inflation november 8, 2010. inflation can be defined as the rate of decline in the purchasing power...
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Inflation
November 8, 2010
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Inflation can be defined as the rate of decline in the purchasing power of money.
Purchasing power might be defined as:
a) kg of wheat you can get for a dollar
b) floating-point operations you can performfor a dollar
c) hours of human labour you can purchase for a dollar
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Measuring Inflation
1. The Consumer Price Index
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Measuring Inflation
1. The Consumer Price Index
2. The Industry Selling Price Index
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Measuring Inflation
1. The Consumer Price Index
2. The Industry Selling Price Index
3. The Implicit Price Index
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Hyperinflation
In some countries, the purchasing power of money has
declined rapidly and catastrophically – for example,
the Weimar Republic in the 1920’s.
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Hyperinflation
…and in Yugoslavia in the 1990’s…
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Hyperinflation
…and in Zimbabwe right now…
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Why Does it Matter?
If there is consistent inflation at a given rate, your wages go up by the same percentage as your bills.
So there should be no net effect on the economy.
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Causes of Inflation
One cause is the government printing money.
But inflation can also occur in a gold-backedcurrency – for example, when Pizarro conqueredPeru
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Why is there never Deflation?
There has been…
In the US, 1873-1896 (after the Civil War), and again in the GreatDepression
In the UK, 1919 (after WWI).
In Japan, 1996--2006.
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Dealing with Inflation
a) Less than 3%: ignore it
b) more than 3%: plan for it
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Actual Dollars and Constant Dollars
1. Establish a reference point in time (e.g., Nov 08, 2010)
2. At the reference point, 1 constant dollar = 1 actual dollar
3. At any other time, an actual dollar is a loonie, whereas a constant dollar is that sum of money needed to buy the goods that a loonie would have bought on November 08, 2010.
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Confusing Terminology
Uninflated Inflated
Real cash flowReal dollarsToday’s dollarsConstant dollarsNow dollarsConstant worth dollars
Nominal cash flowActual dollarsCurrent dollarsThen-current dollarsThen dollarsActual cash flow
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Two Strategies:
1.Convert all cash flows to constant dollars(not recommended)
2. Perform calculations using actual dollars(recommended, especially for after-taxanalysis)
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Example:
An asset can be purchased for $120,000. It costs $12,000/year to operate, and generates a revenue of $40,000/year (both these estimates assume no inflation). If the real MARR is 15% and the inflation rate is 8%, do a pre-tax analysis to see if itshould be purchased.
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Real-dollar Analysis:
PW = -120,000 +28,000(P/A,15,6)
= -120,000 + 28,000(3.7844)
= -14,037
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Analysing with Actual Dollars
To perform calculations with actual dollars, we needto adjust the MARR.
The adjusted, or inflated, or nominal MARR, MARR*,can be calculated from the real MARR via
MARR* = (1+MARR)(1+f) -1
where f is the rate of inflation.
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The adjusted, or inflated, or nominal MARR
MARR* = (1+MARR)(1+f) -1
Real MARR
Which is bigger, nominal MARR or real MARR?
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We will also refer to MARR* as if
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Year Real cash flow
Inflation factor
Actual cash flow
(P/F,if,N) Present Worth
0 -120,000 (F/P,8%,N) -120,000 1 -120,000
1 28,000 1.08 30,340 0.8052 24,348
2 28,000 1.1664 32,659 0.6482 21,172
3 28,000 1.2597 35,272 0.5220 18,410
4 28,000 1.3604 38,091 0.4202 16,007
5 28,000 1.4693 41,141 0.3384 13,921
6 28,000 1.5868 44,430 0.2724 12,105
if = (1+i)(1+f) – 1 = (1.15)(1.08)-1 = 0.242
-14,037
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This seems like a lot of extra work for nothing. But we need it if we’regoing to do after-tax analysis.
Consider the same problem, and suppose the asset is in Class 8
(declining balance depreciation at 20%) and the tax rate is 40%.
Year BTCFActual
CCA TaxedIncm.
Taxes(40%)
ATCFActual
Infl.Factr
ATCFReal
P/F,15,N PW
0 -120,000 -120,000 -120,000 -120,000
1 30,240 12,000 18,240 7,296 22,944 0.926 21,245 0.869 18,474
2 32,240 21,600 10,640 4,256 27,984 0.857 23,992 0.756 18,141
3 35,272 17,280 17,992 7,197 28,075 0.794 22,287 0.657 14,654
4 38,091 13,824 24,267 9,707 28,384 0.735 20,863 0.572 11,928
5 41,141 11,059 30,082 12,033 29,108 0.680 19,811 0.497 9,849
6 44,430 8,847 35,583 14,233 30,197 0.630 19,029 0.432 8,227
CCA Adjustment 1,068
-37,658So present worth, after tax, is
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Based on the cost of capital, your company’s MARR is 10%
You expect 5% inflation in the future.
You calculate the IRR of a proposed project, based on actualcash flows. What is the minimum value of IRR needed foryou to accept the project?
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Buying Versus Leasing
A piece of heavy equipment can be bought for $100,000It will last for 10 years, and falls into Class 8 (d=0.2).
Alternatively, the equipment can be leased for $20,000 ayear, with an option to buy for $5,000 at the end of theeighth year.
Assuming we would buy it at the end of the eighth year, and that we can deduct the lease cost from pre-tax income,should we lease or buy?
(The tax rate is 40% and the after-tax cost of capital is 10%.)
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Buy Now
Year UCC CCA taxes saved P/F,0.1,N PW
0.00 0.00 0.00 1.00 -100000.00
1.00 50000.00 10000.00 4000.00 0.91 3636.36
2.00 90000.00 18000.00 7200.00 0.83 5950.41
3.00 72000.00 14400.00 5760.00 0.75 4327.57
4.00 57600.00 11520.00 4608.00 0.68 3147.33
5.00 46080.00 9216.00 3686.40 0.62 2288.96
6.00 36864.00 7372.80 2949.12 0.56 1664.70
7.00 29491.20 5898.24 2359.30 0.51 1210.69
8.00 23592.96 4718.59 1887.44 0.47 880.50
9.00 18874.37 3774.87 1509.95 0.42 640.37
10.00 15099.49 3019.90 1207.96 0.39 465.72
total -75787.38
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Lease
Year Lease CostAfter-Tax Lease
Cost taxes saved P/F,0.1,N pw
0.00 0.00 0.00 1.00 0.00
1.00 20000.00 12000.00 0.00 0.91 -10909.09
2.00 20000.00 12000.00 0.00 0.83 -9917.36
3.00 20000.00 12000.00 0.00 0.75 -9015.78
4.00 20000.00 12000.00 0.00 0.68 -8196.16
5.00 20000.00 12000.00 0.00 0.62 -7451.06
6.00 20000.00 12000.00 0.00 0.56 -6773.69
7.00 20000.00 12000.00 0.00 0.51 -6157.90
8.00 20000.00 12000.00 0.00 0.47 -5598.09
9.00 5000.00 0.00 -200.00 0.42 -2015.82
10.00 0.00 0.00 -360.00 0.39 138.80
total -65,895.50
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Now suppose we expect 10% inflation over the next ten years.
Case 1: The lease costs are fixed by contract; do we buy or lease?
Case 2: The lease costs rise at the same rate as inflation; do we buy or lease?
if = (1+i)(1+f) – 1 = (1.10)(1.10)-1 = 0.21
In either case the inflated MARR is:
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Buying: Both cases
Year UCC CCA taxes saved P/F,0.21,N pw
0.00 0.00 0.00 1.00 -100000.00
1.00 50000.00 10000.00 4000.00 0.83 3305.79
2.00 90000.00 18000.00 7200.00 0.68 4917.70
3.00 72000.00 14400.00 5760.00 0.56 3251.37
4.00 57600.00 11520.00 4608.00 0.47 2149.67
5.00 46080.00 9216.00 3686.40 0.39 1421.27
6.00 36864.00 7372.80 2949.12 0.32 939.68
7.00 29491.20 5898.24 2359.30 0.26 621.28
8.00 23592.96 4718.59 1887.44 0.22 410.76
9.00 18874.37 3774.87 1509.95 0.18 271.58
10.00 15099.49 3019.90 1207.96 0.15 179.56
total -82,531.36
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Case 1: The lease costs are fixed by contract
Year Lease CostAfter-Tax
Lease Cost taxes saved P/F,0.21,N pw
0.00 0.00 0.00 1.00 0.00
1.00 20000.00 12000.00 0.00 0.83 -9917.36
2.00 20000.00 12000.00 0.00 0.68 -8196.16
3.00 20000.00 12000.00 0.00 0.56 -6773.69
4.00 20000.00 12000.00 0.00 0.47 -5598.09
5.00 20000.00 12000.00 0.00 0.39 -4626.52
6.00 20000.00 12000.00 0.00 0.32 -3823.57
7.00 20000.00 12000.00 0.00 0.26 -3159.98
8.00 20000.00 12000.00 0.00 0.22 -2611.55
9.00 5000.00 0.00 -200.00 0.18 -864.03
10.00 0.00 0.00 -360.00 0.15 53.51
total -45,517.42
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Case 2: The lease costs rise with inflation
Year Lease CostAfter-Tax
Lease Cost taxes saved P/F,0.21,N pw
0.00 0.00 0.00 1.00 0.00
1.00 22000.00 13200.00 0.00 0.83 10909.09
2.00 24200.00 14520.00 0.00 0.68 9917.36
3.00 26620.00 15972.00 0.00 0.56 9015.78
4.00 29282.00 17569.20 0.00 0.47 8196.16
5.00 32210.20 19326.12 0.00 0.39 7451.06
6.00 35431.22 21258.73 0.00 0.32 6773.69
7.00 38974.34 23384.61 0.00 0.26 6157.90
8.00 42871.78 25723.07 0.00 0.22 5598.09
9.00 11789.74 0.00 -471.59 0.18 2035.67
10.00 0.00 0.00 -933.75 0.15 -138.80
total 65,915.99
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Leasing Versus Buying.
A company is considering whether to rent or to buy a Plebney machine.It costs $100,000 to buy, and $40,000/year to rent. The company will need the machine for another three years, after which it will have a salvage value of $20,000.
The machine depreciates at 30% per year.
The company’s pre-tax MARR is 10%; lease charges are paid on Dec 31.
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Case 1: No Tax, No Inflation
Buy: PW = -100,000 + 20,000(P/F,0.1,3)
= -100,000 + 20,000(0.7513)
= -84,974
Lease: PW = -40,000(P/A,0.1,3)
= -40,000(2.487)
= -99,480
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Case 2: 50% Tax, No Inflation
After tax MARR = 0.1 × 0.5 = 0.05
Buy: PW = -100,000×CCTF* + 20,000(P/F,0.05,3)×CCTF
CCTF = 1 – td/(i+d) = 1 – 0.5×0.3/0.35 = 0.57
CCTF* = 0.58
So PW = -58,000 + 11,300(0.86) = -$48,282
Lease: PW = -40,000(P/A,0.05,3)(1-0.5)
= -40,000(2.72)(0.5)
= --$54,400
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Case 3: 50% Tax, 15% Inflation
After tax MARR = 0.1 × 0.5 = 0.05
Inflated after-tax MARR* = (1+MARR)(1+f) -1 = 1.05×1.15-1 = 0.21
Assume salvage price does not inflate
Buy: PW = -100,000×CCTF* + 20,000(P/F,0.21,3)×CCTF
CCTF = 1 – td/(i+d) = 1 – 0.5×0.3/0.51 = 0.706
CCTF* = 0.73
So PW = -73,000 + 14,012(0.56) = -$65,153
If salvage price rises with inflation, then
PW = -100,000×CCTF* + 20,000(P/F,0.05,3)×CCTF = -$60,857
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Case 3: 50% Tax, 15% Inflation
Lease Costs fixed by Contract (actual dollar costs constant):
PW = -40,000(P/A,0.21,3)(1-0.5)
= -40,000(2.07)(0.5)
= -$41,400
Lease Costs rise with inflation (actual dollar cost increases, real dollar cost constant):
PW = -40,000(P/A,0.05,3)(1-0.5)
= -40,000(2.72)(0.5)
= -$54,400