Chapter 11
Inflation and Its Impact on Project Cash Flows
Measure of Inflation
11.1
11.3
(a) Average price index
11.4
100(1 0.05)(1 0.08) 113.40
100( / , , 2) 113.40
6.4894%
F P f
f
+ + =
=
=
Actual versus Constant Dollars
11.6
Given: 8%, 4%if= =
, 10 annuity payments in actual dollars
11.7
Given: 13%, 5%,i f= =
maintenance costs are given in constant dollars.
0.13 0.05
‘ 7.62%
1 0.05
1
i f
if
− −
= = =
+
+
11.8
Given: 14%, 5%i f= =
(a)
11.9
Given: $25,000, 0.75%Pi= =
per month,
0.33%f=
per month
• 20th payment in actual dollars:
n
Actual dollars Constant Dollars
0 $25,000 $25,000(P/F,5%,0) = $25,000
11.10
(a) Constant-dollar analysis: we need to find the inflation-free interest rate.
(b) Actual–dollar analysis
Period
Net Cash Flow
in Constant $
Conversion
factor
Net Cash Flow
in Actual $
1 $10,000
1
(1 0.07)+
$10,700
Comments: As an alternative way of finding the equivalent cash flows in
actual dollars, we may use the compound growth rate (geometric growth and
inflation):
11.11
Given: 9%, 3.8%if= =
, we find the inflation-free interest rate as follows:
11.12
Given: 12%, 6%if= =
, bond interest rate = 9% compounded semiannually,
face value = $1,000
• The 15th interest payment in actual dollars:
Equivalence Calculation under Inflation
11.13
11.14
Given: 1%i=
per month,
0.5%f=
per month, P = $25,000, N = 60 months
11.15
Given: ‘ 6%, 5%, 5 years, $2.2i f N A= = = =
million in constant dollars
• Market interest rate:
0.06 0.05 (0.06)(0.05) 11.3%i= + + =
• Actual dollar analysis:
Period
Net Cash
Flow
in Constant $
Net Cash Flow
in Actual $
Equivalent
Present Worth
1
$2,200,000
$2,310,000
$2,075,472
11.16
1
Given: 12%, 5%, 7%, 5 years, $5,000i f gN A= = = = =
in constant dollars
• Actual dollar analysis:
Period
Net Cash
Flow
in Constant $
Net Cash Flow
in Actual $
Equivalent
Present Worth
1
$5,000
$5,250
$4,688
2
5,350
5,898
4,702
3
5,725
6,627
4,717
4
6,125
7,445
4,732
5
6,554
8,365
4,746
11.17
Given: 0.75%i=
per month,
0.5%f=
per month,
$8,000, 24P N= =
months
2
2,425,500
1,957,992
3
2,546,775
1,847,162
4
2,674,114
1,742,606
5
2,807,819
1,643,968
(a) Inflation–free interest rate:
11.18
Given: 6%i=
compounded monthly,
f
= 4% compounded annually, number
of months to deposit = 240 months, number of annual withdrawals = 15, first
withdrawal = 6 months after retirement.
• Effective inflation rate per semiannual: Since the first withdrawals is made after 6
months from retirement, it is necessary to calculate the effective inflation rate per
semiannual.
• Then, the conversion of constant dollar to actual dollar is as follows:
N
Actual
dollars
41
$134,050
43
$139,411
45
$144,986
47
$150,784
49
$156,815
51
$163,086
53
$169,608
55
$176,391
57
$183,445
59
$190,782
63
$206,364
• Equivalence calculation: To find the required equal monthly deposit amount (A),
we establish the following equivalence relationship:
12
0.06 0.5%
12
0.06
1 1 6.168%
12
m
a
i
i
= =
= + −=
11.19
Given : 0.5%i=
per month,
4%f=
per year
(a)
• Actual dollar analysis:
$232,131
(b)
• Effective annual interest rate:
12
(1 0.06 /12) 1 6.1678%
a
i= + −=
• Amount of the first deposit
1
()A
:
1
1
1
1
( $12,196.20)( / , 6.1678%, 40) $4,801, 021
( $12,196.20)(161.4438) $4,801,021
$12,196.20 $29,738.03
$17,541.83
A FA
A
A
A
+=
+=
+=
=
11.20
Given: 8%i=
per year,
6%f=
per year
(b) Equivalent single-sum amount at
0n=
(c) Required annual deposit in actual dollars:
$129,077( / ,8%,10) $19, 236A A P= =
Effects of Inflation on Project Cash Flows
11.21 Consider the following project’s after-tax cash flow and the expected annual
general inflation rate during the project period:
End of
year
Cash flow
in actual dollars
Expected general
inflation rate
0 -$45,000
(a) The average annual general inflation rate:
(b) Constant dollars:
n
Actual
dollars
Constant
dollars
0
-$45,000
-$45,000
Conversion factors:
( / ,3.5%,1) 0.9662
( / , 4.2%,1)( / ,3.5%,1) 0.9272
( / ,5.5%,1)( / , 4.2%,1)( / ,3.5%,1) 0.8789
PF
PF PF
PF PF PF
=
=
=
(c) The project is still profitable in an inflationary economy.
11.22 (a) and (b)
Income Statement
Revenue $114,000 $114,000
Expenses:
O&M 56,490$ 59,315$
Depreciation 11,000$ 8,800$
11.23 (a) and (b)
0 1 2 3 4 5 6
Income Statement
Revenue $152,250 $159,863 $167,856 $176,248 $185,061 $194,314
Expenses:
Cash Flow Statement
Cash from operation
Net Income $18,810 $12,155 $29,935 $37,651 $39,949 $46,508
Depreciation $24,000 $38,400 $23,040 $13,824 $13,824 $6,912
(c) Present value gain (or loss) due to inflation:
Project Cash Flows without Inflation
0 1 2 3 4 5 6
Income Statement
Revenue $145,000 $145,000 $145,000 $145,000 $145,000 $145,000
Expenses:
O&M 82,000$ 82,000$ 82,000$ 82,000$ 82,000$ 82,000$
Depreciation 24,000$ 38,400$ 23,040$ 13,824$ 13,824$ 6,912$
Interest 10,800$ 10,800$
(d) Present value gain due to borrowing:
Comments: Present value gain due to inflation in (c) is largely from the
fact that the firm was able to finance the project at 9% interest whereas
the market interest rate is 18%. In practice, it is not likely that the firm
would be able to access such a cheap money during the inflationary
period.
Net Financing Cost Net
nPrincipal Interest (A/T) Loan Flow
0+$120,000 +$120,000
Cash Flow Statement
11.24 Effects of inflation on cash flows:
(a) Project Cash Flows with Inflation
0 1 2 3 4 5
Income Statement
Revenue $23,100 $20,948 $17,364 $18,233 $19,144
Cash Flow Statement
Cash from operation
Net Income $10,260 $7,891 $7,676 $9,557 $10,795
Depreciation $4,000 $6,400 $3,840 $2,304 $1,152
(b) Income Statement (without inflation)
0 1 2 3 4 5
Income Statement
Revenue $22,000 $19,000 $15,000 $15,000 $15,000
Expenses:
Depreciation 4,000 6,400 3,840 2,304 1,152
Interest 2,000 1,396 731
11.25 (a), (b), and (c); The project is acceptable
Income Statement
0 1 2 3
Income Statement inflation
Revenue (Labor Savings) 5% $94,500 $99,225 $104,186
Expenses:
O&M
Cash Flow Statement
Cash from operation
Net Income $41,267 $33,086 $53,067
Depreciation $25,722 $44,082 $15,741
Note: The general inflation rate is 6% and this rate should be used in converting
the actual dollars to it equivalent constant dollars