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Principles of Taxation
Chapter 3
Taxes as Transaction Costs
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Objectives
Slide 3-2
 Compute tax costs of income and tax savings
from deductions.
 Compute net present value of after-tax cash
flows.
 Identify sources of tax uncertainty
 Maximize after-tax values versus minimize
taxes.
 Tax planning in private market transactions.
 Distinguish arm’s length from related-party
transactions.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Taxes as transaction cost
Slide 3-3
 Goal - MAXIMIZE AFTER-TAX values,
 NOT MINIMIZE TAXES
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-4
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Irwin/McGraw-Hill
Terminology
Present Value Example
Future Value Example
Present Value of an Annuity Example
Future Value of an Annuity Example
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-5
 Terminology
 Time Value of Money: this refers to the notion that a
dollar available today is worth more than a dollar to be received
in some future period.
 Present value: the value of a dollar today.
 Discount Rate
 the rate of interest on invested funds for the deferral period.
 As r increases, what does the present value do? How is r related to
risk? Should you always use the same r to evaluate 2 different
planning schemes?
 Net Present Value: the sum of the present values of
cash inflows and outflows relating to a transaction.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-6
 Terminology
 Future Value
 The value at a future date of a sum increased by an
interest rate.
 Present Value of an Ordinary Annuity
 The value today of a series of constant dollar payments
available at the end of each period for a specific number
of periods.
 Future Value of an Ordinary Annuity
 The value at a future date of a series of constant dollar
payments available at the end of each period for a
specific number of periods increased by an interest rate.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-7
 Present Value example
 Assume that at the beginning of your freshman
year your great Uncle makes the following offer
Receive $20,000 on your graduation day 4 years
hence, or
Receive $15,000 now.
 How do you decide?
To compare the $20,000 with the $15,000 you
must compare them in present value terms. In
other words, what is the present value of the
$20,000 and how does that compare to $15,000.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-8
 Present value formula
1
PV ($ 1 ) 
(1  r ) n
Where :
PV($1) = Present value of one dollar today
r
= Interest Rate
n
= Number of Periods
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-9
 Present Value
 Let’s assume you expect an annual interest rate of
10% on invested funds. Specifying an annual rate
also determines the number of periods 4 (4 years
till graduation). Use 10% for R, and 4 for n.
 The present value of the $20,000 using a 10 percent
discount rate is $13,660. Thus, should you take
your Uncle’s offer of $15,000 today?
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-10
 Future Value
 Assume that you accepted your Uncle’s offer of
$15,000 today. What would that amount
accumulate to by your graduation 4 years hence if
you invest the money in an activity that provided
an annual return of 10%?
 Specifically, you need to determine the future
value of the $15,000. For that we need yet another
formula:
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-11
 Future Value Formula (NOTE - this formula
is NOT in your tax book).
FV ($ 1 )  P (1  r )
Where:
FV($1) =
P
=
r
=
n
=
Irwin/McGraw-Hill
n
Future value of a dollar
Present value of invested amount
Interest Rate
Number of Periods
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-12
 Future Value
 Using 4 periods and $15,000 we can use the
formula on the previous slide to determine
that the future value of the $15,000 at
graduation is $21,962. It is clear that your
decision to take the $15000 NOW is the
wiser decision.
 Conclusion is the same whether compare
PV or FV. KEY is to compare both choices
at the SAME point in time.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-13
 Present Value of an Ordinary Annuity
 Assume your great Uncle feels particularly
generous and makes the following offer:
Receive 4 payments of $15,000 at the
end of your freshman through senior
year, or
Receive $46,000 now
The first option is an example of an
ordinary annuity.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-14
 Formula for the Present Value of an Ordinary
Annuity
1
1
Pa  
n
r r (1  r )
Where:
Pa = Present value of Ordinary Annuity
r = Interest Rate
n = Number of Periods
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-15
 Present Value of an Ordinary Annuity
Keeping with our previous
examples (a 10 percent annual
interest rate for 4 periods) the
present value of the annuity is
$47,548. Thus, you should choose
the ANNUITY.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-16
 Future Value of an Ordinary Annuity
 Not to be out done by your great Uncle, your
grandmother (who wants you to be a doctor
and not an accountant) makes the following
offer
 she will invest $16,000 at the end of your
freshman through senior year. The money, if
you make the right decision, will go toward
paying medical school tuition and expenses.
You can keep anything in excess of the medical
school costs. How much will you have to pay
for medical school?
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-17
 Future Value of an Ordinary Annuity
Formula
(1  r ) 1
Fa 

r
r
n
Where:
Fa = Future value of payment series
r = Interest Rate
n = Number of periods
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Time Value of Money
Slide 3-18
 Future Value of an Ordinary Annuity
 Assuming a 10 percent return on
grandma’s invested funds and 4 periods.
Your medical school fund will be worth
$74256.
Is there a doctor in the house?
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Risk
Slide 3-19
 Many classroom examples (like the ones
above) assume that all cash flows are equally
risky.
 Higher risk projects demand higher expected
returns = higher discount rate.
 Assume that discount rates state in examples
already reflect the relative risk of the
transaction, and that the risk does not change
over time.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Relation between taxes and cash
flows - step by step
Slide 3-20
 1) determine yearly PRE-TAX cash inflows and outflows.
 2) determine yearly TAXABLE income and deductions.
Taxable income may not be equal to cash inflows.
Deductible expenses may not be equal to cash outflows (e.g.
depreciation).
 3) compute yearly cash outflows to pay TAX on taxable
income and cash inflow from tax deductions = 2) x MTR
 4) Compute yearly net AFTER-TAX cash inflows or
outflows. 1) - 3)
 5) Compute NPV of yearly net cash flows.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Relation between taxes and cash
flows - step by step
Slide 3-21
 George buys a computer for $3000 in 1998.
He expects to earn $4000 in cash revenues
each of the next three years designing web
pages. For tax purposes, he can deduct
the cost of the computer as follows: year
1: $1000, year 2: $1500, year 3: 500. He
expects to be in a 28% tax bracket for all
three years. Assume a discount rate of
10%. What is the net present value of his
after-tax cash flows?
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Relation between taxes and cash
flows - step by step
Slide 3-22
 Use steps 1 - 5
1) Pretax cash
2) Taxable income
3) Tax
4) After-tax cash
5) Present value
Irwin/McGraw-Hill
Begin1
-3000
-3000
-3000
End 1
4000
3000
-840
3160
2873
End2
4000
2500
-700
3300
2727
SUM
End3
4000
3500
-980
3020
2269
4869
©The McGraw-Hill Companies, Inc., 2000
Relation between taxes and cash
flows - other issues
Slide 3-23
 The marginal tax rate that applies (Step 3)
may differ by type of income.
 See AP 2, 3, Q5.
 Most of the problems and examples in the text
assume that payments occur at the
BEGINNING of the year.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Tax Uncertainty
Slide 3-24
 Audit risk - the tax law may be unclear - risk
that the IRS may disagree with taxpayer
treatment. Possible interest plus penalties
plus tax.
 Tax law uncertainty - the tax law may change.
For example, the capital gains rates and
holding periods have changed frequently.
See Q7.
 Marginal rate uncertainty - the taxpayer may
not be able to predict annual income and tax
position at the time transaction happens. See
Q10.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000
Structuring Transactions
Slide 3-25
 Private market - both parties can customize
the transaction. Examples: executive and
employer, merger target and acquirer. See
TPC1.
 Public market - without direct negotiation, tax
planning is one-sided.
 Related party markets - extreme tax
avoidance may create suspicion of tax
evasion.
Irwin/McGraw-Hill
©The McGraw-Hill Companies, Inc., 2000