Borrowing, Depreciation, Taxes in Cash Flow Problems

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Borrowing, Depreciation, Taxes in Cash Flow Problems

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Title: Borrowing, Depreciation, Taxes in Cash Flow Problems


1
Borrowing, Depreciation, Taxes in Cash Flow
Problems
  • H. Scott Matthews
  • 12-706 / 19-702 /73-359
  • Lecture 5

2
Admin Issues
  • Who bought Boardman book? Can return.
  • Campbell Textbook due today. First 20 names will
    be sent
  • TA Office Hours in CEE Lounge (PH 118 hallway
    near my office)
  • Joe and Paulina will swap coverage next week
    (i.e, go to office hours in lounge, but look for
    Joe instead)

3
Notes on Tax deductibility
  • Reason we care about financing and depreciation
    they affect taxes owed
  • For personal income taxes, we deduct items like
    IRA contributions, mortgage interest, etc.
  • Private entities (eg businesses) have similar
    rules pay tax on net income
  • Income Revenues - Expenses
  • There are several types of expenses that we care
    about
  • Interest expense of borrowing
  • Depreciation (can only do if own the asset)
  • These are also called tax shields

4
Goal Find Cash Flows after taxes
  • Master equation conceptually
  • CFAT -equity financed investment gross income
    - operating expenses salvage value - taxes
    (debt financing receipts - disbursements)
    equity financing receipts
  • Where taxes Tax Rate Taxable Income
  • Taxable Income Gross Income - Operating
    Expenses - Depreciation - Loan Interest - Bond
    Dividends

5
After-tax cash flows
  • Dt Depreciation allowance in t
  • It Interest accrued in t
  • on unpaid balance, - overpayment
  • Qt available for reducing balance in t
  • Wt taxable income in t Xt tax rate
  • Tt income tax in t
  • Yt net after-tax cash flow

6
Equations
  • Dt Depreciation allowance in t
  • It Interest accrued in t
  • Qt available for reducing balance in t
  • So At Qt - It
  • Wt At-Dt -It (Operating - expenses)
  • Tt Xt Wt
  • Yt At - Xt Wt (pre tax flow - tax) OR
  • Yt At At - Xt (At-Dt -It)

7
Simple example
  • Firm 500k revenues, 300k expense
  • Depreciation on equipment 20k
  • No financing, and tax rate 50
  • Yt At At - Xt (At-Dt -It)
  • Yt(500k-300k)0-0.5 (200k-20k)
  • Yt 110k

8
Notes
  • Mixed funds problem - buy computer
  • Below Operating cash flows At
  • Four financing options in At

9
Further Analysis (still no tax)
  • MARR (disc rate) equals borrowing rate, so
    financing plans equivalent.
  • When wholly funded by borrowing, can set MARR to
    interest rate

10
Effect of other MARRs (e.g. 10)
  • Total NPV higher than operation alone for all
    options
  • All preferable to internal funding (equity
    financing)
  • Why? Internal funds could earn 10, were only
    paying 8
  • First option gets most of loan, is best

11
Effect of other MARRs (e.g. 6)
  • Now reverse is true
  • Why? Internal funds only earn 6 !
  • First option now worst

12
First Complex Example
  • Firm will buy 46k equipment
  • Yr 1 Expects pre-tax benefit of 15k
  • Yrs 2-6 2k less per year (13k..5k)
  • Salvage value 4k at end of 6 years
  • No borrowing, tax50, MARR6
  • Use SOYD and SL depreciation

13
Results - SOYD
  • D1(6/21)42k 12,000
  • SOYD really reduces taxable income!

14
Results - Straight Line Dep.
  • NPV negative - shows effect of depreciation (why
    lower?)
  • Negative tax? Typically treat as credit not cash
    back
  • Projects are usually small compared to overall
    size of company - this project would create tax
    benefits

15
Lets Add in Interest - Computer Again
  • Price 22k, 6k/yr benefits for 5 yrs, 2k
    salvage after year 5
  • Borrow 10k of the 22k price
  • Consider single payment at end and uniform yearly
    repayments
  • Depreciation Double-declining balance
  • Income tax rate50
  • MARR 8

16

Single Repayment
  • Had to manually adjust Dt in yr. 5
  • Note loan balance keeps increasing
  • Only additional interest noted in It as interest
    expense

17
Uniform payments
  • Note loan balance keeps decreasing
  • NPV of this option is lower - should choose
    previous (single repayment at end).. not a
    general result

18
Leasing
  • Make payments to owner instead of actually
    purchasing the asset
  • Since you do not own it, you can not take
    depreciation expense
  • Lease payments are just a standard expense (i.e.,
    part of the Ct stream)
  • At Bt - Ct Yt At - At Xt
  • Tradeoff is lower expenses vs. loss of
    depreciation/interest tax benefits

19
Social Discount Rate
  • Rate used to make investment decisions for
    society
  • Discounting rooted in consumer preference
  • We tend to prefer current, rather than future,
    consumption
  • Marginal rate of time preference (MRTP)
  • Face opportunity cost (of foregone interest) when
    we spend not save
  • Marginal rate of investment return

20
Intergenerational effects
  • We have tended to discuss only short term
    investment analyses (e.g. 5 yrs)
  • What about effects in distant future?
  • Called intergenerational effects
  • Economists agree that discounting should be done
    for public projects
  • Do not agree on positive discount rate

21
Discounting handout
  • How much do/should we care about people born
    after we die?
  • Higher the discount rate, the less future values
    will count compared to today
  • Ethically, no ones interests should count more
    than anothers
  • Implies there is no justification for discounting
    across long time periods
  • Called equal standing

22
Climate Change
  • Discussions ongoing about how best to manage
    global CO2 emissions to limit effects of global
    change
  • Should we sacrifice short-run economic growth to
    do something to improve environment and leave
    resources for the future?
  • Really asking 2 separate questions!

23
Two Questions
  • What duty do we have to make sacrifices for
    future generations?
  • If we sacrifice, what is the optimal policy to
    maximize benefit?
  • So we should compare global change proposals with
    alternatives
  • Perhaps higher RD spending on science or
    medicing would have higher benefits!

24
Humes Law
  • Thus discounting issues are normative vs.
    positive battles
  • Hume noted that facts alone cannot tell us what
    we should do
  • Any recommendation embodies ethics and judgment
  • E.g. focusing on highest NPV implies net
    benefits is only goal for society

25
Some evidence
  • Cropper et al surveyed 3000 homes
  • Asked about saving lives in the future
  • Found a 4 discount rate for lives 100 years per
    now
  • Equal standing does not imply different
    generations have equal claims to present
    resources!
  • Harsanyi says only do so if their marginal gain
    is higher than our loss

26
More evidence
  • If future generations will be better off than us
    anyway
  • Then we might have no reason to make additional
    sacrifices
  • There might be special standing in addition to
    equal standing
  • Immediate relatives vs. distant relatives
  • Different discount rates over time
  • Why do we care so much about future and ignore
    some present needs (poverty)
  • Based on these arguments, what discount rates
    should we use for policy problems (eg climate)

27
Government Discount Rates
  • US Government Office of Management and Budget
    (OMB) Circular A-94
  • http//www.whitehouse.gov/omb/circulars/a094/a094.
    html
  • Discusses how to do BCA and related performance
    studies
  • Match real values with real discount rates, etc
  • How to do sensitivity analysis / which inputs to
    vary
  • What discount, inflation, etc. rates to use
  • Basically says use this rate, but do sensitivity
    analysis with nearby rates

28
OMB Circular A-94, Appendix C
  • Provides the current suggested values to use for
    federal government analyses
  • http//www.whitehouse.gov/omb/circulars/a094/a94_a
    ppx-c.html
  • Revised yearly, usually good until January of
    the next year
  • How would the government decide its discount
    rates?
  • What is the governments MARR?

29
Historic Nominal Interest Rates (from OMB A-94)
30
Real Discount Rates (from A-94)
31
Effect of these Discount Rates
  • These are effectively zero
  • What does this mean for projects and project
    selection decisions?
  • What does it say about intergenerational effects?
  • What are implications of zero or negative
    discount rates?

32
Next Up Sensitivity Analysis
  • Skim Clemen Chapter 5 Refers to decision/trees,
    etc that we have not done yet.
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