment, it will be necessary to contract for
some maintenance support during the first three years. The
maintenance contract will cost $2,800 per year. This
equipment will be depreciated under the MACRS (GDS)
method, and it is in the five-year property class. The effective
income tax rate (t) is 38%; the selected analysis period is 10
years; the projected general price inflation rate (f) is 8% per
year; and the MARR (after taxes) is ic = 15% per year.
Dr. C.J. Su, IEEM Dept. HKUST


PW(15%) = - 180,000 + 36,050(P/F,15%,1) + ... +
40,156(P/F,15%,10) = 33,790 (A$ analysis)
PW(6.48%) = -180,000 + 33,379(P/F,6.48%,1) +...
+ 18,600(P/F,6.48%,10) = $33,790 (R$ analysis)
Calculating an Effective
General Price Inflation Rate
If inflation rate varies f1, f2, f3,….., fN
The effective inflation rate
f = [ ( 1 + fk)]1/N - 1 , k = 1, …, N
Dr. C.J. Su, IEEM Dept. HKUST
Using Effective Inflation Rate

f = [ (1.04) (1.055)2 (1.07)3 (1.08)4 ] 1/10 - 1 = 6.79%

If the effective inflation rate was used, the results
would be slightly different for years one through
N - 1. However, the operating cost savings in the
last year (N) would be the same.
$36,000(1.0679)10 = $69,440
Dr. C.J. Su, IEEM Dept. HKUST
HomeWork
Chapter 9
# 10, 12, 28
Due: Dec. 1, 1998
Dr. C.J. Su, IEEM Dept. HKUST