Topic 6

Capital Budgeting – Taxation

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Outline

Taxation and Depreciation
- After tax cash flows
- Depreciation
- Timing
Inflation
Non Identical Replacement – Perpetual Chain
- Replacing an existing asset with a new asset and when that should be done
Brief coverage of Methods to handle risk and uncertainty
- Scenario Analysis
- Sensitivity Analysis
- Break Even
- Simulation
- Decision Tree analysis Look at very briefly
- Adjusting for Systematic Risk (next week)

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Learning Objectives

Understand the effect of taxation on project cash flows
Calculate NPV using after tax cash flows
Conduct sensitivity analysis (will be covered during a tutorial next week)

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Taxation

• Taxation is a cash flow

Profits è Paying taxes or Losses è Receiving tax credits

• NPV needs net cash flows

Tax is a relevant cash flow

• Three steps in investment analysis

calculate tax cash flows (work out the taxable income)
- calculate net cash flows (normal cash flow analysis)
- find the present value

• Need to consider

depreciation: it is relevant now because it affects tax.
- timing of tax payments and receipts: Without any assumptions,

taxes are paid in the same year of income.

special tax provisions

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Depreciation

Depreciation is the allocation of the cost of assets over

its useful life

it shows how much of an asset’s value has been used
Depreciation is calculated according to tax legislation

not accounting standards

Many variations in Tax Act, but 2 main types
- straight line [SL] (prime cost)
- diminishing value [DV] reducing value
Note salvage value is ignored when calculating depreciation for tax purposes

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Straight Line or Prime Cost

• Prime Cost Method assumes asset value decreases uniformly

tax savings are constant

• For NPV (do not use accounting formula)

Straight line in dollars = cost/life

• Cost $100000 and 5 year life: Dep = 20000

In percentage 1/life = 1/5 = 20%

• The salvage value is accounted for at the end of the life of the asset

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Diminishing Value or Reducing Balance

Diminishing Value Method assumes asset value declines as a constant fraction of undepreciated asset value

– tax savings are decreasing each year

DV or RV depreciation calculates a different amount for depreciation for each year.
The rate used is normally 2 times the straight line rate (In percentage 1/life).
Eg a life of three years implies a straight line rate of 33.33% and a diminishing value rate of 2 x 33.33 = 66.67%

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PV of Cash Flows from Depreciation of Assets

Prime Cost Method:

CF from Depreciation = T

= T

´Depreciation Expense

Asset’s Cost ´ d %

where d % =

100%

Asset’s Effective Life InYears

The tax savings are constant.

PV of Cash Flows from Depreciation of Assets

Diminishing

CF from Depreciation = T ´Depreciation Expense

Value Method:

where d % =

= T ´Base Value´ d % 200%

Asset’s Effective Life InYears

Base Value = Asset’s Cost

Cummulative Depreciation Value


Acquisition Cost	100000	Straight Line	Diminishing Value
Life	5	Prime Cost	Reducing Value
S/L	20%
D/V	40%
	O/B	100000	100000
	Depreciation Year 1	20000	40000
	BV 1	80000	60000

	Depreciation Year 2	20000	24000
	BV2	60000	36000

	Depreciation Year 3	20000	14400
	BV3	40000	21600

	Depreciation Year 4	20000	8640
	BV4	20000	12960

	Depreciation Year 5	20000	5184
	BV5	0	7776

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Gain or Loss on Sale

• Selling Price – Book Value

Positive is a taxable gain (add to TI)

• Negative is a loss (deduct from TI)

Selling Price
- Disposal Value
- Salvage Value or Residual Value

• Book Value

Written down value
- Depreciated value

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Timing of Taxation

Very often, for simplicity, it is assumed that tax cash flows occur in the year that taxable income is earned or
In the year following the year of income
read exam questions carefully
Sometimes firms will deliberately time a transaction to minimise tax

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Special Tax Provisions

• Investment allowance

the bonus deduction
- E.g., you might have the investment allowance for 20% of the cost of assets, which is 100 million è you can get extra deduction of 20 million upfront

• R&D depreciation allowance

if you invest in R&D, then you can get extra tax deduction
- it can stimulate corporate R&D investment and could lead to enhanced innovation, which is good for

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Special Tax Provisions

• Capital gains tax

capital gains tax can vary from normal income tax.
- under capital gains tax provision, tax will be applied differently to ordinary income tax.

• Special write-off for different types of assets and time

E.g., eligible businesses can claim an immediate deduction for the business portion of the cost of an asset in the year the asset is first used or installed ready for use.

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Special Tax Provisions

• Accelerated depreciation

Accelerated depreciation means you can deduct costs for eligible depreciating assets in your tax return at varying percentages in the income year it has been first used or installed ready for use.
- You can then use existing depreciation measures for the same asset for the remainder of the value.

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NPV after tax – Lecture Example

A machine costs $28,000. The salvage value at the end of three years is $500. Net cash benefits are $16,000, $20,000, $12,000 in years 1,2,and 3. Assume an investment allowance of 20%, a depreciation rate of 40% diminishing value and a taxation rate of 30%. Assume tax is paid in the year that income is earned. The company requires a return of 15% after tax for projects of this type of risk. Will borrow $20,000 at 10% to finance the project

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NPV after tax – Lecture Example

• Shows how to do an NPV calculation with taxation

First calculate the tax cash flows (first table)

• Then the net cash flows (second table)

Then NPV = $5,974 increase in value

• Three methods to do the same thing

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Lecture Example

Table One: Calculate the impact on taxable income (TI) and then the tax cash flows
- Table Two: Set out all the cash flows to calculate NCFAT

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Method One

Beginners Method (two tables one for tax and one for cash flows)

TAX	0	1	2	3
Cash Benefits		16,000	20,000	12,000
Inv Allow 20%		-5,600
Deprec		-11,200	-6,720	-4,032
Loss on Sale				-5,548
Taxable Income		-800	13,280	2,420
Tax @ 30%		240	-3,984	-726

Cash Flows	0	1	2	3
Tax		240	-3,984	-726
Cash Benefits		16,000	20,000	12,000
Salvage Value				500
Outlay	-28,000
NCFAT	-28,000	16,240	16,016	11,774
DCF @ 15%	-28,000	14,122	12,110	7,742
NPV	5,974

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Method Two
*Calculate* *EBIAT* *and* *add* *back* *non-cash* *flow* *items* to *get* *NCFAT*

	0	1	2	3
Cash Benefits		16,000	20,000	12,000
Inv Allow 20%		-5,600
Deprec		-11,200	-6,720	-4,032
Loss on Sale				-5,548
EBIT		-800	13,280	2,420
Tax @ 30%		240	-3,984	-726
EBIAT		-560	9296	1694
Add back Non-Cash flow Items		16,800	6,720	9,580
NCFAT including Outlay	-28000	16240	16016	11774

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Adjusting for tax as you go

• Adjust Taxable Cash Flow Revenue by (1 – t)

Adjust Deductible Cash Flow Expense by (1 – t)

• Calculate tax savings from non cash flow deductions [ E x t ], eg Depreciation

Calculate tax payments on non cash flow revenue: R x t

• This method requires adjustment if tax is paid in the year following the year of income.

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Method Three

*Adjust* *for* *tax* as *you* go *through*

	0	1	2	3
Revenue after tax		11200	14000	8400
Outlay	-28000
Tax Savings on Depreciation		3360	2016	1210
SV				500
Tax Savings on Loss on Sale				1664
Tax Savings on Investment Allowance		1680
NCFAT	-28000	16240	16016	11774


Cash Revenue after tax = R*(1-t)
Tax Savings on Depreciation = D*t
Tax Savings on Loss = L*t
Cash Expense after tax = E*(1-t)
Tax on Gain = G*t
Tax Savings on Investment allowance = IA*t

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Lecture Example Method Three as Equation

-28000 + [16000(1-.3]/1.15 + [20000(1-

.3)]/1.152 + [12000(1-.3)]/1.153 + 500/1.153

+ [5548(.3)]/1.153 + [11200(.3)]/1.15 +

[6720(.3)]/1.152 + [4032(.3)]/1.153 + 5600(.3)/1.15 = 5974

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Consistency

NPV =

–I0

+å

t =1

When using the NPV method the net cash flow in the numerator should be defined in a way that is consistent with the way the discount rate is defined

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Consistency

Real Cash Flows Real Discount Rate Before Tax Cash Flows Before Tax Discount Rate After Tax Cash Flows After Tax Rate

Nominal Cash Flows Nominal Discount Rate Risky Cash Flows Risk Adjusted Rate Cash Flows In $US $US Discount Rate

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Inflation and Project Evaluation

Inflation and interest rates
- Fisher effect
- Nominal rate = f (inflation rate + real rate)

– (1+N) = (1+R)(1+Inf)

Inflation and Cash flows
- Nominal and real cash flows
- Discount Nominal cash flows at nominal rates and real cash flows at real rates.
- If we have real cash flows (cash flows without inflation), then we need real discount rate without inflation.
- If we have nominal cash flows (cash flows with inflation), then we need the discount rate with inflation.

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Nominal v Real

(1+

Nominal)

= (1+

Real)(1+

Inf)

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Lecture Example

This example illustrates the relationship between the real rate, nominal rate and inflation. The project is the purchase of a pump with a three year life. Assume prime cost depreciation over three years. Calculate the NPV using nominal after tax cash flows and a nominal rate and again using real after tax cash flows and a real rate. The two NPV’s should be the same.

Cost	$30,000	Maintenance	$3,000pa (real)
Life – Yrs	3	Real Rate	8%
Salvage	$0	Inflation Rate	5%
Tax	40%	Revenue	$17,000pa (real)
Depreciation	1/3yr	Discount Rate	13.40%

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Deflated depreciation

= Dep./(1+inflation)

è Year 1:

= 10000 =

1.05

$9,524

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Non Identical Replacement and NPV of Perpetual Chain

• Self Test Problem 2 page 160

Solution is in Appendix B of the textbook

• Considering replacement of 10 CB Trailers with 6 AZ Flexivans – two choices

Continue with CB and replace with AZ in 3 years
Replace CB’s now with AZ’s
Once CB’s replaced continue to use AZ Flexivans into foreseeable future
Rate 10%
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Information

CB – remaining life, 3 years
- AZ – estimated life, 5 years
- CB – salvage value now, $5000 each
- CB – salvage value in 3 years, $1000 ea
- CB – annual cash flows, 30000 ea
- AZ – cost, 70000 ea
- AZ – salvage value in 5 years, 5000 ea
- AZ – annual cash flows, 40000 ea

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0 3 8

300000 300000 300000

1341190

0 5

50000

1341190

NPV One Flexivan = -70000 + 40000*PVIFA(.1,5) + 5000/1.15 = 84736

AE of six Flexivans = 84736*6/PVIFA(.1,5) = 134119 NPV Perpetual Chain = AE/i = 134119/.1 = 1341190

NPV1 = 300000*PVIFA(.1,3) + 10000*1.1-3 + 1341190*1.1-3 = 1761224

NPV2 = 50000 + 1341190 = 1391189

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Analysing Project Risk

We look at best estimates of cash flows, and then we discount them at the best estimate of required rate of returns.

Risk is incorporated into project analysis through the discount rate which reflects the risk of the project. (systematic risk)

However, the NPV is based on forecasts of cash flows which hardly ever turn out to be correct. (non systematic)

Therefore need to analyse risk of changing assumptions

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Scenario Analysis

Scenario analysis examines the effect of changing multiple variables at the same time on the outcome.
- A simple example involves:
  - Making pessimistic, optimistic and expected estimates of each variable
  - Calculating the NPV holding every variable except one at the expected level and calculating Pessimistic, Expected and Optimistic NPV’s.

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Scenario Analysis

For example, three possible scenarios are as below:
- Base-case scenario (the most likely scenario)
  - 10% sales growth rate, No change in costs, 6% discount rate, 40% tax rate
- Worst-case scenario
  - – 5% sales growth rate, 10% increase in costs, 12% discount rate, 50% tax rate
- Best-case scenario
  - 20% sales growth rate, 10% decrease in costs, 4% discount rate, 30% tax rate

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Sensitivity Analysis

Sensitivity Analysis involves assessing changes in NPV due to changes in inputs.
It shows how sensitive NPV is to the assumptions of the

model.

It usually turns out that there are one or two key variables which are critical.

Simulation

Sensitivity analysis and scenario analysis do not suggest

probabilities of success of the project.

Simulation involves defining the probability distributions for the variables and the relationship between the variables.
A computer is used to simulate the project’s cash flows and produce a probability distribution.

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