Transcript
Engineering Economics
ECO 1192
Lecture 7: Depreciation, Taxes and Cash Flows
Claude Théoret University of Ottawa
Recommended Reading
• Fraser et al. chapters 6, 7 & 8
• Newnan et al. chapter 11 & 12
• Park chapter 8 & 9
Lecture 7: Depreciation, Taxes and Cash Flows
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Lecture Objective
• Examine the impact of depreciation and income taxes on a project’s • Before- and After-Tax income • Cash flows • Worthiness
Lecture 7: Depreciation, Taxes and Cash Flows
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Working Assumptions
Assumptions dropped with this lecture
• Owner/equity capital only
no debt capital • No income taxes; no depreciation of capital assets
Assumptions still applicable
• No price changes
• No uncertainty or risk
• No intangibles or imponderables
Lecture 7: Depreciation, Taxes and Cash Flows 4
Depreciation of capital assets
(also known as “fixed” assets)
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Revenue-producing assets
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Working Capital
• Cash necessary to begin and sustain operations
• Purchase materials, build inventory
• An inflow at the beginning of a project • An outflow at the end of a project • Termed « capital » but ignored as a cost for tax purposes
• neither depreciable nor tax deductible
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Cash Flows (thus far)
• Net cash flows = Cash Inflows – Cash Outflows • Cash Inflows Revenues from sales, investments, gifts, inheritances …. • Cash Outflows Initial investment (P), operating expenses such as utilities, wages and salaries, advertising, interest on loans … • Before-Tax Cash Flows (BTCF) = Revenues - costs • After-Tax Cash Flows (ATCF) • Revenues – operating costs - income taxes
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Depreciation (business expense)
• Definition : Decrease in the market value of a physical or fixed asset • e.g., buildings, machinery and equipment • Assets that can be depreciated must • be used or held for the production of income • have a definite service life that exceeds one year • wear out, decay, get used up, become obsolete or decrease in value from natural causes • These assets are treated differently from operating expenses (e.g., wages & utilities) • Operating expenses are expensed at the time they are incurred (wages are paid for a specific period of time). • Physical assets are capitalized because they usually provide services beyond an accounting period.
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Depreciation of Physical Assets
Reasons
1. use-related physical loss (wear & tear) 2. time-related physical loss (even if asset is not used)
Example
car; light bulb; slide rule
car; manure spreader; slide rule affected by humidity, dust, sunshine slide rules; 1st generation calculators and computers (software and hardware)
3. functional loss (asset is unable to meet demand expectations)
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Tax Treatment of Depreciation
• The Canadian tax system defines the maximum depreciation claimable in any year for a depreciable asset • capital cost allowance (CCA) • Generally • companies wish to depreciate assets as quickly as possible in order to maximize tax savings from depreciation. • governments want companies to depreciate assets as slowly as possible to keep tax savings at a minimum. • Instead of focusing on depreciable assets individually (e.g., a specific truck in a fleet of trucks), a company’s assets are grouped by asset class for which specific rates are used to determine depreciation charges.
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The Capital Cost Allowance (CCA) System
• The purchase of a long-term depreciable asset generates a capital expense
• all tangible assets are depreciable except for land.
• For a variety of reasons discussed earlier, a tangible asset (e.g., a pizza delivery vehicle) decreases in value over time (i.e., it depreciates). • Depreciation is intended to capture the loss in value of the tangible asset each year or during some other timeframe. • Depreciation expenses decrease the asset’s book value over time (recorded in the company’s balance sheet by accountants).
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Sample CCA (Depreciation) Rates
(Canada Revenue Agency)
CCA Rate (%)
5 to 10
25 40 50
Class
1, 3, 6
9 16 22
Description
Buildings
Aircraft, aircraft furniture, and equipment Taxis, rental cars, freight trucks Power-operated moving equipment
CCA ≡ Capital Cost Allowance ≡ depreciation
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Advantages of a Reliable Depreciation Model
1.
Provides an accurate value of owned assets to make good managerial decisions
•
For example, the optimal time to replace an asset
Assists in planning (e.g., when to keep or sell an asset to minimize economic costs i.e., period of use or ownership) 3. Contributes to the accurate determination of the production cost of a good or service for elaborating prices. 4. Provides a more accurate picture of taxes payable and profits (financial health of firm)
2.
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General Depreciation Rules
• Depreciate a physical asset (e.g., delivery truck) as
• rapidly as is legally possible to derive the largest
benefit from offsetting tax credits • early (soon) as possible in an asset’s life
•
Depreciation has an indirect effect on cash flows but a direct effect on net income
• Depreciation affects cash flows through another
variable (not a direct effect)
∆+ DEPRECIATION CHARGES ∆- TAXABLE INCOME ∆- TAXES PAYABLE ∆+ AFTER TAX CASH FLOW (ATCF)
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Economic & Accounting Depreciation
Economic Depreciation
• Economic depreciation = Market value of an asset
(t1) less its market value (t0) • Market value of asset on January 1, 2006 – its market value on December 31, 2006
Accounting Depreciation
• Formula-based methods for distributing the cost of
a physical asset over its useful life (Note: There are many definitions of "life") • Systematic allocation of an asset's value over its depreciable life. • Major focus: book value and tax depreciation
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Economic & Accounting Depreciation
Economic Depreciation • A truck’s market value was
• $150,000 on January 1, 2004 • $130,000 on December 31, 2004. • Its economic depreciation in 2004 was
($150,000 - $130,000) = $20,000
Accounting Depreciation • Based on a variety of depreciation formulas such as Sum-of-years’-digits (SOYD), straight line (SL) and declining balance (DB) and combinations of these methods.
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Categories of Asset Values
Initial Cost X Salvage X Scrap S X c a Description r p Current market value (what it would sell for today) Depreciated value of an asset based on depreciation formulas
Asset values
Market
Book
Scrap
Actual (market) value at the end of an asset’s physical life
Either the actual value at the end of the useful life or an estimate of the salvage value based on depreciation formulas
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Salvage
For this course: Scrap and salvage values are identical
Accounting Depreciation Methods 1. Straight line (SL) 2. Declining balance (DB)
Description
The book value of an asset diminishes by an equal amount each year; total asset depreciation = (P – SV) The book value of an asset diminishes by an equal proportion each year; a constant depreciation rate (d) is applied to a decreasing book value; full depreciation i.e., (P - SV) is seldom obtained The annual depreciation is calculated by summing the digits corresponding to the years of asset life; leads to full depreciation; applies a declining ratio to a constant depreciation base (depreciation charges decrease over time) Twice the rate of “single” declining balance method Annual depreciation is based on the actual FOR THIS COURSE production level in a specific year relative
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3. Sum-of-years-digits (SOYD)
NOT REQUIRED FOR THIS COURSE
4. Double-declining balance (DDB) 5. Units-of-production (UOP) NOT REQUIRED
N
to the total production during the service life of the asset Lecture 7: Depreciation, Taxes and Cash Flows
Example: Quickie Pizzeria
ITEM 2001 2002 2003
A. REVENUES (Pizza Sales)
100,000
125,000
150,000
B. OPERATING EXPENSES Pizza Ingredients + Labour 50,000 20,000 55,000 25,000 60,000 30,000
+ Utilities
+ Rental cost B. TOTAL OPERATING EXPENSES C. = (A. - B.) Before-Tax Cash Flow D. Depreciation (on the $30,000 van purchased on January 1, 2001) E. TAXABLE INCOME F. TAXES (50%) G. NET INCOME H.= C.- F. After-Tax Cash Flow
5,000
5,000 80,000 20,000
6,000
6,000 92,000 33,000
7,000
10,000 107,000 43,000
10,000 10,000 5,000 5,000
10,000 23,000 11,500 11,500
10,000 33,000 16,500 16,500 43,000-16,50020 = 26,500
Lecture 7: Depreciation, Taxes and Cash Flows 20,000-5,000 33,000-11,500 = 15,000 = 21,500
BTCF and ATCF
After-Tax Cash flow (ATCF) = Before-tax cash flow (BTCF) – Income taxes = Net Income (After Taxes) + Depreciation
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Example: ATCF and Net Income
ITEM Gross Income Expenses 1. Cost of Goods Sold 2. Depreciation 3. Operating Expenses Taxable Income Taxes (40%) 20,000 4,000 6,000 20,000 8,000 -8,000 -6,000 -20,000 INCOME 50,000 After-Tax Cash Flow +50,000
Net income (after taxes)
After-Tax Cash Flow
+12,000
+16,000**
After-tax cash flow** = $50,000-20,000-6,000-8,000 = $16,000
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Depreciation Methods
1. Straight Line Method
• constant annual depreciation charges {constant rate applied to a constant depreciation base = (P - SV)}; • method fully accounts for the depreciation base (P - SV)
2. Sum-Of-Years'-Digits (SOYD) [not required]
• declining annual depreciation charges • a variable annual rate is applied to a constant depreciation base) • This method fully accounts for the depreciation base (P-SV)
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Depreciation Methods (cont’d)
3. Declining Balance (DB)
• declining annual depreciation charges
• constant depreciation rate applied to a
declining depreciation base • DOES NOT usually account for the full depreciation base (P-SV)
overshoots or undershoots (P-SV)
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Other Depreciation Methods (cont’d)
• 4. Sinking Fund • 5. Production Rate • 6. Combination of Linear and Non-Linear Methods • 7. ....
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Straight Line Depreciation
Initial Cost Less Cumulative Depreciation
Initial Investment (P)
Salvage Value (SV)
0
1
1
2
3
4
5
End-of-Year
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Lecture 7: Depreciation, Taxes and Cash Flows
Declining Balance Depreciation
Initial Cost Less Cumulative Depreciation
Initial Cost (P)
P – Σ Depreciation ≠ SV
A
Salvage Value
B 1 1 2 3 4 5
N = 5 years
0
End-of-Year
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Lecture 7: Depreciation, Taxes and Cash Flows
Sum-of-Years’ Digits Depreciation
Initial Cost Less Cumulative Depreciation
FOR INFORMATION ONLY
Initial Cost (P)
P – Σ Depreciation = SV
N = 5 years
1 1 2
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Salvage Value
0
3
4
5
End-of-Year
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Key Depreciation Parameters
1. Annual depreciation charges 2. Cumulative depreciation = sum of depreciation charges over the life of a capital asset = Σ Depreciation Charges 3. Book Value = asset's first cost less its cumulative depreciation = Initial Cost (P) – ΣDepreciation Charges
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Depreciation & Book Value
(These formulas DO NOT account for the “Half-Year” Rule)
DEPRECIATION METHOD
STRAIGHT LINE METHOD (SL) SUM-OF-YEARS' DIGITS (SOYD)
ANNUAL DEPRECIATION {P-SV}/N
CUMULATIVE DEPRECIATION n{(P-SV)/N}
BOOK VALUE
P - n{(P-SV)/N}
Information Only
P*d(1 –d)n-1 P{1-(1-d)n}
2(P-SV)(N-n+1) -------------N(N+1) This is a decaying arithmetic series
2(P-SV)(2N-n+1) -------------N(N+1)
P - 2(P-SV)(2N-n+1) ---------------N(N+1)
DECLINING BALANCE (DB)
P(1-d)n
Book Value = Initial cost of asset – cumulative depreciation
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Straight Line Depreciation
Given: P=$900; SV=$70; N= 5 years; no half-year rule
Year
Annual Depreciation
Cumulative Depreciation
Book Value
0
1 2 3 4 5
-166 166 166 166 166
-166 332 498 664 830
900
734 568 402 236
70 = SV
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Asset is fully depreciated after 5 years
Lecture 7: Depreciation, Taxes and Cash Flows
Example: Straight Line Depreciation
• Annual Depreciation = (P-SV)/N = (900-70)/5 = 166 • Cumulative Depreciation (end of year N*) = N*(P-SV)/N = 3{(900-70)/5} = 498 (N* = 3 years) • Note that the asset’s book value (BV) equals its salvage value (=$70) at the end of the 5th year
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Example: Declining Balance (DB)
Given: P=$900; SV=$70; N= 5 years; d=0.20; no half-year rule Year 0 1 2 3 4 5 Annual Depreciation -(1/5)(900)= 180 (1/5)(720)= 144 (1/5)(576)= 115.2 (1/5)(460.8)= 92.2 (1/5)(368.6)= 73.7 Cumulative Depreciation -180 324 439.2 521.4 595.1 Book Value 900 = P 900-180=720 720-324=576 460.8 368.64
294.17 ≠ SV
The depreciation base (P-SV) = (900-70=830) is not fully accounted for as the book value is $294.17 at the end of the fifth year and not $70 as in the case of other depreciation Lecture methods. 7: Depreciation, Taxes and Cash Flows 33
Example: SOYD (Sum-of-years’-digits)
Given: P=$900; SV=$70; N= 5 years;
Year 0 Annual Depreciation -Cumulative Depreciation --
No half-year rule
Book Value 900
1 2
3 4 5
(5/15)(900-70) = 277 (4/15)(900-70) = 221
(3/15)(900-70) = 166 (2/15)(900-70) = 111 (1/15)(900-70) = 55
277 498
664 775 830
623 402
236 125
70 = SV
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Asset is fully depreciated after 5 years
Lecture 7: Depreciation, Taxes and Cash Flows
Income Taxes
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Income Taxes
• Not a comprehensive tax treatment of income generated by capital and other assets.
• Objective is to examine the impact of income taxes on
project cash flows and on project summary measures (e.g., Present Worth values).
• To simplify tax calculations, we assume
• constant and common (all sources of income) tax rate
(t) • the absence of capital gains or losses • simple accounting of depreciation recapturing
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Introduction
• Taxes levied by different levels of government can have significant impacts on the viability of projects • important to include income taxes in the economic analysis of all projects • For economic analyses, the most important tax is a tax on income i.e., income taxes which are a charge on net income. In this context, net income is the difference between a project’s receipts and expenses. • Before- and After-Tax MARR • MARR after-tax ≈ (1 – t)MARR before-tax where “t” is the income tax rate (both an average and marginal tax rate for the purposes of this course)
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Canadian Tax System
• The system defines the maximum amount of depreciation that is claimable in any year for a depreciable asset. This amount is called the “capital cost allowance”. • Note that companies want to depreciate assets as quickly as possible in order to maximize tax savings from depreciation while governments want companies to depreciate assets as slowly as possible to keep tax savings at a minimum. • Instead of focusing on depreciable assets individually, a company’s assets are grouped by capital cost allowance asset class for which specific rates are used to determine depreciation charges.
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Key Features of Canadian Tax Rules
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Corporate Tax Rates Around the World
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Reminder
↑ Annual depreciation charges
↓ Taxable income ↓ Taxes payable ↑ After-Tax Cash Flow (ATCF)
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Example
• Straight Line Method used to depreciate capital assets (machinery, buildings ..) • Income tax rate of 50% applies to operating profits and losses, and to depreciation recapturing where applicable • There is
• No half-year rule (see next slide)
• No debt capital (owner equity only)
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Half-Year Rule
• Since November 1981, only 50% of the initial or capital cost of acquiring an asset (its “P”) can be used as the basis for the calculation of depreciation in the year of purchase. • The remaining 50% of the asset’s capital cost is included in subsequent years for the calculation of depreciation charges.
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Half-Year Rule: Example
• A “trucker” had a very profitable year and decided to purchase a new truck ($200,000) in late December to reduce his income tax burden. • In the absence of the half-year rule, the truck owner would have applied the full CCA rate (say 10%) to the $200,000 to determine 2004 depreciation charges = 200,000(0.10) = $20,000 • With the half-year rule, the trucker could use only 50% of $200,000 (i.e., $100,000) as the depreciation base for 2004 leading to depreciation charges of $10,000 (or 50% less than without the half-year rule).
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Annual Depreciation Changes
(Without the Half-Year Rule)
End of Year 1 2 3 4 5 6 7 8 Depreciation Charges 0.10(200,000)= $20,000 0.10(180,000)= 18,000 0.10(162,000)= 16,200 0.10(145,800)= 14,500 0.10(131,220)= 13,122 …..
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Annual Depreciation Changes
(With the Half-Year Rule)
End of Year 1 (half-year rule) 2 3 4 Depreciation Charges 0.10(200,000*0.5) = 10,000 0.10(190,000)= 19,000 0.10(171,000)= 17,100 0.10(153,900)= 15,390
5 6 7 8
0.10(138,510)= 13,850 …..
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Example
The following information is provided on an investment:
• A revenue-generating capital asset has first cost (P) = $70,000 three-year life (N = 3) salvage value after 3 years (SV) = $10,000 • Before-Tax Cash Flow (BTCF) in next Table = Operating Revenues – Operating Costs
• Before-Tax MARR = 15%
• After-Tax MARR = 10%
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The Effect of Taxes on Salvage or Scrap Value
• • When an asset is salvaged or scrapped, unless the value received is zero, money comes into the firm as income. Any money received that is in excess of the asset’s remaining book value is new revenue, and is taxable.
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SV & NSV
• Net salvage value (NSV) = After-tax salvage value = Salvage value – (salvage value – book value)tax rate • NSV = [SV – (SV – BV)t] where t ≡ tax rate • If (SV > BV), a tax liability arises SV > NSV • If (SV < BV), a tax credit arises SV < NSV • If (SV = BV), SV = NSV (no tax credit or liability) Note that NSV = SV for SL depreciation NSV ≠ SV for DB depreciation
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Example (con’td)
Year BTCF (Operating Revenues – Operating Expenses) (1) -70,000 40,000 50,000 Annual (Straight Line) Depreciation (2) -20,000 20,000 Taxable Income (3) = (1) - (2) -20,000 30,000 Taxes Payable (4) = (3)t -10,000 15,000 ATCF
(5) = (1) – (4) -70,000 30,000 35,000
0 1 2
3
30,000 10,000 (SV)
20,000 ---
10,000 ---
5,000 ---
25,000 + 10,000
No half-year rule; BTCF= Before-Tax Cash Flow; ATCF = After-Tax Cash Flow
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BTCF and ATCF: NPW Calculation
Present Worth (BTCF) = -70,000 + 40,000(P/F,15%,1)
Year BTCF (Operating Revenues – Operating Expenses) (1) -70,000 40,000 50,000 30,000 10,000 (SV) Annual (Straight Line) Depreciation (2) -20,000 20,000 20,000 --Taxable Income (3) = (1) - (2) -20,000 30,000 10,000 --Taxes Payable (4) = (3)t -10,000 15,000 5,000 --ATCF
+50,000(P/F,15%,2) + [30,000+10,000](P/F,15%,3)
(5) = (1) – (4) -70,000 30,000 35,000 25,000 + 10,000
0 1 2 3
Present Worth (ATCF) = -70,000 + 30,000(P/F,10%,1)
+35,000(P/F,10%,2) + [25,000+10,000](P/F,10%,3)
• •
Before-Tax MARR = 15% After-Tax MARR = 10%
No half-year rule; BTCF= Before-Tax Cash Flow; ATCF = After-Tax Cash Flow
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BTCF and ATCF: Annuity Method
AEW (BTCF) = -70,000(A/P,15%,3)
Year BTCF (Operating Revenues – Operating Expenses) (1) -70,000 40,000 50,000 30,000 10,000 (SV) Annual (Straight Line) Depreciation (2) -20,000 20,000 20,000 --Taxable Income (3) = (1) - (2) -20,000 30,000 10,000 --Taxes Payable (4) = (3)t -10,000 15,000 5,000 --ATCF
(5) = (1) – (4) -70,000 30,000 35,000 25,000 + 10,000
+ {40,000(P/F,15%,1) + 50,000(P/F,15%,2) + [30,000+10,000](P/F,15%,3)} (A/P,15%,3)
0 1 2 3
AEW (ATCF) = -70,000(A/P,10%,3)
+ {30,000(P/F,10%,1) + 35,000(P/F,10%,2) + [25,000+10,000](P/F,10%,3)} (A/P,10%,3) • • Before-Tax MARR = 15% After-Tax MARR = 10%
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No half-year rule; BTCF= Before-Tax Cash Flow; ATCF = After-Tax Cash Flow
Lecture 7: Depreciation, Taxes and Cash Flows
Before-tax rate of return (BTRR)
(Rate of return on the BTCF)
Equation Find i* (from column 1) such that AE cash inflows = AE cash outflows OR Find i* such that PW cash inflows = PW cash outflows Using PW cash inflows = PW cash outflows = 40,000(P/F,i*,1)+50,000(P/F,i*,2)+ (30,000+10,000)(P/F,i*,3) = $70,000 Solve for i*; i*= 39%
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After-tax rate of return (ATRR)
(Rate of return on the ATCF)
Equation Find i* (from column 5) such that AE cash inflows = AE cash outflows OR PW cash inflows = PW cash outflows Using PW cash inflows = PW cash outflows 35,000(P/A,i*,2)+(25,000+10,000)(P/F,i*,3) = 70,000 Solve for i* ; i* = 10% (MARR=10%)
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Book value of capital asset after 2 years
Book Value (BV) = P - cumulative asset depreciation = 70,000 - (20,000+20,000) = $30,000
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Multiple IRRs are now possible
• We need to differentiate between two rates of return (IRR)
1. For the project 2. On the owner’s (or owners’) equity or
investment.
•
The project’s and the owners’ IRR are identical in this example because funds were not borrowed from external sources
•
the owners supplied ALL the capital funds
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Example: Two Rates of Return (Before and After Taxes)
• Assumptions
• Straight-Line Depreciation
• 50 per cent tax rate • No inflation (no price changes)
• No debt capital (all equity capital)
• Negligible salvage value (SV = 0) • No half-year rule
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Example: BTCF and ATCF
Year (A) BTCF (Before-Tax Cash Flow) (B) Annual Depreciation (SL) (C) Taxable Income (D) Taxes Payable (t=50%) (E) After-Tax Cash Flow (ATCF) (F)
0 1 2 3 4
-2,991 1,000 1,000 1,000 1,000
--598 598 598 598
--402 402 402 402
--201 201 201 201
-2,991 799 799 799 799
5
1,000
598
402
201
799
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Lecture 7: Depreciation, Taxes and Cash Flows
BTCF and BTRR
Example: BTCF and ATCF
Year (A) BTCF Annual (Before-Tax Depreciation Taxable Cash Flow) (SL) Income (B) (C) (D) Taxes Payable (t=50%) (E) After-Tax Cash Flow (ATCF) (F)
0 1 2 3 4 5
-2,991 1,000 1,000 1,000 1,000 1,000
--598 598 598 598 598
--402 402 402 402 402
--201 201 201 201 201
-2,991 799 799 799 799 799
Column B Find i* such that PW (Cash Outflows) = PW (Cash Inflows) 2,991 = 1,000(P/A,i*,5); i* = 0.2 or 20%
BTCF = Before-Tax Cash Flow; BTRR = Before-Tax Rate of Return
Lecture 7: Depreciation, Taxes and Cash Flows 59
ATCF and ATRR (After-tax rate of return)
Example: BTCF and ATCF
Year (A) BTCF Annual (Before-Tax Depreciation Taxable Cash Flow) (SL) Income (B) (C) (D) Taxes Payable (t=50%) (E) After-Tax Cash Flow (ATCF) (F)
0 1 2 3 4 5
-2,991 1,000 1,000 1,000 1,000 1,000
--598 598 598 598 598
--402 402 402 402 402
--201 201 201 201 201
-2,991 799 799 799 799 799
Column F Find i* such that PW (Outflows) = PW (Inflows) 2,991 = 799(P/A,i*,5) i* = 0.105 or 10.5%
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Is the ATCF (or the Net Income) sensitive to depreciation methods?
The following examples have identical cash flows but different depreciation methods.
? ? ?? ? ?
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Answer: Yes the bottom line (ATCF) is sensitive to depreciation methods.
Lecture 7: Depreciation, Taxes and Cash Flows
Is the ATCF (or Net Income) sensitive to depreciation methods?
• Different depreciation methods have different impacts on a project's bottom line. • Generally, non-linear methods provide higher aftertax profits
• Goal: depreciate an asset as quickly as legally possible
• However, one must be careful with the declining balance method (DB) because it does NOT explicitly account for a project’s salvage value (SV).
• Reason why non-linear methods such as DB are
combined with the linear method of depreciation.
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Example 1: SOYD
Annual Depreciation (SOYD) Taxable Income Taxes Payable (t=50%) After-Tax Cash Flow (ATCF) -46,000 12,000 10,000 3,000 3,000 1,500 1,500 13,500 11,500
Year 0 1 2
BTCF -46,000 15,000 13,000
3
4
11,000
9,000
8,000
6,000
3,000
3,000
1,500
1,500
9,500
7,500
5
6
7,000
5,000 4,000
4,000
2,000
3,000
3,000
1,500
1,500
5,500
3,500 4,000
63
Lecture 7: Depreciation, Taxes and Cash Flows
Example 1: SOYD
• • • • No half-year rule 50 per cent tax rate no inflation (no price changes) no debt capital (all equity capital) Based on a 6% after-tax rate of return (after-tax MARR), Present Worth (project) = - 46,000 + 13,500(P/A,6,5) - 2,000(P/G,6,5)
+ 7,500 (P/F,6,6) = -$4,314
Lecture 7: Depreciation, Taxes and Cash Flows 64
Example 2: Straight Line Depreciation
Year 0 1
BTCF -46,000 15,000
Annual Depreciation (Straight Line)
--7,000
Taxable Income --8,000
Taxes Payable (t=50%)
--4,000
After-Tax Cash Flow (ATCF)
-46,000 11,000
2
3 4
13,000
11,000 9,000
7,000
7,000 7,000
6,000
4,000 2,000
3,000
2,000 1,000
10,000
9,000 8,000
5
6
7,000
5,000 4,000
7,000
7,000
0
-2,000
0
-1,000
7,000
6,000 4,000
65
Lecture 7: Depreciation, Taxes and Cash Flows
Example 2: Straight Line (SL)
• NO half-year rule • 50 per tax rate • No inflation i.e., no price changes • No debt capital i.e., 100% equity capital Based on a 6% after-tax rate of return, the net Present Worth of this project is -46,000 + 11,000(P/A,6,6) - 1,000(P/G,6,6) + 4,000 (P/F,6,6)
=-$5,518
Lecture 7: Depreciation, Taxes and Cash Flows 66
Example 3: Declining Balance (DB)
• • • • NO half-year rule 50 per cent tax rate No inflation i.e., no price changes No debt capital i.e., 100% equity capital
Based on an after-tax MARR = 6%, the NPW of this project = -46,000 + 12,100(P/F,6,1)+10,180(P/F,6,2) + (P/F,6,3)+(P/F,6,4)+(P/F,6,5)+(P/F,6,6) = -1,000(P/G,6,6) + 4,000 (P/F,6,6)
= -$5,423
Lecture 7: Depreciation, Taxes and Cash Flows 67
Example 3: Declining Balance (DB)
Year 0 1 2 3 4 5 6 BTCF -46,000 15,000 13,000 11,000 9,000 7,000 5,000 4,000 9,200 7,360 5,888 4,710 3,768 3,015 5,800 5,640 5,112 4,290 3,232 1,985 2,900 2,820 2,556 2,145 1,616 993 Annual Depreciation (DB) Taxable Income Taxes Payable (t=50%) After-Tax Cash Flow (ATCF) -46,000 12,100 10,180 8,444 6,855 5,384 4,007 8,029.5
i* = 12%
i* = 6%
68 Lecture 7: Depreciation, Taxes and Cash Flows
Book Value = 46,000-9,200-7,360-5,888-4,710-3,768-3,015 = $12,059
Results: Bottom line sensitivity to depreciation methods
Year 0 1 2 3 4 5 6 SOYD -46000 13500 11500 9500 7500 5500 7500 SL -46000 11000 10000 9000 8000 7000 10000 DB -46000 12100 10180 8444 6855 5384 12036.5 ($5,423.29)
NPW= ($4,314.43) ($5,518.41)
Lecture 7: Depreciation, Taxes and Cash Flows
69
Perspectives on Project Analysis
• Two perspectives
• Sponsors (owners)
• Project
• In the absence of borrowed funds, the project and sponsor perspectives are identical. • If the sponsors borrow money (from friends, financial institutions, etc.), the project and sponsor perspectives differ.
Lecture 7: Depreciation, Taxes and Cash Flows
70
Example: Project Perspective
1. 2. 3. 4. 5. Truck Purchase: $30,000 Expected truck life: 3 years Salvage value: $5,000 Revenues and costs from operations: Table 1. The truck is depreciated using DB depreciation with a 20% (=d) depreciation rate. 6. Before-tax interest rate = 10%. 7. After-tax interest rate = 5%. 8. 50% tax rate on income from operations and depreciation recapturing 9. No half-year rule (does not apply). 10. $20,000 loan @ 10%: see Table 2. 11. No working capital
Lecture 7: Depreciation, Taxes and Cash Flows 71
Operating Revenues (OR) and Operating Expenses (OC) Before Taxes and Depreciation
TABLE 1
End of Year
(OR – OC)
1
$15,000
2
$20,000
3
$20,000
Lecture 7: Depreciation, Taxes and Cash Flows 72
Loan Repayment Schedule
TABLE 2
Loan Repayment (End of Year) 1 Percentage of Loan Repaid at end of year 10%
2 3
40% 50%
= 100%
Lecture 7: Depreciation, Taxes and Cash Flows
73
End-of-year
Item 1. Before-Tax Cash Flow (BTCF) 2. Interest on Loan ($) 0 -30,000 1 15,000 2 20,000 3 20,000 + 5,000 = 25,000 1,000 3,840 15,160
2,000 6,000 7,000 3,500
1,800 4,800 13,400 6,700
PROJECT 3. Depreciation ($) PERSPECTIVE
4. Taxable Income ($) 5. Taxes Payable ($)
(See next slide)
12,230
10,000 1,000 1,230
12,770**
6. After-Tax Cash Flow (ATCF)
7. Repayment of Loan
-30,000
11,500
2,000 2,000
13,300
8,000 1,800 3,500
OWNER 9. Cash Flow on Equity PERSPECTIVE
(CFOE)
8. (=2.) Interest on Loan
-10,000
7,500
Lecture 7: Depreciation, Taxes and Cash Flows
74
Example: Project Perspective
End-of-year
Item 1. Before-Tax Cash Flow (BTCF) 2. Interest on Loan ($) 0 1 2 20,000 1,800 4,800 13,400 6,700 13,300 8,000 1,800 3,500 3 20,000 + 5,000 = 25,000 1,000 3,840 15,160 -30,000 15,000 2,000 6,000 7,000 3,500 -30,000 11,500 2,000 2,000 -10,000 7,500
PROJECT 3. Depreciation ($) PERSPECTIVE
4. Taxable Income ($) 5. Taxes Payable ($) 6. After-Tax Cash Flow (ATCF) 7. Repayment of Loan
(See next slide)
12,230 10,000 1,000 1,230
12,770**
Taxes Payable = Taxable Income(t) + (SV-BV)t = 15,160(0.5) - (5,000-15,360)0.5 = $12,770 BV3= 30,000 - 6,000 - 4,800 - 3,840 = $15,360 Before-tax return on project
-30,000 = 15,000(P/F,i*,1) + 20,000(P/F,i*,2)+ 25,000(P/F,i*,3) Solve for i*; i* = 40%
OWNER Loan 9. Cash Flow on Equity PERSPECTIVE
(CFOE)
8. (=2.) Interest on
Lecture 7: Depreciation, Taxes and Cash Flows
75
Example: Project Perspective
End-of-year
Item 1. Before-Tax Cash Flow (BTCF) 2. Interest on Loan ($) 0 1 2 20,000 1,800 4,800 13,400 6,700 13,300 8,000 1,800 3,500 3 20,000 + 5,000 = 25,000 1,000 3,840 15,160 -30,000 15,000 2,000 6,000 7,000 3,500 -30,000 11,500 2,000 2,000 -10,000 7,500
PROJECT 3. Depreciation ($) PERSPECTIVE
4. Taxable Income ($) 5. Taxes Payable ($) 6. After-Tax Cash Flow (ATCF) 7. Repayment of Loan
(See next slide)
12,230 10,000 1,000 1,230
12,770**
After-tax return on project -30,000 =11,500(P/F,i*,1) +13,300(P/F,i*,2) +12,230(P/F,i*,3) Solve for i*; i* = 11% After-tax return on owner equity (i.e., on owner funds)
-10,000 = 7,500(P/F,i*,1) + 3,500(P/F,i*,2) + 1230(P/F,i*,3)
OWNER 9. Cash Flow on Equity PERSPECTIVE
(CFOE)
8. (=2.) Interest on Loan
Solve for i*; i*= 15%
Lecture 7: Depreciation, Taxes and Cash Flows
76
Summary: After-tax cash flow
(End-of-Year “n”; t = tax rate)
= -Pn (capital investment) + Sn (revenues from sales of assets) - (Sn - Bn) (taxes on gains from capital assets - W (Working capital) + (1-t)Rn (after-tax ordinary revenues) - (1-t)En (After-tax operating expenses) + tDn (depreciation tax savings) - (1-t)IPn (after-tax interest payments) - PPn (Principal payments) + B (Loans received)
Lecture 7: Depreciation, Taxes and Cash Flows 77
Case 1: No Inflation INCOME STATEMENT 1 Sales 0 1 30,000
End of Year
2 30,000 3 30,000 4 30,000
2
3 4 5 6
Operating Costs
CCA Taxable Income Income Tax (40%) Net Income
10,000
4,500 15,500 6,200
10,000
7,650 12,350 4,940
10,000
5,355 14,645 5,858
10,000
3,749 16,251 6,500
9,300
7,410
8,787
9,751
CASH FLOW STATEMENT
7 7a 7b 8 9 10
Cash from operations Net Income CCA Investment Salvage Disposal Tax Effect 3,499 (30,000) 9,300 4,500 7,410 7,650 8,787 5,355 9,751 3,749
11
12
Working Capital
Net Cash Flow
(5,000)
5,000
(35,000)
13,800
15,060
14,142
21,999
Lecture 7: Depreciation, Taxes and Cash Flows
78
Case 2: With Inflation =10% INCOME STATEMENT 1 2 3 4 5 6 Sales Operating Costs CCA Taxable Income Income Tax (40%) Net Income 0 1 33,000 11,000 4,500 17,500 7,000 10,500
End of Year
2 36,300 12,100 7,650 16,550 6,620 9,930 3 39,930 13,310 5,355 21,265 8,506 12,759 4 43,923 14,641 3,749 25,533 10,213 15,320
CASH FLOW STATEMENT
7 7a 7b 8 9 10 11 12 13
Cash from operation Net Income CCA Investment Salvage Disposal Tax Effect Working Capital Net Cash Flow (Actual $) Net Cash Flow (Real $) (5,000) (35,000) (35,000) (500) 14,500 13,182 (550) 17,030 14,074 (605) 17,509 13,155 3,499 6,655 29,223 19,960 (30,000) 10,500 4,500 9,930 7,650 12,759 5,355 15,320 3,749
Lecture 7: Depreciation, Taxes and Cash Flows
79
Tax Savings
• Based on tax rules (including the depreciation rate for a specific asset class), it is possible to calculate the tax savings from capital cost allowances. • See following examples.
Lecture 7: Depreciation, Taxes and Cash Flows
80
Example 1: Tax Savings (With the HalfYear Rule)
Year (1) Adjustments to UCC from Purchases (+) & Disposals (-) (2) Base UCC Amount for CCA (3) CCA (4) Remaining UCC (5) Tax Savings Due to CCA (6)
Assume that d=20% (Declining Balance), t=50% and the half-year rule applies.
1998 1999 2000
$500,000 0 0
250,000 450,000 360,000
50,000 90,000 72,000
450,000 360,000 288,000
25,000 45,000 36,000
2001
0
288,000
57,600
230,400
28,800
CCA: capital cost allowance = depreciation UCC: undepreciated capital cost
Lecture 7: Depreciation, Taxes and Cash Flows 81
Example 1: Tax Savings
Assume that a business acquired only one asset (in its class) between 1998 and 2001. Note that (column) : (2) = Net purchases or net disposals (sales) of assets in this class during a specific year. (3) = Depreciation base for the calculation of CCA = (5)t-1 – Net Disposals OR (5)t-1 + 50% Net Acquisitions (2)t (4) = Capital cost allowance based on tax rules = depreciation rate (column 3) (5) = (3) – (4) + 50% of net acquisitions for a year OR = (3) – (4) [if net disposals]
Lecture 7: Depreciation, Taxes and Cash Flows
82
Example 1: Tax Savings
Assume that the $500,000 asset was purchased on January 1, 1998. Its after-tax cost on December 31, 2001 would be: (based on an after-tax MARR of 10%). • After-tax cost = 500,000 – 25,000(P/F,10%,1) - 45,000(P/F,10%,2) - 36,000(P/F,10%,3) - 28,800(P/F,10%,4) = $357,600 (compared to the Before-Tax Cost of $500,000)
Lecture 7: Depreciation, Taxes and Cash Flows 83
Example 2: Tax Savings
Adjustments to UCC Base UCC from Amount for Purchases & CCA Disposals $500,000 250,000 Tax Savings Due to CCA
Year
CCA
Remaining UCC
Assume that d=20% (Declining Balance), t=50% and the half-year rule applies. 1998 50,000 450,000 25,000
1999
2000
0
300,000
450,000
510,000
90,000
102,000
360,000
558,000
45,000
51,000
2001
(100,000)
458,000
91,600
366,400
45,800
CCA: capital cost allowance = depreciation UCC: undepreciated capital cost
Lecture 7: Depreciation, Taxes and Cash Flows 84
Capital Tax Factors (CCTF)
• Values that capture the effect of future tax savings arising from the capital cost allowances (CCA) of a depreciable asset. Subtracting the value of these tax savings from the acquisition cost of the asset (P) gives the asset’s after-tax present worth. There are two CCTFs:
1. CCTF for the acquisition cost (P) which is based on the half-year rule
2. CCTF for an asset’s salvage value which does not require a half-year rule adjustment
•
CCTFNEW = 1 – {[td[1+(i/2)]/[(i+d)(1+i)]}
•
CCTFOLD = 1 – {td/(i+d)} NOTE: These factors ARE provided on all exams.
t ≡ tax rate; d ≡ CCA rate; i% ≡ After-Tax MARR
Lecture 7: Depreciation, Taxes and Cash Flows 85
Example 1: CCTF
A new tractor has a $60,000 price tag in1999 and is expected to reduce maintenance and operating costs by $20,000 per year for the next six years. Assume:
• after-tax MARR =10% • SV of $6,000 in six years • 20% CCA rate • 50% corporate income tax
Find the after-tax annual equivalent worth of this tractor.
Lecture 7: Depreciation, Taxes and Cash Flows
86
Example 1: CCTF (cont’d)
NOTE: We will convert the present worth OF EACH COMPONENT to an annual equivalent at the end of the solution. • PW(first cost) = -60,000(CCTFnew) where CCTFnew = 1 - {[(0.5)(0.2)(1+0.05)]/[(0.10+0.2)(1+0.1)]} = 0.6818 Thus the after-tax PW (first cost) = $-40,908 • After–tax PW (salvage value) = 6,000(P/F,10%,6)(CCTFold) where (CCTFold) = 1 - {[(0.5)(0.2)]/[(0.1+0.2)]} = 0.6667 After-tax PW (salvage value) = $2,258
Lecture 7: Depreciation, Taxes and Cash Flows 87
Example 1: CCTF
Example 1: CCTF
A new tractor has a $60,000 price tag in1999 and is expected to reduce maintenance and operating costs by $20,000 per year for the next six years. Assume:
• after-tax MARR =10% • SV of $5,000 in six years • 20% CCA rate • 50% corporate income tax
Find the after-tax annual equivalent worth of this tractor.
October 2007
83
After-tax PW (annual savings) = 20,000(P/A,10%,6)(1-0.5) = $43,550 After-tax PW of tractor = -40,908+2,258+43,550 = $4,900 After-tax annual equivalent worth = $4,900(A/P,10%,6) = $1,125
88
Lecture 7: Depreciation, Taxes and Cash Flows
Tax Savings From Depreciation: CCTF versus Tabular Approach
• • • • Initial Investment = $300,000 Annual decrease in market value of P = 20% Depreciation Method (Rate): DB (10%) Tax rate = 50%
Lecture 7: Depreciation, Taxes and Cash Flows
89
Example : Tax Savings (With the HalfYear Rule): Tabular Approach
Adjustments to UCC from Purchases & Disposals (2) Base UCC Amount for CCA (3) Remaining UCC (5) Tax Savings Due to CCA (6)
Year (1)
CCA (4)
Assume that d=20% (Declining Balance), t=50% and the half-year rule applies.
2003 2004 2005 2006 ---
$300,000 $0 $0 $0 ---
$150,000 $285,000 $256,500 $230,850 ---
$15,000 $28,500 $25,650 $23,085 ---
$285,000 $256,500 $230,850 $207,765 ---
$7,500 $14,250 $12,825 $11,543
---
---
---
---
---
---
---
CCA: capital cost allowance = depreciation; UCC: undepreciated capital cost
90 Lecture 7: Depreciation, Taxes and Cash Flows
Modified Purchases Year Or Sales Depreciation Base $0 2003 2004 2005 $300,000 $0 $0 $150,000 $285,000 $256,500 $15,000 $28,500 $25,650 CCA Depreciation Base $0 $285,000 $256,500 $230,850 $7,500 $14,250 $12,825 Tax Savings
PW of Tax Savings After-Tax Cost of P
$6,818 $18,595 $28,231
$293,182 $281,405 $271,769
2006
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
$0
$0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0
$230,850
$207,765 $186,989 $168,290 $151,461 $136,315 $122,683 $110,415 $99,373 $89,436 $80,492 $72,443 $65,199
$23,085
$20,777 $18,699 $16,829 $15,146 $13,631 $12,268 $11,041 $9,937 $8,944 $8,049 $7,244 $6,520
$207,765
$186,989 $168,290 $151,461 $136,315 $122,683 $110,415 $99,373 $89,436 $80,492 $72,443 $65,199 $58,679
$11,543
$10,388 $9,349 $8,414 $7,573 $6,816 $6,134 $5,521 $4,969 $4,472 $4,025 $3,622 $3,260
$36,114
$42,565 $47,842 $52,160 $55,693 $58,584 $60,948 $62,883 $64,467 $65,762 $66,822 $67,689 $68,398
$263,886
$257,435 $252,158 $247,840 $244,307 $241,416 $239,052 $237,117 $235,533 $234,238 $233,178 $232,311 $231,602
2019
2020 2021 2022
$0
$0 $0 $0
$58,679
$52,811 $47,530 $42,777
$5,868
$5,281
$52,811
$47,530
$2,934
$2,641 $2,376 $2,139
$68,979
$69,454 $69,842 $70,160
$231,021
$230,546
91 $230,158
Lecture 7: Depreciation, Taxes and Cash Flows $4,753 $42,777
$4,278
$38,499
$229,840
Tax Savings: CCTF and Tabular Method
CCTFNEW = 0.76136464
CCTFOLD = 0.75
After-Tax P EOY 5 10 SV $98,304.0 $32,212.3 BV $186,989 $110,415 NSV $142,646.25 $71,313.55 with NSV $168,863.3 $211,557.1
CCTF Method $182,630 $219,095
Difference CCTF - Tab $13,767 $7,538
15
20
$10,555.3
$3,458.8
$65,199
$38,499
$37,877.09
$20,979.02
$223,243.6
$226,721.4
$226,514
$228,023
$3,270
$1,302
Lecture 7: Depreciation, Taxes and Cash Flows
92
Tractor problem in BTCF & ATCF Format
Years Item 1. BTCF (Before-Tax Cash Flows) 2. Interest on Loan 3. Depreciation 4. Taxable Income 6,000 14,000 10,800 9,200 8,640 11,360 6,912 13,088 5,530 14,470 4,424 15,576 0 (60K) 1 20,000 2 20,000 3 20,000 4 20,000 5 20,000 6 20,000 + 5,000
5. Taxes Payable
6. ATCF (After-Tax Cash Flows) (60K)
7,000
13,000
4,600
15,400
5,580
14,420
6,544
13,456
7,235
12,765
7,788
12,212 + NSV = 23,559
93
Lecture 7: Depreciation, Taxes and Cash Flows
Tractor problem in BTCF & ATCF Format
• NSV = 5,000 - (5,000-17,694)0.5 = $11,347 • After-tax PW = -60,000 + 13,000(P/F,10%,1) +15,400(P/F,10%,2) + 14,420(P/F,10%,3) +13,456(P/F,10%,4) + 12,765(P/F,10%,5) + 23,559(P/F,10%,6) = $5,794 (compared to $4,900 with the CCTF method) • After-tax AEW = 5,794(A/P,10%,6) = $1,330 (compared to $1,125 with the CCTF method)
Lecture 7: Depreciation, Taxes and Cash Flows
94
Example: BTCF & ATCF
• A firm is considering the purchase of a truck for $300,000 fully installed. It is expected to last 3 years with a salvage value of $100,000 at that time. Revenues from operations will be $250,000 each year and operating and maintenance costs will be $75,000 each year 1. Depreciate the truck using the DB method (d=25%). 2. The before-tax interest rate is 10%. 3. The after-tax interest rate is 5%. 4. A 50% tax rate on income from operations and depreciation recapturing 5. The half-year rule does NOT apply. 6. The firm gets a $100,000 loan (at a 10% rate of interest) which is repaid as shown in the next Table.
Lecture 7: Depreciation, Taxes and Cash Flows
95
Example: BTCF & ATCF (cont’d)
Loan Repayment at End of Year 1 2 3
Percentage of Loan Repaid at End of Year 30% 30% 40%
Lecture 7: Depreciation, Taxes and Cash Flows
96
Years
Item 1. Before-Tax Cash Flow (BTCF) 2. Interest on Loan ($) 3. Depreciation ($)
0 (300,000) 1 175,000 10,000 75,000 2 175,000 7,000 56,250 3 175,000 + 100,000 4,000 42,188
4. Taxable Income ($)
5. Taxes Payable ($) 6. After-Tax Cash Flow (ATCF) 7. Repayment of Loan 8. (=2.) Interest on Loan 9. Cash Flow on Equity (CFOE)
(200,000) (300,000)
90,000
45,000 130,000
111,750
55,875 119,125
128,812
64,406 110,594 + 113,282 = 223,876 40,000 4,000 179,876
30,000 10,000 90,000
30,000 7,000 82,125
Lecture 7: Depreciation, Taxes and Cash Flows
97
Example: BTCF & ATCF (cont’d)
Project’s book value after three years. Book Value (BV) = P(1 - d)3 = 300,000(1 - 0.25)3 = $126,562.5 Net salvage value (NSV) at the end of three years. NSV = SV - Taxes Payable (tax credits received) on capital gains (losses) and depreciation recapturing NSV = SV - t(SV - BV) where “t” is the tax rate NSV = 100,000 - 0.5(100,000 - 126,563) NSV = 100,000 - (-13,282) NSV = $ 113,282
Lecture 7: Depreciation, Taxes and Cash Flows 98
Example: BTCF & ATCF (cont’d)
Determine the before-tax PW of this project. From the BTCF (row 1): = -300,000 + 175,000(P/A,10%,3) + 100,000(P/F,10%,3) = $210,339
Lecture 7: Depreciation, Taxes and Cash Flows
99
Example: BTCF & ATCF (cont’d)
• Determine the after-tax PW of this project. From the ATCF (row 6): -300,000 + 130,000(P/F,5%,1) + 119,125(P/F,5%,2) + 223,876(P/F,5%,3) = $125,252
• Determine the PW of the owner’s equity. From the CFOE (row 9): -200,000 + 90,000(P/F,5%,1)+ 82,125(P/F,5%,2) + 179,876(P/F,5%,3) = $115,588
Lecture 7: Depreciation, Taxes and Cash Flows 100
Next Week: Lecture 8
Replacement Analysis
• Fraser et al.* chapter 7 • Newnan et al. chapter 13 • Park chapter 11
Lecture 7: Depreciation, Taxes and Cash Flows
101
Engineering Economics
ECO 1192
Lecture 7: Depreciation, Taxes and Cash Flows
Claude Théoret University of Ottawa