Topic 1
Lecturer
:
:
THE FIRM’S INVESTMENT DECISION
SHELLEY DONNELLY
donnellys@ukzn.ac.za
Required reading:
Chapters 8, 9, 10 and 15 of your prescribed text: Correia, C. (2019) Financial Management
9th Edition. Juta Press.
Timetable:
LECTURES &
TUTS
DATE
TOPIC
Lectures 1 & 2
25/07
Lectures 3 & 4
27/07
Revision of Incremental cash flows, OCF, and Estimating cash
flows.
Inflation and Capital Budgeting.
Taxation effects
Capital rationing
Lectures 5 & 6
02/09
Risk and Uncertainty
Tut 1.1
02/09
Questions provided on Learn
Lectures 7 & 8
04/09
Risk and Uncertainty concluded
Lectures 9 & 10
08/08
Projects with Unequal Lives
The Replacement Decision
Lectures 11 & 12
10/08
The Replacement Decision concluded
Leasing
Topic 1 Revision
15/08
Tut 1.2
15/08
Questions provided on Learn
TOPIC 1:
THE FIRM’S INVESTMENT
DECISION
Incremental Cash Flows and estimating Cash Flows
revised
Inflation and Taxation and Capital Budgeting
Capital Rationing (including PI)
Risk and Uncertainty:
•
Adjusting the Discount rate
•
Certainty Equivalents
•
Sensitivity and Scenario Analysis
•
Break Even NPV Analysis
•
Probability Analysis and Decision Trees
•
Comprehensive Example – SEC.
Unequal Lives – EAC method
Replacement Decision
Leasing
RECAPTHE INVESTMENT DECISION IN PREVIOUS
COURSES:
Financial Managers face three main decisions,
one of which pertains to Capital Budgeting –
what Long Term investments should the firm
take on?
 FINA202


Topic 2 included the Investment Decision.
You learned how to use various capital budgeting
techniques such as the NPV, IRR, Payback and Discounted
Payback periods (Profitability Index to come).
 You should recall the importance we placed on NPV due to
its many advantages over the other techniques.
 We learned about incremental cash flows and how to arrive
at the OCF’s and estimated cash flows.


In this topic we will further develop a number of these concepts, hence it is
vital that you review your notes from last year as it will be assumed that you
have.
INCREMENTAL CASH FLOWS
The cash flows that should be included in a
capital budgeting analysis are those that will
only occur if the project is accepted
 These cash flows are incremental cash flows
 The stand-alone principle allows us to analyze
each project in isolation from the firm simply
by focusing on incremental cash flows


You should always ask yourself “Will this cash flow
occur ONLY if we accept the project?”
If the answer is “yes”, it should be included in the analysis
because it is incremental
 If the answer is “no”, it should not be included in the
analysis because it will occur anyway
 If the answer is “part of it”, then we should include the part
that occurs because of the project

INCREMENTAL CASH FLOWS REVISED

Sunk costs


Opportunity costs



Only include those that are exclusive to the project
Changes in NWC


Positive side effects – benefits to other projects
Negative side effects – costs to other projects, sometimes known
as Erosion Costs
Overheads


Costs of lost options (eg using property the firm already owns –
what else could it have been used for/ what could it have been
sold or rented out for)
Side effects/Spillover effects/Externalities


Costs that have accrued in the past/are accrued regardless of
project being accepted or not.
When the project winds down, NWC is recovered
Financing costs

We do not include interest paid or other financing costs – we are
interested in cash flow from assets (not to lenders or
shareholders). Avoid double counting.
ESTIMATING CASH FLOWS - REVISED
TOTAL CASH FLOW CALCULATION (Cash Flow from assets)
Total Cash flow
= Operating Cash Flow (OCF) – Additions to NWC –
Capital Spending
CALCULATION OF OCF:
S = sales C = operating costs
rate
D = Depreciation
TC =Corporate tax

Conventional method:
OCF
= PBIT + D - Taxes

Top-Down method:
OCF
= (S – C) – (S – C – D) x TC

Bottom-Up method:
OCF
= Net Profit + D

Tax-shield Approach:
OCF
= (S – C) x (1 - TC ) + (D x TC )
Which to use??
REVISION EXERCISE
Best Manufacturing Company new investment proposal.
Corporate tax rate 34%.
Appropriate discount rate 12%.
Projected year-end accounting data (R 000’s) as follows:
YEAR
Sales
revenue
Operating
costs
Investment
Depreciation
NWC
0
1
7 000
2
7 000
3
7 000
4
7 000
2 000
2 000
2 000
2 000
2 500
250
2 500
300
2 500
200
2 500
0
10 000
200
 Calculate OCF using four known techniques
 Calculate project NPV
INFLATION AND CAPITAL BUDGETING



Investors should have an expectation of future inflation. It affects both cash
flows and the discount rate used.
The Reserve Bank includes the effects of expected inflation in deciding on
interest rate policy. The cost of capital will include an inflation premium to
protect investors against a decline in purchasing power, hence it is usually
nominal.
There are two methods of adjusting for inflation:
1. Estimate cash flows in NOMINAL terms and use a NOMINAL discount
rate (nominal cash flow = prices expected to rule when cash flow occurs.
Inflation not applied to deprecation which uses historical value).

This is the more commonly used method.

Nominal cash flows have already been adjusted for inflation.

Costs of Capital (used to determine the discount rate) are usually
inclusive of inflation so already nominal.
OR
Method 2 overleaf..
INFLATION AND CAPITAL BUDGETING
2. Estimate cash flows in REAL terms and use a REAL discount rate
(real cash flows = future cash flows expressed in terms of Date 0
purchasing power).


Real flows exclude inflation effects.

Need to convert nominal discount rates to real to remove inflation
effects.
Use the Fisher Effect which expresses the relationship between
NOMINAL and REAL rates of return:
1 + Nom rate = (1 + Real rate) x (1 + inflation rate)
(R)
(r)
hence R = (1 + r) (1 + h) – 1 or
(h)
r= 1+R
1+h
-1
INFLATION – AN EXAMPLE
Dixie Co has a nominal RRR of 20% at a time where
there is an 8% inflation expectation. An NPV
analysis is required of the following project:
 Initial outlay: R50 000
 Project lifespan: 4 years (zero salvage value)
 Current estimation of after-tax cash savings from
the project: R30 000 p.a.
Use both the NOMINAL and REAL methods of
adjusting for inflation, to perform the NPV analysis.
INFLATION EXAMPLE SOLUTION
1. Using nominal RRR and nominal cash flows:
Inflate the cash flows:
yr 1 = 30 000 x 1.08 = 32 400
yr 2 = 30 000 x 1.082 = 34 992
yr 3 = 30 000 x 1.083 = 37 791
yr 4 = 30 000 x 1.084 = 40 815
 NPV using a fin. calculator:
-50 000 CF0; 32 400 CF1; 34 992 CF2; 37 791 CF3;
40 815 CF4; 20 I/YR; NPV = R42 852.95

2. Using real RRR and real cash flows:
r = (1.20 / 1.08) – 1 = 11.11%
 NPV using a fin. calculator:
-50 000 CF0; 30 000 CF1; 4 Nj; 11.11 I/YR;
NPV = R42 855.20

ANOTHER EXAMPLE OF CAPITAL BUDGETING UNDER
INFLATION
Sony International has an investment opportunity
to produce a new stereo color TV.
The required investment on January 1 of this year
is $32 million. The firm will depreciate the
investment to zero using the straight-line method,
over the project’s lifespan of 4 years. The firm is in
the 34% tax bracket.
The price of the product on January 1 will be $400
per unit. The price will stay constant.
Labour costs will be $15 per hour on January 1.
They will increase at 2% per year.
Energy costs will be $5 per unit; they will increase
3% per year.
12 and
The inflation rate is 5%. Revenues are received
costs are paid at year-end.
EXAMPLE OF CAPITAL BUDGETING UNDER INFLATION
GIVEN:
Year 1
Year 2
Year 3
Year 4
Physical
Production
(units)
100 000
200 000
200 000
150 000
Labour Input
(hours)
2 000 000
2 000 000
2 000 000
2 000 000
Energy input,
physical units
200 000
200 000
200 000
200 000
The real discount rate is 3.81%.
Calculate the NPV, using the nominal method of adjusting for
13
inflation.
YEAR 1 AFTER-TAX NOMINAL CASH FLOWS

Real Cash Flows
Price: $400 per unit with zero annual price increase
 Labour: $15 per hour with 2% annual wage increase
 Energy: $5 per unit with 3% annual energy cost increase


Year 1 After-tax nominal Cash Flows:
Revenues
= $400 × 100 000
= $40 000 000
Labour costs = $15 × 1.02 × 2 000 000
= $30 600 000
Energy costs = $5 × 1.03 × 200 000
= $1 030 000
After-tax operating profit =
($40 000 000 – $30 600 000 – $1 030 000) x (1 – 0.34) 14
= $8 370 000 x 0.66
= $5 524 200
YEAR 2 AFTER-TAX NOMINAL CASH FLOWS

Real Cash Flows
Price: $400 per unit with zero annual price increase
 Labour: $15 per hour with 2% annual wage increase
 Energy: $5 per unit with 3% annual energy cost increase


Year 2 After-tax nominal Cash Flows:
Revenues
Labour costs
Energy costs
= $400 × 200 000
= $80 000 000
= $15 × 1.022 × 2 000 000
= $31 212 000
= $5 × 1.032 × 200 000
= $1 060 900
After-tax operating profit
=
($80 000 000 – $31 212 000 – $1 060 900) x (1 – 0.34)
= $47 727 100 x 0.66
= $31 499 886
15
YEAR 3 AFTER-TAX NOMINAL CASH FLOWS

Real Cash Flows
Price: $400 per unit with zero annual price increase
 Labour: $15 per hour with 2% annual wage increase
 Energy: $5 per unit with 3% annual energy cost increase


Year 3 After-tax nominal Cash Flows:
Revenues
= $400 × 200 000
= $80 000 000
Labour costs = $15 × 1.023 × 2 000 000
= $31 836 240
Energy costs = $5 × 1.033 × 200 000
= $1 092 727
After-tax operating profit =
($80 000 000 – $31 836 240 – $1 092 727) x (1 – 0.34)
16
= $47 071 033 x 0.66
= $31 066 882
YEAR 4 AFTER-TAX NOMINAL CASH FLOWS

Real Cash Flows
Price: $400 per unit with zero annual price increase
 Labor: $15 per hour with 2% annual wage increase
 Energy: $5 per unit with 3% annual energy cost increase


Year 4 After-tax nominal Cash Flows:
Revenues
= $400 × 150 000
= $60 000 000
Labour costs = $15 × 1.024 × 2 000 000
= $32 472 964.80
Energy costs = $5 × 1.034 × 200 000
= $1 125 508.81
After-tax operating profit =
($ 60 000 000 – $ 32 472 964.80 – $ 1 125 508.81) x (1 – 0.34)
17
= $26 401 526.39 x 0.66
= $17 425 007
EXAMPLE OF CAPITAL BUDGETING UNDER INFLATION
The depreciation tax shield is a nominal cash
flow, and must therefore be discounted at
the nominal rate.
Project life = 4 years
Annual depreciation expense:
$32 000 000
= $8 000 000
4 years
Depreciation tax shield
= $8 000 000 × 0.34
= $2 720 000 per annum
18
EXAMPLE OF CAPITAL BUDGETING UNDER INFLATION
[OCF = (S – C) (1 – TC) + (D X TC)]
OCF
0
$32 000 000
$5 524 200
$31 499 886
$31 066 882
$17 425 007
+ 2 720 00
+ 2 720 000
+ 2 720 00
+ 2 720 000
= 8 244 200
= 34 219 886
= 33 786 882
= 20 145 007
1
2
3
4
The project NPV can now be computed by discounting the nominal
cash flows at the nominal discount rate:
Nominal rate (R) = (1.0381 x 1.05) – 1 = 9%
NPV:
-$32 000 000 CF0; 8 244 200 CF1; 34 219 886 CF2; 33 786 882 CF3;
20 145 007 CF4; 9 I/YR; NPV = $44 726 582.62 Accept 19
TAXATION AND INVESTMENT APPRAISAL


Tax definitely a cash outflow, therefore after-tax
cash flows of projects need to be evaluated
2 Rules:
Accommodate INCREMENTAL tax effects
 Get the timing right


2 specific items need to be dealt with:
Depreciation and
 Salvage values

DEPRECIATION





Non-cash expense, so only has cash flow implications
insofar as it influences the tax bill
When claimed as an expense for tax purposes, depreciation
is termed a “wear and tear allowance”
Firms can use the straight-line or declining balance
method. The former is more advantageous from a cash flow
perspective due to higher wear and tear allowances in the
early years (illustrated on next slide).
There may be a difference between Receiver of Revenue
allowances, and the rate at which the firm may choose to
depreciate its assets, in which case 2 separate asset
registers are maintained.
Firms who choose a lower depreciation rate, will reflect a
higher profit figure. They use this approach in the belief
that the wear and tear allowance does not reflect the true
operating life of the asset, and that the higher profit
figures are more realistic.
DIFFERENT DEPRECIATION METHODS:
Declining/Reducing Balance
Straight-Line method
Opening Book
Wear and Tear
Closing Book
Open Wear & Tear Closing
Value
@ 33.3% of decl.
Value
Book
@ 33.3%
Book
Value
of cost
Value
Book Value
300 000
100 000
200 000
300 000 100 000
200 000
200 000
66 666
133 334
200 000 100 000
100 000
133 334
44 444
88 890
100 000 100 000
0
88 890
29 630
59 260
59 260
19 753
39 507
39 507
13 169
26 338
etc
CHOOSING A LOWER DEPRECIATION RATE:
Purchase price of asset: R180 000
Wear and Tear allowance: 33.3% of cost per annum
Firm wishes to depreciate over 4 years
Tax rate = 35%
For Tax Purposes
Own Books
Operating Profit (before depr.)
150 000
150 000
Wear & Tear allowance (33.3%)
60 000
Depreciation (180 000/4)
45 000
Profit before Tax
90 000
105 000
Tax @ 35% on R90 000
31 500
31 500
Net Profit after Tax
58 500
73 500
SALVAGE VALUES


If Market Value = Book Value, then asset has been
depreciated correctly and taxes have been correctly paid.
If Market Value exceeds Book Value, then the asset has
been over-depreciated and too little was paid in taxes.

Example:





Market value R15 000, Book value R8 000.
Then R7 000 too much was deducted in wear and tear.
Therefore R7 000 x 35% too little was paid in taxes i.e. R2 450 is owed
in tax (cash outflow).
Sale of vehicle is treated as a ‘profit’ for tax purposes.
If Book Value exceeds Market value, then too little
depreciation was deducted and too much tax was paid.

Example:




Market value R4 000, Book value R8 000.
Then R4 000 too little was deducted as wear and tear.
Therefore R4 000 x 35% in taxes need to be recouped from Revenue
Services (cash inflow of R1 400 ).
Sale of vehicle treated as a ‘loss’ for tax purposes.
WORKING EXAMPLE
Harry is financial manager of a company. He is nearing retirement and you have
been appointed as his deputy with a view to taking over from him in 12 months
time.
The company is considering an investment in a new product that will cost
R1 200 000 in new machinery and will result in profit before depreciation and tax of
R375 000 per annum in real terms for 5 years. At the end of the 5 years, the
machinery can be sold for its written-down book value. The investment will require
working capital at the beginning of each year as follows (figures in real terms):
Year
Amount (R)
1
100 000
2
200 000
3
300 000
4
400 000
5
500 000
Harry is proposing to evaluate the investment using the company’s nominal
weighted average cost of capital (WACC) of 16%.
The following notes are relevant:





At the end of Year 5, the total working capital can be released in cash back to
the company.
Inflation is expected to be 4% per annum on all operating cash flows and
working capital for the period under review.
The company pays tax at the rate of 33%. There is a 12-month time lag for
tax payments or refunds.
Tax relief is available on capital expenditure at 25% on a reducing balance.
Assume all cash flows occur at year-end except the purchase of the new
machinery and the working capital. Both these items of expenditure occur at
the beginning of the year.
You are required to:
Evaluate the investment using the company’s WACC, as suggested by Harry.
WORKING EXAMPLE SOLUTION
Cash flows (R’000)
Time
0
1
2
3
4
5
6
Pre tax/depn profit (W2)
390
405.6
421.82
438.70
456.25
Capital allowances (W3)
(300)
(225)
(168.75)
(126.56)
(94.92)
90
180.6
253.07
312.14
361.33
(29.7)
(59.60)
(83.51)
(103.01)
(119.24)
90
150.9
193.47
228.63
258.32
(119.24)
+ Capital allowances
300
225
168.75
126.56
94.92
OCF
390
375.9
362.22
355.19
353.24
PBIT
Tax on profits @ 33%
NPAT
Machinery
Working capital (W1)
Net cash flow*
(1 200)
(119.24)
284.77
(W3)
(100)
(108)
(116.48)
(125.47)
(134.98)
584.93
(1 300)
282
259.42
236.75
220.21
1 222.94
(119.24)
Net present value = R (57 493)
-1 300 CF0; 282 CF1; 259.42 CF2; 236.75 CF3; 220.21 CF4; 1 222.94 CF5; -119.24 CF6; 16 I/YR
The negative NPV indicates that the project is not acceptable when appraised at the WACC
WORKING EXAMPLE SOLUTION NOTES
1.
Working capital
The relevant cash flow is the increase in working capital required from one year to the
next:
Time
0
1
2
3
4
5
200
300
400
500
x
x
x
x
(1.04)
(1.04)2
(1.04)3
(1.04)4
W/cap balance
(nominal terms)
R’000
100
208
324.48
449.95
584.93
Cash injection
(outflow)
R’000
-100
-108
-116.48
-125.47
-134.98
W/cap recovered
R’000
+584.93
2.
Pre-tax/depreciation profit
These figures are obtained by applying the inflation rate of 4% for the appropriate
number of years, eg, for time 3: R375 000 x (1.04)3 = R421 824
3.
Capital allowances/scrap value
Time
Book Value
0
1
25%
2
25%
3
25%
4
25%
5
25%
Scrap value
R’000
1,200
(300)
900
(225)
675
(168.75)
506.25
(126.56)
379.69
(94.92)
284.77
Capital allowance
(depreciation)
R’000
300
225
168.75
126.56
94.92
CAPITAL RATIONING IN CAPITAL BUDGETING



We now need to drop the unrealistic assumption that there
are no finance limits in capital budgeting.
CAPITAL RATIONING is when funds are not available to
finance ALL wealth-enhancing projects
There are 2 types of capital rationing:
- SOFT RATIONING = internal management-imposed
limits on investment expenditure e.g. Mgmt may want to
maintain a fixed debt/asset ratio
- HARD RATIONING = relates to capital from external
sources. Financial institutions won’t supply unlimited
capital, despite +’ve projected NPV’s. Banks don’t like to
see debt ratio’s exceed certain parameters either (risk
control).
We also need to look at ONE-PERIOD capital rationing (for
divisible and indivisible projects), as well as MULTIPERIOD capital rationing.
ONE-PERIOD CAPITAL RATIONING DIVISIBLE PROJECTS
This is where limits are placed on finance availability for one year only
(thereafter unlimited funds), and the projects can be undertaken in part or in
full.
2 methods:

Can rank according to absolute NPV’s e.g.
(R million)
TIME 0
1
2
NPV @ 10%
A
-2
6
1
4.281
B
-1
1
4
3.215
All positive, so all
C
-1
1
3
2.389
acceptable
D
-3
10
10
14.355
PROJECT
But capital rationed to R4.5m for 1 year…
ONE-PERIOD CAPITAL RATIONING
CONTINUED - DIVISIBLE PROJECTS:
Method 1: Ranking according to highest absolute NPV
OUTLAY
NPV
All of project D
3
14.355
3/4 of project A
1.5
3.211
4.5
17.566
This method will often give an incorrect result and is
biased towards the larger projects. Sometimes
investing in a number of smaller projects will be
better.
ONE-PERIOD CAPITAL RATIONING
CONTINUED - DIVISIBLE PROJECTS:

Method 2: Use the PROFITABILITY INDEX or the BENEFIT-COST RATIO
Profitability Index =
Gross Present Value (without deducting initial outlay)
Initial Outlay
Benefit -Cost Ratio =
Net Present Value
Initial Outlay
Both provide a measure of profitability per R1 invested. The choice between the
2 is a personal one. You would choose one method and then arrange the projects
in order of highest P.I or B-C Ratio. Then work down the list until the capital
limit is reached
For the purposes of our example, we will choose the Profitability Index:
ONE-PERIOD CAPITAL RATIONING DIVISIBLE PROJECTS CONCLUDED
Project
NPV @ 10%
GPV @ 10%
P.I
A
4.281
6.281
6.281 / 2 = 3.14
4.281 / 2 = 2.14
B
3.215
4.215
4.215 / 1 = 4.215
3.215 / 1 = 3.215
C
2.389
3.389
3.389 / 1 = 3.389
2.389 / 1 = 2.389
D
14.355
17.355
17.355 / 3 = 5.785
14.355 / 3 = 4.785
Ranking according to highest P.I:
Project
P.I.
Initial Outlay
NPV
D
5.785
3
14.355
B
4.215
1
3.215
1/2 OF C
3.389
0.5
1.195
0 OF A
3.14
0
0
4.5
18.765
Via this method, an extra R1.199m is created for shareholders
(than via the absolute NPV method).
So always use Method 2 with divisible projects!
B-C Ratio
ONE-PERIOD CAPITAL RATIONING INDIVISIBLE PROJECTS:
Easiest approach is to examine the total NPV values of all feasible
alternative COMBINATIONS of whole projects (trial and error):
Assume same projects but a capital constraint of R3m:
Combination
1
2
NPV
R2m in A
4.281
R1m in B
3.215
Answer:
7.496
You would choose
R2m in A
4.281
Comb.4 (highest NPV)
R1m in C
2.389
6.670
Note that any
unutilized
capital could be
3
4
R1m in B
3.215
invested, giving rise to
R1m in C
2.389
an additional NPV, to
5.604
be added to the total
14.355
NPV.(e.g. Comb.3)
R3m in D
MULTI-PERIOD CAPITAL RATIONING:


This is a more complicated issue. We are
talking about capital constraints in more
than one period e.g. Capital limit of R240
000 at time 0, and a further constraint of
R400 000 at time 1.
To solve, a mathematical program is
required and a computer would be
employed. If projects are divisible, linear
programming is used; if indivisible,
integer programming is used.
(beyond the scope of this course)
RISK AND UNCERTAINTY IN CAPITAL BUDGETING INTRO
Businesses operate in an uncertain environment. There is an
upside (earning more than expected) and a downside (earning
less than expected) to uncertainty.
 The presence of risk in capital budgeting decisions means the
possibility exists of more than one outcome. Probabilities can be
assigned to possible outcomes, with the probability of all
possible outcomes summing to one.
 Some of the approaches we have learnt so far do make
adjustments for risk. With the PBP for example, by insisting on
early cut-off dates, the chance of distant cash flow forecasts
proving unreliable, is eliminated (hence risk is reduced). Even
within the discounting process there is a safeguard included for
risk: the present value of a future cash flow is worth less the
further into the future it will be received.
 Now we will focus on various other ways in which we can
accommodate the risk of uncertain future outcomes into an
NPV analysis:

1. ADJUSTING FOR RISK THROUGH THE DISCOUNT RATE
This method recognizes that there is a reward for bearing risk. In this approach, a
number of % points (the premium) are added to the risk-free discount rate, which
is then used to calculate NPV in the normal manner. In this way, marginally
profitable projects are less likely to have a +‘ve NPV.e.g.
Level of Risk
Risk-free rate
Risk premium
Risk-adjusted
rate
Low
9%
+ 3%
12%
Medium
9%
+ 6%
15%
High
9%
+ 10%
19%
The project to be evaluated has the following cash flows:
Time(years)
0
1
2
Cash flow(R)
-100
55
70
If project judged low risk: -100 CF0; 55 CF1; 70 CF2; 12 I/YR; NPV = R4.91
ACCEPT
If project judged med risk: -100 CF0; 55 CF1; 70 CF2; 15 I/YR; NPV = R0.76
ACCEPT
If project judged high risk : -100 CF0; 55 CF1; 70 CF2; 19 I/YR; NPV = -R4.35
REJECT
Drawbacks: Subjective risk assessment and arbitrary selection of risk premiums.
2. CERTAINTY EQUIVALENT METHOD

Expected “risky “cash flows are converted to “riskless” or “certainty
equivalent” values, and discounted at a risk-free discount rate. e.g.
Year
Cash flow
NPV: 10 I/YR
0
- 9 000
CF0
1
7 000
CF1
2
5 000
CF2
3
5 000
CF3
NPV = 5 252.44
Project appears worthwhile, but management are uncertain of
future cash flows, so take only 70% of year 1 flow, 60% of year 2 flow
and 50% of year 3 flow:
Hence above cash flows will be adjusted to R4 900 (year 1), R3 000
(year 2) and R2 500 (year 3).
The risk-adjusted NPV of the project would then be -R188 (if we use
10% as the risk-free rate) i.e. Reject.
Disadvantage of this method: Subjectivity and arbitrariness in
selecting certainty equivalents.
3. SENSITIVITY ANALYSIS






NPV analysis relies on assumptions about crucial variables
e.g. the selling price of a particular product.
‘What if’ these variables were to change? How would these
changes influence the viability of the project?
This approach measures how sensitive NPV is to changes in
underlying assumptions/values.
The greater the volatility in NPV in relation to a specific
variable, the larger the forecasting risk associated with that
variable and the more attention we want to pay to its
estimation.
One variable is analysed at a time and the results are
examined.
SA is usually a computer-driven exercise, but we can do a
few manual ‘what-if’s’ by way of illustration:
SENSITIVITY ANALYSIS
Expected cash flow of Project X: R300 000 p.a for 4
years.
 RRR = 15%
 Initial investment = R800 000.
 Likely annual demand for product = 1 000 000 units.
 Sale price / unit = R1.
 Total costs R0.70 / unit (labour 0.20, materials 0.40,
overhead 0.10).
 Cash flow / unit = R0.30 (hence the R300 000 annual
cash flow).

-800 000 CF0; 300 000 CF1; 4 Nj; 15 I/YR;
NPV = +56 493.51 (accept)
SENSITIVITY ANALYSIS

What if price is only R0.95?
Annual cash flow = R0.25 x 1 000 000 = R250 000
-800 000 CF0; 250 000 CF1; 4 Nj; 15 I/YR;
NPV = -R86 255.41 (reject)

What if demand is 10% less than expected?
Annual cash flow = R0.30 x 900 000 = 270 000
-800 000 CF0; 270 000 CF1; 4 Nj; 15 I/YR;
NPV = -R29 155.84 (reject)

What if the discount rate is 20% higher than originally assumed? i.e. 18%
as opposed to 15%?
-800 000 CF0; 300 000 CF1; 4 Nj; 18 I/YR;
NPV = R7 018.54 (accept)
SENSITIVITY ANALYSIS

Advantages:
At the very least it allows decision-makers to be
more informed regarding project sensitivities, to
know how much margin they have for judgemental
error, and to decide whether they are prepared to
accept the project risks or not.
 It points out the most crucial variables, thereby
saving time and money.
 Contingency plans can be developed once the key
variables have been identified.


Disadvantages:
Absence of any formal assignment of probabilities to
the variations of parameters.
 Sensitivity analysis alters each variable in isolation,
when in reality some variables are likely to be
related.

SCENARIO ANALYSIS
What happens to NPV under different cash flows
scenarios?
 At the very least look at:




Best case – revenues are high and costs are low
Worst case – revenues are low and costs are high
Measure of the range of possible outcomes
Best case and worst case are not necessarily
probable, they can still be possible.
 Sensitivity Analysis is a subset of Scenario
analysis.
 Scenario analysis addresses the main drawback of
sensitivity analysis (that only one variable is
changed at a time).

4. BREAK-EVEN ANALYSIS
A common finding is that sales volume is seen to be a crucial
variable.
 Break-even analysis is a common tool in analysing the
relationship between sales volume and profitability.
 The accounting break-even point is where sales = costs i.e.
the point where the project generates no profits or losses. As
long as sales are above this point, the firm will make a profit. It
can be calculated as:

Sales Break-even = (Fixed Costs + Depreciation) x (1 - T)
(Sales price - variable cost) x (1 - T)
Accounting break-even takes into account accounting expenses
but it fails to account for the economic opportunity cost of the
initial outlay of the investment.
 Firms that breakeven on an accounting basis might really be
losing money because they are losing the opportunity cost of the
initial investment.

BREAK-EVEN ANALYSIS
With Present Value Break-even, we ascertain the extent to
which some variables can change, before the decision to
accept changes to a decision to reject (the point at which
NPV swings from +’ve to -’ve).
 This method also indicates the sensitivity of the project to
certain key variables.
 Example:
Given a discount rate of 15%, we have:
Unit Sales
NPV(Rm)
0
-5 120
1 000
-2 908
3 000
1 517
10 000
17 004
The NPV is negative if 1 000 units are sold, and positive if 3
000 units are sold. Obviously the zero NPV point occurs
between the 2 sales units.

PV BREAK-EVEN CONTINUED

The firm originally invested R1.5m. We need to annualize this
like all the other variables in the equation, so we express it as a 5year EAC (equivalent annual cost), by solving for PMT on the
financial calculator:
-1 500 000 PV; 5 N; 15 I/YR; PMT = R447 473.33
PV Breakeven point = EAC + Fixed Costs x (1-T) – (D x T)
(in sales units)
(sales price - Variable cost) x (1-T)

By calculating the PV break-even point, we learn what the
minimum sales level needs to be in order for a project to breakeven (Zero NPV). If we consider this minimum unlikely we would
not risk investing in the project.
BREAK-EVEN EXAMPLE

1.
2.
3.
Consider a project to supply UKZN with 10 000 dormitory beds
annually for each of the next three years. Your firm has half of
the wood-working equipment to get the project started; it was
bought years ago for R200 000, is fully depreciated and has a
market value of R60 000. The remaining R90 000 of equipment
will have to be purchased. The engineering department
estimates that you will need an initial net working capital
investment of R10 000. Annual fixed costs will be R25 000, and
the variable costs should be R90 per bed. The initial fixed
investment with be depreciated straight line to zero over three
years. The salvage value of all equipment is estimated to be
R10 000. The marketing department estimates that the sales
price per bed will be R200. You require an 8% return and face
a tax rate of 34%.
Should your firm proceed with this project?
What is the break-even price per bed for this project?
What is the present value break-even sales volume (in units)?
BREAK-EVEN EXAMPLE – SOLUTION TO Q1.
Year 0
Year 1
Year 2
Year 3
Net Capital Spending
New Equipment
Opportunity cost of not selling
old equipment
-90 000
-60 000 (1-0.34)
Salvage Value
TOTAL NCS
10 000 (1-0.34)
-129 600
6 600
Total Cash Flows
Sales (10 000 x R200)
Fixed Costs
Variable Costs (10 000 x R90)
Depreciation (90 000 / 3)
PBIT
Less Taxes (34%)
NPAT
+ Depreciation
OCF
Net Working Capital
2 000 000
2 000 000
2 000 000
-25 000
-25 000
-25 000
-900 000
-900 000
-900 000
-30 000
-30 000
-30 000
1 045 000
1 045 000
1 045 000
-355 300
-355 300
-355 300
689 700
689 700
689 700
30 000
30 000
30 000
719 700
719 700
719 700
-10 000
10 000
NCS (from above)
-129 600
6 600
TOTAL CASH FLOWS
-139 600
719 700
719 700
736 300
BREAK-EVEN EXAMPLE – Q1 SOLUTION CONCL.
 NPV:
-139 600 CF0; 719 700 CF1; 2 Nj;
736 300 CF2; 8 I/YR; NPV = R1 728 314.32
Therefore, the firm should proceed with the project
as the NPV is positive.
BREAK-EVEN PRICE – Q2 SOLUTION.
 We
should be concerned with the break-even price i.e.
what should we put our bid in for in order to win the
contract. Therefore we need to find the revenue that
gives us a zero NPV.
 The PV of the costs of this project is the sum of the NCS
and NWC required today (R139 600) less the PV of the
salvage value and return of NWC in year 3 (16 600)
 16 600 FV; 3 N; 8 I/YR; PV = 13 177.62
Add the -139 600: -139 600 + 13 177.62 = -126 422.38
 Now we need to find the operating cash flow that the
project must produce each year to break-even i.e. solve
for PMT.
 -126 422.38 PV; 3 N; 8 I/YR; PMT = 49 056.12
BREAK-EVEN PRICE – Q2 SOLUTION CONTD.
Years 1 -3
Sales
10 000 x BE Price
983 872.91
Fixed Costs
-25 000
Variable Costs
-900 000
Depreciation
-30 000
PBIT
28 872.91
Less Taxes
-9 816.79
NPAT
19 056.12
Depreciation
OCF
30 000
49 056.12
Working backwards from the OCF up to Break-Even sales, the breakeven price per bed is 983 872.91 / 10 000 = R98.39.
BREAK-EVEN SALES VOLUME- Q3 SOLUTION
To calculate the break-even sale volume, we need to
annualise the PV of the non-OCF cash flows We already did
this when calculating the break-even price:
PV of non-OCF cash flows = -126 422.38
PMT = 49 056.12 (EAC in PV break-even
formula)
 PV Break-even:
= [49 056.12 + (25 000 x 0.66) – (30 000 x 0.34)]
[(200 - 90) x 0.66]
= 763 beds

PROBABILITY ANALYSIS AND DECISION TREES
 Satisfies
the drawbacks of Sensitivity Analysis in
that probabilities of certain outcomes are
obtained to help with the capital budgeting
decision
 There is usually a sequence of decisions in NPV
analysis, and Decision Trees are a useful tool to
identify such sequential decisions, in the face of
uncertainty.
 A Decision Tree is a diagram showing decision
points, alternatives and possible outcomes with
assigned probabilities.
DECISION TREES
 Decision
trees are relevant when projects involve
sequential investment decisions, or where project
cash flows are partially correlated over time.
 For example, a company needs to develop and test
prototypes and undertake a pilot production prior to
investing in a large plant for full-scale production.
There are two decisions. The decision to develop
prototypes is dependent on the NPV from undertaking
full scale production.
 A company may undertake product tests which will
have a 70% chance of success followed by an
investment in plant at a cost of R40m and possible
cash flows of either R50m or R10m per year for two
years.

53
DECISION TREES

54
DECISION TREE EXAMPLE
Project cost in year 0 is R300 000 and the discount
rate is 10%. Cash flows for project are:
Probability
If Cash Flow in
Year 1 is
Probability
Cash Flow in
Year 2
0.25
100 000
0.25
0
0.50
100 000
0.25
200 000
0.25
100 000
0.50
200 000
0.25
300 000
0.25
200 000
0.50
300 000
0.25
350 000
0.5
0.25
200 000
300 000
DECISION TREE
DECISION TREE ANALYSIS



Top Branch of the Decision tree
 Expected Payoff in Yr 2 = (0.25 x 0) + (0.5 x 100 000) + (0.25 x 200 000) = 100 000
 Cash Flow in Yr 1 = 100 000
 PV at time 0:
0 CF0; 100 000 CF1; 100 000 CF2; 10 I/YR; NPV = 173 553.72 (25% probability)
Middle Branch of the Decision tree
 Expected Payoff in Yr 2 = (0.25 x 100 000) + (0.5 x 200 000) + (0.25 x 300 000) =
200 000
 Cash Flow in Yr 1 = 200 000
 PV at time 0:
0 CF0; 200 000 CF1; 200 000 CF2; 10 I/YR; NPV = 347 107.44 (50% probability)
Bottom Branch of the tree
 Expected Payoff in Yr 2 = (0.25 x 200 000) + (0.5 x 300 000) + (0.25 x 350 000) =
287 500
 Cash Flow in Yr 1 = 300 000
 PV at time 0:
0 CF0; 300 000 CF1; 287 500 CF2; 10 I/YR; NPV = 510 330.58 (25% probability)
E (NPV) at time 0
-300 000 + (173 553.72 x 0.25) + (347 107.44 x 0.5) + (510 330.58 x 0.25) = R44 525
Therefore accept the project.
COMPREHENSIVE EXAMPLE – DECISION TREE,
SENSITIVITY ANALYSIS AND BREAK EVEN.
 Solar
Electronics Corporation (SEC) are
considering the development of a solar airplane.
 Stage 1 involves the development of proto-types
and test marketing which will last one year and
cost R100 mil (now). The firm believes that there
is a 75% chance of success.
 Stage 2 follows once Stage 1 is complete. This
stage involves full scale production, costing
R1 500 mil and taking 5 years. The R1 500
million cost is made upfront (at the beginning of
Stage 2).
 The appropriate discount rate is 15%.
SEC - DECISION TREE
The firm has two decisions to make:
1
To test or not to test (at T0).
To invest or not to invest (at T1).
Succes
s
75%
Test
-100m
Failure
-1500m
900
m
p.a.
Do not
invest
NPV = $0
25%
Do not
test
NPV = $0
Invest
-1500m
-630m
p.a.
59
0
Invest
2–6
SEC – NPV ANALYSIS

Cash flow forecasts (in millions) are given as follows:
Investments
Year 1
Revenues
Variable Costs
Fixed Costs
Depreciation
Pre-tax Profit
Tax (34%)
Net Profit
Cash Flow
Initial Costs
Successful in year 1
Years 2 - 6
6000
(3000)
(1791)
(300)
909
(309)
600
900
Unsuccessful in year 1
Years 2 -6
3000
(1839)
(1791)
(300)
-930
0
-930
-630
(1500)
NPV1 (successful) = R1 516.94
-1500 CF0; 900 CF1; 5 Nj; 15 I/YR
 NPV1 (unsuccessful) = -R3 611.86 (therefore don’t invest)
-1500 CF0; -630 CF1; 5 Nj; 15 I/YR

SEC - DECISION TREE
Decisions are made in reverse order
 Should the firm invest the R1 500 million? If tests are
successful the SEC should invest because the NPV > 0. If
tests are unsuccessful the SEC should not invest as the NPV
< 0.
 Should the firm invest R100 million now in order to obtain a
75% chance of R1 517million in a year’s time?
 Expected Payoff = (Prob of success x payoff if
successful) + (Prob of failure x payoff if fail)
 Should we test and develop?
 Expected Payoff1 = (0.75 x 1 517) + (0.25 x 0) = R1 138 mil
 NPV0 : -100 CF0 ; 1 138 CF1; 15 I/YR; NPV = R890 mil
 Therefore the firm should test the market for solar-powered
jet engines.

SEC - SENSITIVITY ANALYSIS

The SEC Sales Team estimates the following revenues (in the
event of a successful test):

No. of engines sold

Sales Revenue
= Market share x Size of market
= 0.3 x 10 000 = 3 000
= No. of engines sold x Price per engine
= 3 000 x R2mil = R6 000 mil
Therefore revenue estimates depend on three assumptions:
(1) market share, (2) the size of the engine market and (3) the
price per engine.
 Costs are divided into:
(1) variable costs, which change as output changes and are
zero when production is zero, and
(2) fixed costs, which are independent of production.

SEC - SENSITIVITY ANALYSIS

The cost breakdown is as follows:
Variable cost = variable cost/ unit x no. of engines sold =
R1mil x 3 000 = R3 000 mil
 Total cost = Variable cost + fixed cost =
R3 000 mil + R1 791 mill = R4 791 mil



Remember with Sensitivity analysis, one variable is changed
in isolation and the resultant effect on NPV is calculated.
Question 1: Imagine the managers
have overestimated the market size
believe it may only be 5 000 units.
with the project with this change in
15% is required.
are concerned that they
in their calculations and
Should the firm proceed
market size? A return of
QUESTION 1 ANSWER
No. of engines sold = Market share x Size of market
= 0.3 x 5 000 = 1 500
 Sales Revenue = No. of engines sold x Price per engine
= 1 500 x R2 mil = R3 000 mil
 Variable cost
= variable cost/ unit x no. of engines sold
= R1 mil x 1 500 = R1 500 mil
 Total cost
= Variable cost + fixed cost
= R1 500 mil + R1 791 mil = R3 291 mil
 Cash flow:
(S – C – D) (1 – Tc) + D
= {(3 000 – 3 291 – 300) x (1 - 0.34)} + 300
= -90.06
 NPV = -R1 801.90
-1 500 CF0; -90.06 CF1; 5 Nj; 15 I/YR
 Now the project doesn’t look so good.

SCENARIO ANALYSIS
The assumptions on which the NPV were originally
based are shown in the column (best estimate) and in
the other two columns the pessimistic and optimistic
calculations are shown.
 The NPV can be computed for each new scenario,
where several variables are changed at a time.

VARIABLE
PESSIMISTIC
BEST ESTIMATE
OPTIMISTIC
Market share
Market size (per year)
Price
Variable Cost (per plane)
20%
5000
R1.9 mill
R1.2 mill
30%
10000
R2 mill
R1 mill
50%
20000
R2.2 mill
R0.8 mill
Fixed Cost (per year)
Investment
R1891 mill
R1900 mill
R1791 mill
R1500 mill
R1741 mill
R1000 mill
SCENARIO ANALYSIS ANSWER

NPV Calculations as of date 1 using scenario analysis (R
millions and rounded off):
Scenario
Pessimistic
Best estimate
Optimistic
Revenues
1 900
6 000
22 000
Costs
(1 200)
(3 000)
(8 000)
Fixed Costs
(1 891)
(1 791)
(1 741)
(380)
(300)
(200)
(1 571)
909
12 059
(1 037)
600
7 959
(657)
900
8 159
(4 102)
1 517
26 350
Depreciation
. PBT
NPAT
OCF (NPAT+D)
NPV @ 15%
SCENARIO ANALYSIS CONCL.
 If
the probabilities of each scenario occurring are 35%
(pessimistic), 55% (best estimate) and 10% (optimistic)
respectively:
E(NPV) = (0.35 x -4 102) + (0.55 x 1 517) +
(0.10 x 26 350)
= +2 034 (Accept)
SEC – PV BREAK-EVEN ANALYSIS
For SEC, the annual sales are varied and the NPV is computed
as detailed in the table below. It is clear that the present value
break-even sales quantity lies between 1 000 and 3 000 units.
Initial
Inv.
(Yr 1)
Unit
Sales
p.a.
Sales
rev.
Var.
Costs
Fixed
Costs
Depr.
Tax
(34%)
Net
Profit
Cash
Flows
NPV
(date 1)
1500 mil
0
0
0
-1791
-300
711
-1380
-1080
-5120
1500 mil
1000
2000
-1000
-1791
-300
371
-720
-420
-2908
1500 mil
3000
6000
-3000
-1791
-300
-309
600
900
1517
1500 mil
10000
20000 -10000 -1791
-300
-2689
5220
5520
17004
SEC – ACCOUNTING BREAK-EVEN ANALYSIS
Accounting B-E Sales = (FC + Depreciation) x (1 – Tc)
(Sales price – VC) x (1 - Tc)
 Considering the SEC example:
 Accounting Break-Even sales
= (1 791 + 300) x 0.66
(2-1) x 0.66
= 2 091 units
 The denominator is known as the contribution margin as it
measures how much each product contributes towards certain
costs (fixed and depreciation). Thus, the accounting break-even
sales amount effectively measures how many engines must be
sold to offset the after-tax fixed costs and depreciation.
SEC – BREAK-EVEN ANALYSIS

The PV B-E is computed as:
EAC + (FC x (1-Tc)) – (Depreciation x Tc)
(Sales price – VC) x (1 - Tc)
(the Depreciation tax shield is subtracted from the total costs, as it
represents a saving).
where the EAC = annualised PV of Initial Investment
(PMT)
1 500 PV; 5 N; 15 I/YR; PMT = 447.5mil


PV Break-Even Sales = 447.5 + (1 791 x 0.66) – (300 x 0.34)
(2-1) x 0.66
= 2 314 units
Accounting break-even understates the true costs of recovering the
initial investment. If we take into account that the R1 500 mill
could have been invested at 15%, the true cost is R447.5mil p.a.
and not R300 mil p.a. Thus, companies that break-even in an
accounting sense are really losing money because they are losing
the opportunity cost of the initial investment.
WHICH RISK ADJUSTMENT METHODS ARE USED IN PRACTICE IN
SOUTH AFRICA?
(Source: Correia and Cramer, 2008:39)
INVESTMENTS OF UNEQUAL LIVES


There are times when application of the NPV rule can lead to the
wrong decision. One such time is when evaluating 2 mutually
exclusive projects with (1) unequal lives, and (2) when the project is
something that will be replaced at the end of it’s lifespan i.e it is
something that the firm cannot ‘do without’.
In such instances, we could use the following techniques:
 Replacement Chain
 Repeat the projects forever, find the PV of that perpetuity.
 Assumption: Both projects can and will be repeated.
 Matching Cycle
 Repeat projects until they begin and end at the same time (LCM).
 Compute NPV for the “repeated projects”.
 The Equivalent Annual Cost Method (EAC or ANPV):
 The Equivalent Annual Cost is the value of the level payment
annuity that has the same PV as our original set of cash
flows. (solve for PMT)
72
EXAMPLE: EAC
 Cape
Town Cargo is considering the purchase of a
new crane. They have a choice between two models.
 Machine A will cost R10 000 upfront with annual
maintenance of R1 375 and an expected life of 3
years.
 Machine B will cost R12 000 with annual
maintenance of R937.50 and an expected life of 4
years.
 The firm depreciates its assets on a straight-line
basis to zero. The appropriate discount rate for both
projects is 11% and the firm pays tax at 20%.
Salvage values are assumed to be zero.
EXAMPLE
SOLUTION
Present value of costs:
Machine A:
0
1
After-tax maint
-1 100
Depr. Tax Shield
666.67
Initial Cost
-10 000
Total
-10 000
-433.33
NPV = -R11 058.93
-10 000CF0; -433.33 CF1; 3 Nj; 11 I/YR
Machine B:
0
1
After-tax maint
-750
Depr. Tax Shield
600
Initial Cost
-12 000
Total
-12 000
-150
NPV = -R12 465.37
-12 000CF0; -150 CF1; 4 Nj; 11 I/YR
2
-1 100
666.67
3
-1 100
666.67
-433.33
-433.33
2
-750
600
3
-750
600
4
-750
600
-150
-150
-150
Whilst project A has a lower PV of costs, Machine B has a longer life, so we
need to calculate their respective EAC’s.
EXAMPLE

SOLUTION CONCLUDED
Using the PV of costs calculated on the previous slide, we can
calculate an equivalent annual cost by solving for PMT using an
I/YR of 11%, and N of 3 and 4 years respectively:
Machine A:

-11 058.93 PV; 3 N; 11 I/YR; PMT = -R4 525.46
Machine B:

-12 465.37 PV; 4 N; 11 I/YR; PMT = -R4 017.92
Therefore, Machine B should be chosen as it has a lower EAC
than A.
 Importantly, we do not consider the revenues that will be
generated as we assume that these will be the same for both
machines. However, if the revenues did differ, it would be easy
to expand the analysis.
 EAC is not confined to the examination of costs – if your PV of
costs or cash flows were positive, you then choose the project
which had the highest equivalent annual cash flow (also EAC,
but ‘C’ would stand for cash flow, not cost).

THE REPLACEMENT DECISION




It is often wise to examine the business assets used in the production
process to see if they should be replaced with a new improved version
This is a continuous process and even if the existing machine has years
of useful life left, the right decision may still be to dispose of the old and
and bring in the new (if your firm does not produce at lowest cost,
someone else will)
In making the replacement decision, the increased costs associated with
the purchase and installation of the new machine have to be weighed
against the savings from switching to the new method of production i.e.
INCREMENTAL CASH FLOWS remain the focus of attention.
There are 2 different situations to be dealt with:
1. Replacement of an asset with a new, identical asset.
Question: How frequently must the asset be replaced? Assumes zero
technological advancement, so unrealistic.
2. Replacement of an existing asset with a different (more advanced)
asset. Called Non-Identical Replacement.
Question: At what stage should we replace the old with the new?
1. IDENTICAL ASSET REPLACEMENT
 Assumptions




upon which this analysis is based:
That production, with the identical type of equipment,
will continue to perpetuity
That the estimates of the maintenance costs and scrap
values are accurate to maturity
That the cost of capital is known and will not change
That the cash flows always arise at the year-end
EXAMPLE – IDENTICAL REPLACEMENT

Claremont Bicycle Rentals is considering a new standard type of bicycle
and a choice has to be made between three alternative regular
replacement cycles. Details are as follows:
Bicycle Cost
Replacement options
Salvage Value
Maintenance Costs
1
2
3
10 000
10 000
10 000
After one year
After two years
After three years
7 000
5 000
3 000
500
900
1 200
The bicycles are not worth keeping for more than three years due to
breakdowns. Revenue streams and other costs are unaffected by the
cycle selected. All cash flows occur at annual intervals. The bicycles
will be depreciated straight-line to zero over their optimal lifespan.
The appropriate discount rate is 10% and all cash flows are taxed at
20%. Determine the optimum replacement cycle.
EXAMPLE SOLUTION


Because the ‘projects’ have unequal lifespans, and the bikes
are standard and will be replaced once sold, an EAC analysis is
required.
The cash flows are as follows:
 Project 1: (replace in a year):
0
1
After-tax Maint.
-400
Depr. Tax shield
2 000
ATSV
5 600
Initial Cost
-10 000
Total
-10 000
7 200
PV of costs:-10 000 CF0; 7 200 CF1: 10 I/YR; NPV = -3 454.55
EAC: -3 454.55 PV; 1 N; 10 I/YR; PMT = -3 800
EXAMPLE SOLUTION

Project 2: (replace in 2 years time)
0
1
2
After-tax Maint.
-400
-720
Depr. Tax shield
1 000
1 000
ATSV
4 000
Initial Cost
-10 000
Total
-10 000
600
4 280
PV of costs:-10 000 CF0; 600 CF1: 4 280 CF2; 10 I/YR;
NPV = -5 917.36
EAC: -5 917.36 PV; 2 N; 10 I/YR; PMT = -3 409.52
EXAMPLE SOLUTION

Project 3: (replace after 3 years)
0
1
2
3
After-tax Maint.
-400
-720
-960
Depr. Tax shield
666.67
666.67
666.67
ATSV
2 400
Initial Cost
-10 000
Total
-10 000
266.67
-53.33
2 106.67
PV of costs:
-10 000 CF0; 266.67 CF1: -53.33 CF2; 2 106.67 CF3; 10 I/YR;
NPV = -8 218.87
EAC: -8 218.87 PV; 3 N; 10 I/YR; PMT = -3 304.93

Project 3 has the lowest EAC and therefore the optimum
replacement cycle is every 3 years.
2. NON-IDENTICAL ASSET REPLACEMENT
 When
switching from one kind of machine to another,
businesses have to decide on the timing of such a
switch.
 The best option may not be to dispose of the old
machine right away. It may be better to wait for a year
or two because the costs of running the old machine
may amount to LESS than the EQUIVALENT
ANNUAL COST of starting a regular cycle with the
replacement.
 However eventually, the old machine will become more
costly due to its lower efficiency, increased repairs
and/or declining scrap value.
EXAMPLE: NON-IDENTICAL REPLACEMENT
 Milnerton
Manufacturing is considering the purchase of
a new machine to replace their existing one. The new
machine costs R24 000 and will require maintenance of
R1 875 at the end of each year for eight years. At the end
of eight years the machine can be sold for R10 000. The
new asset will be depreciated on a straight-line basis to
zero.
 The existing machine requires increasing amounts of
maintenance each year, and its salvage value falls each
year, as shown in the next table. This asset has been
depreciated in full to a book value of zero. The firm pays
tax at 20% and the appropriate discount rate is 8%.
EXAMPLE CONTD.
YEAR
MAINTENANCE COSTS
SALVAGE VALUE
0
0
7 500
1
1 250
5 000
2
2 500
3 750
3
3 750
3 125
4
5 000
0
This table tells us that if the firm sells the existing
machine now they will receive R7 500. If they sell it in one
year’s time they will receive R5 000 but the machine will
require maintenance for the year of R1 250, and so on.
EXAMPLE SOLUTION

Firstly, we want to calculate the equivalent annual cost of
the new machine:
0
1-7
8
After-tax maint.
-1 500
-1 500
Depr. Tax shield
600
600
NCS
-24 000
Total
-24 000
8 000
-900
7 100
PV of costs:
-24 000 CF0; -900 CF1: 7 Nj; 7 100 CF2; 8 I/YR;
NPV = -24 849.82
EAC: -24 849.82 PV; 8 N; 8 I/YR; PMT = -4 324.24
EXAMPLE SOLUTION CONTINUED
Secondly, we want to calculate the cost of keeping the existing
machine for another year at each year-end (we are not
calculating the present value of the costs at time zero for each
year, but rather the total costs at the end of each year).
 If MM keeps the old machine for one more year they will lose
out on receiving R7 500 now (which is an opportunity cost),
which is subject to tax and which could have earned interest
in that year at 8%, hence the opportunity cost at the end of
year 1 equals the FV of the ATSV invested now at 8% for one
year. They will also have to pay maintenance at the end of the
year of R1 250 (brought onto an after-tax basis). They will
receive R5 000 for the sale of the machine at year-end
however, to offset these expenses (also has to be brought onto
an after-tax basis.
Thus the cost of keeping the old machine for one more year is:


-7 500 (1-0.2) (1.08)1 - 1 250 (1-0.2) + 5 000 (0.8)
= -R3 480
EXAMPLE SOLUTION CONCLUDED

The total costs of keeping the existing machine for another 1,
2, 3 and 4 years respectively are presented as follows:
1
2
3
4
FV of opport. cost
-6 480
-4 320
-3 240
-2 700
After-tax maint
-1 000
-2 000
-3 000
-4 000
4 000
3 000
2 500
0
-3 480
-3 320
-3 740
-6 700
ATSV
Total Cost

The EAC of the new machine (-R4 324.24) is only less than the
annual cost of keeping the old machine for a 4th year and thus
the firm should replace the machine at the end of year 3.
LEASING
TERMINOLOGY:
Lease
– contractual agreement for
use of an asset in return for a series
of payments
Lessee – user of an asset; makes
payments
Lessor – owner of the asset; receives
payments
TYPES OF LEASES
 Operating
lease
 Shorter-term lease
 Lessor is responsible for insurance, taxes and maintenance
 Often cancelable
 Financial lease
 Longer-term lease
 Lessee is responsible for insurance, taxes and maintenance
 Generally not cancelable
 Specific capital leases
Tax-oriented
Leveraged
Sale and leaseback
LEASE ACCOUNTING
 Leases
are governed primarily by IAS17
 Financial leases are essentially treated as debt
financing
 Present value of lease payments must be included
on the statement of financial position (of the lessee)
as a liability
 Same amount shown under the assets of the lessee
as the “capitalized value of leased assets”
 Operating leases are still “off-statement of
financial position” and do not have any impact
on the statement of financial position itself
LEASING VERSUS BUYING
24-91
INCREMENTAL CASH FLOWS
For a lessee:
 After-tax lease payment (outflow)
 Lease

payment x (1 – T)
Lost depreciation tax shield (outflow)
 Depreciation

x tax rate for each year
Initial cost of machine (inflow)
 Inflow
because we save the cost of purchasing the
asset now

May have incremental maintenance, taxes or insurance
depending on the type of lease and whether the leased asset is
replacing one currently owned
EXAMPLE: LEASE CASH FLOWS
 ABC
Ltd needs some new equipment. The equipment would
cost R100,000 if purchased and would be depreciated straightline over 5 years. No salvage is expected. Alternatively, the
company can lease the equipment for R25 000 per year. The
marginal tax rate is 40%.
 What are the incremental cash flows?
After-tax lease payment = 25 000 (1 – 0,4) = 15 000
(outflow years 1 - 5)
Lost depreciation tax shield = (100 000 / 5) x 0.4 = 8 000
(outflow years 1 – 5)
Cost of machine = 100 000 (inflow year 0)
LEASE OR BUY?
 The
company needs to determine whether it
is better off borrowing the money and
buying the asset, or leasing
 Compute the NPV of the incremental cash
flows
 Appropriate discount rate is the after-tax
cost of debt since a lease is essentially the
same risk as a company’s debt. Also the
alternative to leasing is LT borrowing so the
after-tax cost of such borrowing is the
relevant benchmark.
NET ADVANTAGE TO LEASING
The
net advantage to leasing (NAL) is
the same thing as the NPV of the
incremental cash flows
If NAL > 0, the firm should lease
 If NAL < 0, the firm should buy

Consider
the previous example. Assume
the firm’s cost of debt is 10%.
After-tax cost of debt = 10 (1 – 0.4) = 6%
 NAL:
100 000 CF0; -23 000 CF1; 5 Nj; 6 I/YR; NPV = 3 115.63

Should
the firm buy or lease?
GOOD REASONS FOR LEASING
Taxes
may be reduced
May reduce some uncertainty
May have lower transaction costs
May require fewer, if any, restrictive
covenants
Leasing may encumber fewer assets
than secured borrowing
DUBIOUS REASONS FOR LEASING
Statement
of financial position, especially
leverage ratios, may look better if the
lease does not have to be accounted for on
the statement of financial position
100% financing – except leases normally do
require either a down-payment or security
deposit
Low cost – some may try to compare the
“implied” rate of interest to other market
rates, but this is not directly comparable
LEASING EXAMPLE - ANOTHER
What
is the net advantage to leasing for
the following project, and should the firm
lease or buy?
 Equipment
would cost R250 000 if purchased
 It would be depreciated straight-line to zero
salvage over 5 years.
 Alternatively, it may be leased for R65 000/yr.
 The firm’s after-tax cost of debt is 6%, and its
tax rate is 40%
SOLUTION
After-tax lease payment = (1 – 0.4) x R65 000
= R39 000
 Lost tax shield = 0.4 x R50 000 = R20 000

Year
CF
0
250 000
1-5
-R39 000 – R20 000 = -R59 000
 Discount at 6%
 NAL: 250 000 CF0; -59 000 CF1; 5 Nj; 6 I/YR; NPV = R1 470.54
(positive)
 Lease it!

SUPPLEMENTARY NOTES ON LEASING
WHAT IS LEASING?

Terminology:
the lessee (user of the asset, makes the payments)
 The lessor (owner of the asset, receives the payments)

The lease contract specifies the payment frequency (monthly, semiannual etc.), with the first payment normally due as soon as the
contract is signed; that is, the lessee tends to pay in advance for the
use of the asset.
 In corporate finance, leasing is the process by which a firm can obtain
the use of various fixed assets for which it must make a series of
contractual, periodic, tax-deductible payments.
 When a lease is terminated, the leased equipment reverts to the
lessor. However, the lease agreement often gives the lessee the option
to purchase the equipment or take out a new lease.

TYPES OF LEASES
1. Operating Leases:
 short-term: whilst they can be renewed, it is unlikely that
ownership will ever transfer to the lessee. Generally, the total
payments made by the lessee to the lessor are less than the
lessor’s initial cost of the leased asset. Consequently, the
lessor either expects to lease the asset again or sell it at the
end of the lease agreement i.e. assets that are leased under
operating leases have a usable life that is longer than the
term of the lease.
 The lessor usually maintains the asset (insurance, taxes and
maintenance), but these costs will be incorporated into the
lease payment by the lessee. Therefore known as full-service
or rental leases.
 Can be cancelled by the lessee during the contract period, but
the lessee may be required to pay a penalty for cancellation. If
the lessee cancels the contract the asset will be returned to
the lessor.
2. Financial




Leases (capital or full-payout leases):
Long-term: they extend over most of the estimated economic
life of the asset and cannot be cancelled (or if it is cancelled, it
is with a substantial penalty).
All the risks and rewards incidental to ownership are
transferred to the lessee (e.g. insurance, maintenance of the
asset etc). Therefore known as net leases.
Financial leases are a source of financing (borrowing) - there
is an immediate cash inflow because the lessee is relieved of
having to pay for the asset, but the lessee also assumes a
binding obligation to make the payments specified in the lease
contract. Thus the cash flow consequences of leasing and
borrowing are similar. In either case, the firm raises cash now
and pays it back later. Failure to make the lease payment can
result in bankruptcy for the lessee.
May include a purchase option.

According to the Accounting Practices Board, a lease can be
considered a financial lease provided one of the following
conditions is met:






The lease transfers ownership of the asset to the lessee by
the end of the lease term
Cancellation costs are borne by the lessee.
The lease term is for the majority of the estimated economic
life of the asset (more than 80%), even if ownership is not
transferred.
At the beginning of the lease, the PV of the lease payments
is equal to 90% or more of the fair market value of the
leased asset.
If the asset is of such a specialized nature that only the
lessee can use it without major modifications being made.
If the lessee has the ability to continue the lease for a
secondary period at a rent that is substantially below
market rent.
FORMS OF LEASE AGREEMENTS




Direct leases: the lessee identifies the equipment,
arranges for a leasing company to buy it from the
manufacturer, and signs a contract with the leasing
company.
Sales-Type leases: the manufacturer leases the asset
straight to the lessee.
Sale-and-lease-back: the firm sells an asset it already
owns and leases it back from the buyer. Common in
real estate, as a company might want to raise cash by
selling a factory but still retain use of it.
Leveraged leases: these are financial leases in which
the lessor borrows part of the purchase price of the
leased asset (up to 80%), using the lease contract as
security for the loan, and the lease payments to
service the debt. This does not, however, change the
lessee’s obligations.
THE LEASING PARADOX
 So
far we have looked at the cash flows of the lease versus buy
decision from the perspective of the lessee. What do the cash
flows look like from the perspective of the Leasing Company?
 They have to buy the machine upfront (outflow)
 They will depreciate it for which they will receive a tax shield
(inflow)
 They have to maintain the asset (outflow)
 They will receive the annual lease payment (inflow)
 They will sell the asset at the end of the lease agreement to
the lessee (inflow)
 That is, the cash flows are the exact opposite to the lessee!
 This makes sense, because Radebe and the Leasing Company
are the only parties to the lease agreement, and hence leasing is
a zero-sum game. That is, if the lease is a positive NPV activity
to one party it will be a negative NPV activity to the other
party. The leasing company thus hopes Radebe will buy rather
than lease the machine.
WHY LEASE? (IN THE FORM OF FINANCIAL LEASES)
IF ONE PARTY MUST INEVITABLY LOSE OUT IN A LEASE WHY DO THEY STILL HAPPEN?
1. Tax Advantages
 By far the most important reason for leasing is income tax
deferral because firms may pay different tax rates; a
potential tax shield which cannot be used effectively by one
firm can be transferred to another via leasing. Any tax
benefits from leasing can be split between the two firms by
setting the lease payments at the appropriate level, and the
shareholders of both firms will benefit from this
arrangement. Thus SARS is the loser, as the leasing contract
allows the lessor to take advantage of the depreciation and
interest tax shields that cannot be used by the lessee.
2. A Reduction in Uncertainty



At the end of the useful life of the asset it may be sold for its
salvage value. This amount is uncertain at the time the asset
is purchased. A lease contract transfers this uncertainty from
the lessee to the lessor. This makes sense when the lessor is
better able to absorb the risk.
However, this transfer of uncertainty from the lessee to the
lessor is effectively insurance for the lessee and will thus
implicitly be included in the lease payments.
But, if the firm leases instead of buying it gives up the salvage
value which is a cost of the lease agreement.
3. Fewer Restrictions and Security Requirements



If the firm borrows to purchase the asset, certain restrictions
in the form of protective covenants, will be placed on their
activities (e.g. minimum liquidity, subsequent borrowing and
cash dividends). This is not the case with a lease agreement.
Also, in order to secure the loan the firm may have to use
other assets as collateral, but with the lease only the leased
asset is pledged.
Therefore, leasing gives management more balance sheet
flexibility.
Operating Leases are advantageous:
Lower Transaction Costs/More Convenient
 The transaction costs of buying and selling an asset many times
during its useful life are high, and thus the justification behind
many short-term leases is the reduction in transaction costs. A
reduction in transaction costs however, is not really a sufficient
justification for long-term leases.
 Sometimes the cost of short-term rentals may seem prohibitively
high, or it may be difficult to rent at any price. This can happen
for equipment that is easily damaged by careless use. The owner
knows that short-term users are unlikely to take the same care
that they would their own equipment. When the danger of abuse
becomes too high, short-term rental markets do not survive.
Maintenance is provided
 For operating leases, which are full-service leases, the lessee
receives maintenance and other services. However, these
benefits will be incorporated into higher lease payments.