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.