Capital Budgeting Techniques

If you go back to the 7 financial drivers of value (growth duration, sales growth, profit growth, cash taxes, working capital investment, fixed asset investment, weighted average cost of capital), we will see that cash flow is very important in the valuation of companies.  More specifically, we talk about the discounted cash flow of the company, which is what we get when we discount all future cash flows of the company back to today.  Before we do that, I would like to first look at a number of other ways of valuing a company.



In order to deal with issues of valuation, we need to understand that R5 million 10 years from now, is not worth R5 million today.  The reason for this has to do with the concept of time value of money.  What do we mean by “time value of money”?

  • R1 today is worth more than R1 in 1 year’s time.
  • Or we can say that if we can get R10 in 2 years from today, in today’s value it will be worth less than R10.
  • This is due to, amongst other things, inflation.  Also, as time progresses, the certainty of actually receiving the money diminishes, increasing the risk.
  • In order to provide for time value of money, we either discount (bringing the future value to the present value), or we compound (taking the present value to the future value).


Example of discounting:

  • We can get R20 in 1 year’s time.  What is the value today?  The rate of return (interest rate) is 10 %.

Future value                      =        R20

Discount rate                     =        10 %

Period                                   =        1 year


Present value                 =        20/(1 + 0.1) = R18.18


•         We can get R20 in 2 years’ time.  What is the value today?


Future value (FV)              =        R20

Discount rate (r)                 =        10 %

Period    (n)                           =        2 years

Present value (PV)         =        (20/(1 + 0.1)2 = R16.53


We therefore see that the further away into the future we get the cash flow, the less its worth today.

A general formula for discounting is therefore as follows:



When we take the present into the future, we compound.  An example of compounding is as follows:

•         We have R20 today.  What will the value be in 1 year’s time?

Present value (PV)            =        R20

Discount rate (r)                =        10 %

Period (n)                             =        1


Future value (FV)              =        20 x (1 + 0.1)1 = R22


•         We have R20 today.  What will the value be in 2 years’ time?

PV                          =        R20

r                             =        10 %

n                             =        2


FV      =        20 x (1 + 0.1)2 = R24.40


We therefore see that the further away into the future we take the cash flow, the higher it becomes.

R20 today               =        R24.20 in year 2.




R20 in year 2                    =        R16,53 today.


A general formulae for compounding:  FV = PV x (1 + r)n

An important thing to remember is that the discount rate also provides for the riskiness of the cash flows.  Therefore, if we do not discount future cash flows to get a present value that we can compose sensibly, we are ignoring the risk involved with future cash flows.


•         Your Hewlett Packard 10B has a function to determine the PV and FV.


•         PV                =        R20

n                              =        3 years

r                              =        12 %

What is the FV?


We have to compound.  Press the following on your calculator.


-20               PV

3                    N

12               I/YR

Ask for          FV      =        R28.10


•         FV      =        R30

n                  =        5 years

r                   =        15 %

What is the present value (PV)


We have to discount.  Press the following on your calculator:


-30               FV

5                    N

15               I/YR

Ask for                    PV      =        R14.92





The financial manager has as his primary task the answering of the following 3 questions:

•       What long-term investments should the company take on?  That is, what lines of business will they be in and what sorts of buildings, machinery and equipment will they need?


•       Where will the company get the long-term financing to pay for the investment?  Will they retain the profits which they make, will they bring in other owners or will they borrow the money?


•       How will they manage their everyday financial activities such as collecting from customers and paying suppliers?


These are not the only questions, but they are among the most important.


For the purpose of this section, we are primarily interested in the first question.  The process of planning and managing a firm’s long-term investment is called capital budgeting.  In capital budgeting, the financial manager tries to identify investment opportunities that are worth more to the firm than they cost to acquire.

Loosely speaking, this means that the value of the cash flow generated by an asset exceeds the cost of that asset.

The types of investment opportunities that would typically be considered depend in part on the nature of the firm’s business.

•       For Pick ’n Pay, deciding whether or not to open another store would be an important capital budgeting decision.

•       For Lotus or Microsoft, the decision to develop and market a new spreadsheet package would be a major capital budgeting decision.

•       For the SA Navy, to acquire new corvettes would also be a major capital budgeting decision.


Regardless of the specific nature of an opportunity under consideration, financial managers must be concerned with not only how much cash they expect to receive, but also when they expect to receive it and how likely they are to receive it.  Evaluating the size, timing, and risk of future cash flows is the essence of capital budgeting.

We are therefore primarily concerned with capital expenditure, which has the following characteristics:


•         It will probably involve substantial expenditure.

•         The benefits may be spread over very many years.

•         It will be difficult to predict what the benefits will be.

•         It will help the company to achieve its organisational objectives.

•         It will have some impact on the company’s employees.





There is little point in investing in a project unless it is likely to make a profit.  The exceptions are those projects that are necessary on health, defence, social, and welfare grounds, and these are particularly difficult to assess.  In other cases, there are 5 main techniques that are used in the appraisal of capital investments.


•         Payback method.

•         Discounted payback method.

•         Accounting rate of return.

•         Internal rate of return.

•         Net present value.


We will be looking at an example of each of the first 4 techniques, where after we will be studying the net present value (NPV) approach in detail.




The payback period is the length of time it takes to recover the initial investment.  An investment is acceptable if its calculated payback period is less than some pre-specified number of years (determined by top management).

The recovery of an investment in a project is usually measured in terms of net cash flow, which is the difference between cash received and cash paid during a defined period of time.  In order to adopt this method, the following information is required:


•         Total cost of the investment.

•         The amount of cash instalments payable back on the investment.

•         The accounting periods in which the instalments will be paid.

•         The cash receipts and any other cash payments connected with the project.





•         Initial investment               :         R50 000

•         Net cash flow year 1          :         R30 000

•         Net cash flow year 2          :         R20 000

•         Net cash flow year 3          :         R10 000

•         Net cash flow year 4          :         R  5 000



It is useful to draw a time line:


0                  1                      2                      3                  4


-50 000        30 000           20 000           10 000         5 000



In order to determine when the project pays back, we determine the cumulative net cash flow:


Year 1       :                   30 000

2                  :                   50 000

3                  :                   60 000

4                  :                   65 000


As the cost is R50 000, we see that after year 2, the cumulative net cash inflow is also R50 000.  The project therefore has a payback period of 2 years.


When the numbers do not work out exactly, it is customary to work with fractional years.  For example:


•         Initial investment                         :         R60 000

•         Net cash flow year 1                    :         R20 000

•         Net cash flow year 2                    :         R90 000


The cash flows over the first 2 years are R110 000, so the project obviously pays back sometime in the second year.


•       After year 1, the project has paid back R20 000, leaving R40 000 to be recovered.

•       To figure out the fractional year, note that this R40 000, is R40 000/R90 000 = 4/9 of the second year’s cash flow.

•       Assuming that the R90 000 cash flow is paid uniformly throughout the year, the payback would thus be 1 4/9 years.


The following table illustrates cash flows for 5 different projects:


Expected cash flows for projects A through E

Year             A                     B                   C                    D                      E

0                  -R100           -R200     -R200           -R200           -R50

1                  30                   40                40                100                100

2                  40                   20               20                100               -50 000 000

3                  50                  10               10               -200

4                                         60               130              200

•         The payback for A is easily calculated.  The sum of the cash flows for the first 2 years is R70, leaving R30 to be recovered.  In year 3, cash flow is R50.  Therefore, to recover the R30 will take 30/50 = 0.6 years.  Add this to the 2 years we already have, and we see it takes 2.6 years for the project to pay back.  If this is shorter than the criterion determined by the firm, accept the project, otherwise reject it.


•       The payback for B is also easy to calculate – it never pays back.


•       C has a payback of exactly 4 years.


•       D is a little strange.  Because of the negative cash flow in year 3, we can easily verify that it has 2 different payback periods, 2 years and 4 years.  Which is correct?  Both.


•       E is obviously unrealistic, but it does pay back in 6 moths thereby illustrating the point that a rapid payback does not guarantee a good investment.


What are the advantages and disadvantages of the Payback Period Criterion?

•         Advantages

  • Easy to understand
  • Adjusts for uncertainty of later cash flows
  • Biased toward liquidity


•         Disadvantages

•     It ignores the time value of money (concept will be explained shortly).

•     Requires an arbitrary cut-off point.

•     Ignores cash flows beyond the cut-off date.

•     Biased against long-term projects, such as research and development and new projects.





We saw that one of the shortcomings of the payback period criterion was that it ignored time value.  The discounted payback period is the length of time until the sum of the discounted cash flows is equal to the initial investment.

The discounted payback period rule states that an investment is acceptable if its discounted payback period is less than some pre-specified number of years.  We discount at some or other percentage return, normally referred to as the required return (or cost of capital).

The actual determination of the required return is quite a complex process and falls outside the scope of this course.  We can see it as the return that we want in order for the investment to be the worthwhile.  If we were to borrow the money, the required return must at the very least be equal to the interest we pay.


Let’s look at the following example:


The investment costs R300 and has cash flows as follows:


CASH FLOW                                  ACCUMULATED CASH FLOW

Year   Undiscounted          Discounted              Undiscounted          Discounted

1                 100                                   89                          100                              89

2                 100                                   79                          200                           168

3                 100                                   70                          300                           238

4                 100                                   62                          400                           300

5                100                                   55                          500                            355


Before we determine the payback period, let’s recap how we determine the discounted cash flow for year 4.


•         R100 in year 4, is worth how much today?


FV        =        -100

N           =        4

I/Yr     =        12, 5 %         (for example this case)

Ask for          PV      =        R62.43


PV      =     100 / (1 + 0.125)4

=        R62.43



When we go back to the table, we see the following:


  • If we use the undiscounted cash flows, it takes 3 years for the investment to pay back.
  • If we use the discounted cash flows, it takes 4 years for the investment to pay back.


Obviously the latter approach is more correct, as it is a fact of life the R100 in year 4 is not worth R100 today.

What are the advantages and disadvantages of the Discounted Payback Period Criterion?


•         Advantages

  • Includes time value of money
  • Easy to understand
  • Biased toward liquidity


•         Disadvantages

•       Requires an arbitrary cut-off point.

•       Ignores cash flows beyond the cut-off date.

•       Biased against long-term projects, such as research and development, and new projects.





This criterion is also referred to as the accounting rate of return.  It is, however, a flawed approach for the following reasons:


•         The AAR (ARR) is not a rate of return in any meaningful economic sense.  Instead, it is the ratio of 2 accounting numbers, and it is not comparable to the returns offered, for example, in financial markets.

•         It ignores the time value of money and no discounting is involved in the computation of average net profits, for example.

•         Since a calculated AAR is really not comparable to a market return, the target AAR must somehow be specified.  There is no generally agreed upon way to do this.

•         Finally, and perhaps the worst flow in the AAR, is that it doesn’t even look at the right things.  Instead of cash flow and market value, it uses net profit and book value.  These are both poor substitutes.  As a result, an AAR doesn’t tell us what the effect on share price will be from taking an investment, so it doesn’t tell us what we really want to know.


We will later see that these shortcomings have not stopped companies from using the AAR.


The AAR is defined as:      Some measure of average accounting profit divided by some measure of average accounting value


Consider a project expected to earn the following accounting profits over its four-year life:



1                     2                            3                       4                        Total

R20 000        R28 000           R30 000       R18 000                R96 000


The average net profit after tax is:


R96 000/4     =        R24 000

The cost of the project is R200 000.  It will be depreciated over 4 years to zero book value and is expected to have no salvage value.  Therefore, the average book value during the life of the investment is:


(Beginning cost (or book value) + End book value)/2

=        (200 000 + 0)/2       =        R100 000.


The AAR is therefore:  Average net profit after tax/average book value

=        24 000 / 100 000

=        24 %


If the firm has a target AAR of less than 24 %, than this investment is acceptable; otherwise not.





One of the main disadvantages of both the payback method and the AAR is that they both ignore the time value of money.  The NPV method recognizes that cash received today is preferable to cash receivable sometime in the future.  The principle underlying the NPV method is that you compare the present value of the cash outflows with the present value of the cash inflows (with other words, you have discounted both the inflows and outflows).  If the PV of the inflows is more than the PV of the outflows, the NPV is positive.

An investment is worth undertaking if it creates value for its owners.  A positive NPV project will create value or add value.  A negative NPV project uses up value.  The NPV rule therefore states:


•         Accept all positive NPV projects.

•         Reject all negative NPV projects.

•         NPV = PV inflow – PV outflow.


In working with NPV, we work with incremental after-tax cash flows.  We will first have a look at the principle behind tax.

  • TAX


The following rules in respect of tax can be laid down:

  • Current expenses, such as operating costs, repairs to fixed assets (but not improvements), depreciation on fixed assets, loss with sale of fixed assets, etc., are all deductible from taxable income.
  • We therefore deduct the above items from our income before we determine the tax we owe the Receiver of Revenue.
  • The cost price of new assets as such may not be deducted from taxable income.  However, we depreciate the asset and the depreciation is deductible from taxable income.  In the RSA, we primarily use the straight-line method of depreciation.


E.g. an asset costs R10 000 and we can depreciate it over 5 years to a zero book value.  The annual depreciation that we therefore can deduct from taxable income is:


R10 000 / 5 = R2 000 per year.


We talk of a tax shield.  When we deduct depreciation from taxable income, we pay less tax.  The amount depends on the tax rate.  If the tax rate is 35 %, as was the case in the RSA, the amount we pay less is


R2 000 x 0.35 = R700


This is the tax shield that the depreciation gives us.


  • The sales price of old assets is not taxed as such.  Instead, we must determine whether there was a profit or loss with the sale of the fixed asset:
  • Profit = Sales price – book value (per Receiver)
  • Book value = Cost price – accumulated depreciation.
  • Profit with the sale of an asset is taxable, but the taxable amount is restricted to the amount of depreciation previously written off.  Take cases A and B.


A                                      B

Cost price                                             100                                   100


Year 1                                                  (20)                                 (20)

Year 2                                                  (20)                                 (20)

Year 3                                                  (20)                                 (20)


Book value (100 – 60)                     40                                    40

Sales price                                           70                                  120

Profit                                                      30                                    80

Taxable income                                  30                                    80 (60 and 20)


Capital gains are taxable in the RSA.  It is the difference between the sales price of the fixed asset and the original cost price, and results when the sales price is higher than the original cost price.


  • Assume the profit is R30.  The sales price is R70.  Tax is paid on the R30.  If the tax rate is 35 %, the tax payable is R30 x 0.35 = R10.50.  Therefore the after tax income is R70 – R10.50 = R59.50.
  • Assume there was a loss of R20.  The book value is R40 and the sales price is R20.  We can get a tax shield from the loss of R20, namely 35 % of R20 = R7.  Therefore the cash flow associated with the sale is not the R20 received, but R20 + R7 = R27.  The R7 is the tax shield the loss provides.
  • Obviously, the tax shield on depreciation and other expenses work on the same principle.
  • Unless stated otherwise, the book value of an asset is 0 at the end of the life time of an asset when you use the straight-line method of depreciation.  Therefore, any income from the sale of an asset at the end of its lifetime is taxable because the sales price = profit.



We will now proceed with numerous examples of this very important investment criterion.  Basically, it involves taking the following steps:

  • Calculate the annual net cash flows expected to arise from the project.
  • Select an appropriate rate of interest, or required rate of return.
  • Discount the annual net cash flows to the present value.
  • Add together the present values for each of the net cash flows.
  • Compare the total net present value with the initial outlay.


Example 1


We want to buy a new machine costing R100 000.  Depreciation is straight-line over 5 years to a zero book value.  It is estimated that cash flow (after taking into consideration tax and depreciation) will increase with R27 500 per year over 5 years.  The cost of capital is 18 % and the tax rate is 40 %.


a.       What is the NPV of the new machine?

b.       What is the NPV if the machine has a market value of R30 000 after 5 years?

c.       What is the NPV if the machine has a market value of R75 000 after 5 years?



Year                        0                    1                   2                       3                      4                  5

Cost price     (100 000)

Cash flow                             27 500         27 500           27 500         27 500         27 500


In (a)

Market value                                                                                                                            0


In (b)

Sales price                                                                                                                         30 000

Tax                                                                                                                                     (12 000)

Cash flow                                                                                                                           18 000


In (c)

Sales price                                                                                                                        75 000

Tax                                                                                                                                    (30 000)

Cash flow                                                                                                                           45 000


The cash flow identified in a, b and c for year 5 must be added to the R27 500 already calculated.  We will now proceed to use the HP 10B to determine the NPV.


  1. -100 000                 CFj     (First clear the calculator – 1 P/YR)

27 500                    CFj

5                    ▀        Nj

18                          I/YR


▀ NPV          =        -R14 002.80


The NPV rule says:  only accept projects with a positive NPV.  Therefore, reject this project.


  1. -100 000             CFj     (First clear calculator – 1 P/YR)

27 500                    CFj

4                      ▀        Nj

45 000                    CFj     [27 500 + 18 000 (after tax profit)]

18                          I/YR


▀ NPV          =        -R6 134, 83


NPV still negative.  Reject project.


  1. -100 000                   CFj     (First clear the calculator – 1 P/YR)

27 500                    CFj

4                              ▀        Nj

72 500                    CFj     [27 500 + 45 000 (after tax profit)]

18                          I/YR


▀ NPV          =        R5 667,12


NPV is positive.  Accept project.


However, you now need to ask yourself whether you really would like to accept a project that only has a positive NPV under such extreme conditions as an after profit resale value of R45 000!



Example 2

Your company has a tax rate of 40 % and the cost of capital is 14 %.  A new project is considered which will cost R500 000 and have a duration of 10 years.  The net income after tax generated by this project is R60 000 per year.  Assume that the cost price of the project will be depreciated over the duration of the project by means of the straightline method.  The project will have no residual value.  What is the project’s NPV?


Profit after Tax                            :         R60 000 p.a.

Depreciation                               :         R50 000 p.a. (500 000 / 10)

Cash flow                                      :         R110 000


-500 000                 CFj     (First clear; 1 P/YR)

110 000                  CFj

10                            ▀      Nj

14                          I/YR


▀ NPV          =        R73 772.72


Accept the project.



Example 3


We have a choice between Project A or Project B.  The cash flows are determined as follows:


Year   Project A      Project B

0        -R5 000        -R5 000

1        R2 085             0

2        R2 085            0

3        R2 085            0

4        R2 085          R9 677



a.       What is the NPV at 8 % discount rate?


b.       What is the NPV at 14 %?


c.       What project must be accepted?  (You can only choose 1)




a.       NPV   8 %              :         Project A                 =        R1 905.78

Project B                =        R2 112.88


b.       NPV 14 %               :         Project A                =        R1 075.09

Project B                =        R   729.56


c.       It depends on the cost of the capital and therefore the risk of the project.  If the discount rate for A and B are the same (same risk), we will choose A for higher rates (say 10 % and higher) and B for a rate less than 10 %.



Example 4


The AB Company is considering acquiring a certain machine which will save R8 000 in cash costs every year.  The machine costs R22 000 and has a life time of 5 years with an end sales price of zero.  Ignore tax.  Should they buy the machine if the required rate of return is 16 %?


Answer:        As tax is zero, depreciation and all profit/losses with the sale of the fixed asset becomes irrelevant.


-22 000                   CFj     (First clear; 1 P/YR)

8 000                      CFj

5                               ▀   Nj

16                          I/YR


▀ NPV          =        R4 194.35


Accept the project.



Example 5


DEF-company owns a machine which was bought 3 years ago for R56 000.  The machine has a remaining life of 5 years, but requires a major reparation in 2 years’ time at a cost of R10 000.  At present the machine can be sold for R20 000, while this value will decrease to R8 000 over 5 years.  The annual running costs of the machine is R40 000.

A new machine on the market will cost R51 000, or R31 000 plus the old machine.  The old machine is therefore traded in.  This new machine’s annual running cost will be R30 000; it will need no major reparation; and will also have a life of 5 years with a sales price of R3 000 after 5 years.

If the required rate of return is 14 %, use the NPV to determine whether the new machine should be bought (ignore tax).

Answer:        In such a case it is always a good thing to express the cash flows in a diagramme:


Keep old machine:

Year                                             0                       1                     2                         3                       4                      5

Running Costs                                      (40000)         (40000)         (40000)         (40000)         (40000)

Reparation                                                                         (10 000)

Sell old machine                                                                                                                                               8 000

Total                                        0             (40 000)        (50 000)        (40 000)        (40 000)        (32 000)


Replace old machine:

Year                                          0                       1                       2                         3                         4                       5

Buy new machine        (31 000)

Running cost                                        (30 000)        (30 000)        (30 000)        (30 000)        (30 000)

Sell new machine                                                                                                                                            3 000

Total                              (31 000)        (30 000)        (30 000)        (30 000)        (30 000)        (27 000)


We can now use one of two methods:


Method 1:     Calculate the PV of the old and new machine and determine the difference.  If the PV of the costs of the new machine is lower as than PV of the old machine, replace the old machine.


Keep old machine              :         (R140 862.96)


Replace old machine         :         (R132 434.32)


The PV of the costs of the new machine is R8 428.64 less than that of the old machine.  Replace the old machine.


Method 2:     Work on the marginal/incremental cash flow, with other words subtract the cash flow of keep old machine from the cash flow of replace old machine.


0                      1                        2                    3                     4                     5

(31 000)        10 000           20 000        10 000            10 000          5 000



NPV             :         -31 000                 CFj     (First clear; 1 P/YR)

10 000                    CFj

20 000                    CFj

10 000                    CFj

10 000                    CFj

5 000                      CFj

14                          I/YR


▀ NPV          =        R8 428.64



Therefore, the NPV of the decision to replace the old machine is R8 428.64.  As it is positive, replace the old machine.

Take note that when we calculated the cash flow of “Keep the old machine”, we ignored the initial cost price as well as the initial 3 years’ costs.  As they have already taken place, they are considered to be irrelevant for the decision.



Example 6


The L-Company wants to replace an old machine with a new improved machine.  The old machine’s cost price was R22 000, while the book value is presently R10 000.  Depreciation is straightline and the remaining life is 5 years.  The market value of the machine now is R4 000, and will be R600 in 5 years’ time.  It costs the company R50 000 annually in labour.

The new machine costs R15 000, and has an annual labour cost of R46 000.  The life of the new machine is 5 years and the expected sales price is R700.  Depreciation is also straightline.

Asked:  If the required rate of return is 10 % and the tax rate is 40 %, calculate the NPV in order to determine whether the old machine must be replaced or not.  Assume that the old machine will be traded in if the new machine is bought.

Answer:  Draw up a diagramme again.


Keep old machine:

Year                                                 0                       1                                2                               3                                     4                                 5

Depreciation 2 2 000                       2 000                     2 000                          2 000                      2 000

Tax shield on Dep 2 800                          800                           800                             800                         800

Labour                                                              (50 000)                   (50 000)               (50 000)                  (50 000)                (50 000)

Tax shield on labour 3 20 000                    20 000                    20 000                    20 000                    20 000

Sell old machine                                                                                                                                                                                                 600

Tax on old machine 4 (240)

Total 5 0              (29 200)                 (29 200)                   (29 200)                 (29 200)                (28 840)





Replace old machine:

Year                                                   0                     1                                     2                                    3                                4                                  5

Buy new machine             (15 000)

Sell old machine                   4 000

Tax shield on loss 6)           2 400

Labour                                                                 (46 000)                 (46 000)                        (46 000)                     (46 000)            (46 000)

Tax shield on labour                                         18 400                      18 400                            18 400                          18 400                 18 400

Tax shield on Dep 7)                                            1 200                         1 200                             1 200                              1 200                   1 200

Sell new machine                                                                                                                                                                                                          700

Tax on profit                                                                                                                                                                                                                 (280)

Total                                          (8 600)             (26 400)                 (26 400)                          ( 26 400)                     (26 400)             (25 980)


Incremental cash flow


0                              1                            2                                           3                                   4                           5

Replace – Keep                             (8 600)                 2 800                   2 800                               2 800                          2 800                  2 860


NPV = R2 051


Decision:  Replace old machine, because the NPV of replacement is positive.


Notes: 1.       In this case the current book value is R10 000 and the remaining life is 5 yrs.  The depreciation is therefore R2 000 p.a.  The depreciation itself does not play a role, except insofar it serves as a tax shield.

2.       Tax shield on depreciation:  90 % of R2 000 = R800.  This is cash flow and does play a role.

3.       Tax shield on labour:  40 % of R50 000.  Labour can, as is the case with depreciation, be deducted from income to reduce the taxable income.

4.       The old machine is sold for R600 at the end of its life.  Straightline depreciation says that the end book value is supposed to be R0.  Therefore the R600 is profit and taxable.

5.       With the calculation of the total cash flow in this case, depreciation is not added.  It will play a role later on.

6.       The current book value of the old machine is R10 000.  It is sold for only R4 000.  Therefore a loss of R6 000.  We can get a tax relief on the loss of R6 000, namely 40 % of R6 000 = R2 400.  We can add this to the sales price of R4 000 to get the real cash flow involved.

7.       Tax shield on depreciation = 40 % of R3 000 p.a. = R1 200.



Example 7


Nyoni Ltd must decide on the possible replacement of one of the machines in the factory.  The following data is available:


•         Price of new machine                                                          :         R75 000

•         Installation costs                                                                   :         R  5 000

•         Initial training costs                                                           :         R  3 000

•         Annual sales with old machine                                       :         R40 000

•         Price of old machine 3 yrs ago                                         :         R56 000

•         Life of old machine                                                               :         8 years

•         Depreciation                                                                             :     Straightline

•         Cost of sales of old machine                                               :         R20 000

•         Increase in net working capital of new machine       :         R10 000

•         Life of new machine                                                              :         5 years

•         Increase in net working capital of old machine        :         R  8 000

•         Current market value of old machine                           :         R25 000

•         Market value of new machine after 5 years                :         R14 000

•         Cost of viability study of new machine                          :         R  2 000

•         Annual sales of new machine                                             :         R55 000

•         Required rate of return                                                         :         12 %

•         Cost of Sales of new machine                                              :         R27 000

•         Tax rate                                                                                        :         40 %

•         Market value of old machine at end of life                     :         R 5 000


Asked:          Calculate the NPV in order to determine whether the new machine should be bought.


Keep old machine:


Item 0 1 2 3 4 5
Sales 40 000 40 000 40 000 40 000 40 000
-Costs of Sales 20 000 20 000 20 000 20 000 20 000
Profit 20 000 20 000 20 000 20 000 20 000
-Depreciation 7 000 7 000 7 000 7 000 7 000
Profit before Tax 13 000 13 000 13 000 13 000 13 000
-Tax 5 200 5 200 5 200 5 200 5 200
PAT 7 800 7 800 7 800 7 800 7 800
+ Depreciation 7 000 7 000 7 000 7 000 7 000
CFAT 14 800 14 800 14 800 14 800 14 800
Retrieve NWC 1 8 000
Sell old machine 5000
-Tax on profit 2 000
Total CFAT 0 14 800 14 800 14 800 14 800 25 800


Buy new machine:

Item 0 1 2 3 4 5
Price & Installation2 (80 000)
Training Cost 3 (3 000)
Tax shield on Trng 1 200
Sales 55 000 55 000 55 000 55 000 55 000
Costs of Sales (27 000) (27 000) (27 000) (27 000) (27 000)
Profit 28 000 28 000 28 000 28 000 28 000
Depreciation 2 (16 000) (16 000) (16 000) (16 000) (16 000)
Profit before Tax 12 000 12 000 12 000 12 000 12 000
Tax (4 800) (4 800) (4 800) (4 800) (4 800)
PAT 7 200 7 200 7 200 7 200 7 200
+ Depreciation 16 000 16 000 16 000 16 000 16 0000
CFAT 23 200 23 2000 23 200 23 200 23 2000
Sell Old Machine 2 500
Tax shield on loss of R10 000 4 000
Sell new machine 14 000
Tax on profit (5 600)
NWC of new machine (10 000) 10 000
Retrieve NWC of old machine 8 000
Total CFAT (54 800) 23 200 23 200 23 200 23 200 41 600



Incremental CFAT     (54 800)         8 400           8 400              8 400                    8 400            15 800

NPV =       -R20 320,92


Do not replace the old machine, as the NPV of the replacement decision is negative.





1.       Sometimes a project needs increased working capital.  This amount is made available in year 0 and retrieved in the last year.  Therefore, when you keep the old machine, you ignore the fact that you increased the working capital 3 years ago – it is a sunk cost.  However, when you end the project, you can still retrieve the WC.  Obviously, when you sell the old machine in order to buy the new machine, you also retrieve the working capital associated with the old machine in year 0.  The same argument is applicable when you buy the new machine.  In this case you show the increase in working capital in year 0 as a cost, and you retrieve it in year 5.  There are no tax implications.  The only impact is time value of money that has been lost.

2.       The price of the old machine is irrelevant except in so far as it serves to determine the depreciation.  The price of the new machine is relevant.  To this one must add the installation costs.  We are thus “capitalising” the installation costs.  The increased sum is used to determine the depreciation.  In this case depreciation = R75 000 + R5 000 = R80 000 / 5 = R16 000.  In practice we frequently find that companies do not capitalize the installation costs, but write it all off in year 0, claiming a tax shield.  We will not follow this practice.

3.       Training costs are not capitalised, but shown as an expense.  As such it provides a tax shield = R3 000 x 40 % = R1 200.

4.       How did we determine the R10 000 loss on the sale of the old machine?  Remember.

•         Current market price of old machine = R25 000.

•         The book value of the old machine is:  ??

•         Cost price of old machine / 8 yrs = depreciation per year

•         Depreciation of 3 yrs = R21 000 (R7 000 x 3)

•         Therefore book value = R56 000 (cost price) – R21 000 (Depreciation) = R35 000

•         Therefore we have a loss of R10 000 (Market price – Book Value)

•         40 % of R10 000 = R4 000 tax shield on loss!

I think we now have more than enough examples on how to calculate the NPV of a project.  The reason why I went into such depth with NPV is that it is the best criterion of them all.

You will notice that we completely ignored one item in Example 7, namely the viability study costs associated with the new machine.  The reason why we did this is that the viability study costs are sunk costs and irrelevant for the decision.  Whether we proceed with the project or not, the costs that have been paid remain sunk.  Another item that also will be ignored, is the issue of head office costs that are retrieved from new projects.





This method is very similar to the NPV method.  However, instead of discounting the expected net cash flows by a predetermined rate of return, the IRR seeks to answer the following question:

What rate of return would be required in order to ensure that the NPV = 0, or that the PV inflow = PV outflow?


In theory, a rate of return lower than the required rate of return would be rejected.

How do we calculate the IRR?  We use the exact same incremental CFAT we determined for the NPV.  After we asked for the NPV, we press ▀ IRR and it gives us the IRR for the project.


Let’s determine the IRR for each of the examples done with the NPV:

•         Example 1:

a.       IRR 11,65 %.  The required rate of return is 18 %.  Reject the project.

b.       IRR 15,44 %.  Still too low.  Reject.

c.       IRR 20,13 %.  Higher than RRoR.  Accept.


•         Example 2

a.       IRR = 17,68 %.  Higher than RRoR (10 %).  Accept.



•         Example 3

•         IRR of project A:     24,14 %.

•         IRR of project B:     17,95 %.


•         Example 4

•         IRR = 23,92%.  RRoR is 16 %.  Accept.


•         Example 5

•         IRR = 26,13 %.  RRoR is 14 %.  Replace old machine.


•         Example 6

•         IRR = 18,93 %.  RRoR is 10 %.  Replace old machine.


•         Example 7

•         IRR = -3,06 %.  RRoR is 12 %.  Do not replace old machine.


We see that the IRR and the NPV gives the same decision.  This will always be the case, unless the cash flows are not conventional.  With a conventional cash flow we mean that we have an initial cash outlay in year 0, with positive cash flows for the duration of the project.  The moment we find a negative cash flow other than in year 0, we could find more than one IRR for the same project.  The rule is that the number of IRR’s = the number of changes in the signs of the cash flow.  When you have unconventional cash flows, do not use the IRR as it could be misleading.  Use the NPV criterion.




Up to now we have assumed a certain rate as a discount rate in calculating the NPV.  In this section we look at the weighted average cost of capital (WACC) – it is the cost of capital of the company as a whole.  Up till now we spoke of required return.  Now we speak of cost of capital.  There is no difference between the 2 concepts – it depends from which side you look at it:


•         For investor                      :         required return.

•         For company                     :         cost of capital.


Do not make the mistake of equating WACC to required return.  The company’s WACC is a weighted average of the cost of equity and the cost of debt.  For the investor buying shares, the cost of equity is relevant.  For the investor lending money to the company, the cost of debt is relevant.  As a whole, the WACC is equal to the returns what the investor in equity wants plus the returns the investor in debt wants.

It is also important to remember that the cost of capital is an opportunity cost – it depends on where the money is used and not on the source of it.  Therefore we can construct the following formula:


•         Cost of Capital = Cost of Debt Capital + Cost of Equity Capital



The overall cost of capital is a mixture of the returns needed to remunerate the shareholders and lenders.

The assumption is that the company maintains a given capital structure.  What is important here is the target capital structure, the combination of debt and equity that minimizes the company’s cost of capital and maximizes the company’s value.






In determining the cost of equity, there are 2 approaches:


•         Dividend growth model

•         Security Market Line approach


Dividend Growth Model


The price of a share can be obtained from:


P0 = D1 / (Re-g)

Re = D1 / (P0 + g)



where           D1 = dividend in next period

P0 = price of share today

g  = growth rate in dividends.

RE is therefore equal to:


Yield (D1 / P0) +  Growth


In calculating RE ,


•         P0 is easy to obtain.

•         D1 is easy to calculate.

•         g has to be calculated.



How can g be calculated?

•         Historical growth

  • take annual % change and determine average.
  • take geometric mean.  Only uses first and last value and could be a problem.

•         Analytical forecasts – available from a number of sources.

•         g=b x ROE , where we assume that the ratio of dividends to earnings is constant.


The advantage of using the dividend growth model to calculate RE is that it is easy and widely applicable.  The disadvantages are:


•         It is only applicable to companies paying constant dividends.

•         It is sensitive to estimates of g.

•         It makes no direct adjustment for risk.



The SML Approach


The cost of equity is equal to:


E(Re) = rf + B [E(Rm) – rf]


For this we need:


•         rf (riskfree interest rate) – use T Bill rate, NCD, BA rate.

•         βE – get from UCT or BFA Net.

•         (Rm – r f) – Riskpremium of the market.



The advantages of the SML Approach are:


•         It is widely applicable.

•         It makes adjustments for risk.


The disadvantage is that it needs estimates for βE and the market risk premium.


The question could be asked which of 2 approaches should be used.  In the best of worlds both should give the same answer.  We could even use the average of the 2 answers.  In order to standardize the calculations for the purposes of this course, I would like you to use the SML Approach, unless I explicitly state the contrary.





Cost of Debt


The cost of debt is the interest rate on new loans.  It is observable as:


•         the return on current outstanding debt;

•         the return on newly issued similar rated debt (AA, BB or whatever).


A β is not necessary for debt, as the interest rate is directly observable in the market.


We could also use the Yield to Maturity of bonds as the cost of debt.





In calculating the WACC we assume the current debt/equity ratio (D/E) is optimal.  If we want R100 million and the optimal D/E ratio is 1/3 , (or the optimal debt ratio is 0,25 or 25 %), we assume we will get R25 million of debt and R75 million of ordinary shares.

In the practical world it happens that companies do not issue both debt and equity, but only one of them.  This will distort the optimal debt ratio, but it shouldn’t be any problem if subsequent issues take the company back to its optimal debt ratio.

The point is that the company’s capital structure can fluctuate on the short term.  The target weights should always be used in the calculation of the WACC.  In respect of this point, I would like to mention that there are a diversity of opinions around the issue of weights.


  • There are those that use book value weights.  These weights refer to an ex post – approach based on accounting values.  The original book values on the balance sheet when the financing was obtained originally, is used to determine the weights.

Book value weights are not suitable as they are not consequent with the RRoR that is directly concerned with the minimum RoR needed to maintain the current market value of the respective financial components.

  • Then there are those that use market value weights.  Under this system the WACC reflects that RoR needed by investors rather than the historical rates fixed in the balance sheets.  In die USA it was found in 1982 that market values were the most popular weighting system and that together with target structures formed 88 % of the systems in use.  Iro the RSA Lambrechts found in 1975 that 55 % of the respondents used market values.
  • Target value weights reflect the capital structure the company would like to have.  This system refers to a capital structure whereby market values are maximised and the RRoR is minimised.  Numerous academics are of the opinion that this is the system that should be used.  However, Gitman (1988) stated the following:

“… when one considers the somewhat approximate nature of the calculations, the choice of weights may not be critical …”


For the purposes of this course, we will assume that the current market value weights are the target value weights.  We will also use the market value weights throughout.


For interest sake, the following findings of a 1991-study on the use of WACC as a RRoR.  The number of respondents was 174.


•         Use always             :         87      (50 %)

•         Frequently              :         26      (14.9 %)

•         Seldom                   :         17      (9.8 %)

•         Never                     :         29      (16.7 %)

•         No response           :         15      (8.6 %)


The same study shows that more than 50 % of the respondents make use of target capital structure weights, but very few use market capital weights and even less use historical capital structure weights or balance sheet capital structure weights.  Aside from the non-use of market capital structure weights, which is contrary to financial theory, the findings are in line with normative prescriptive financial theory.

40 % of the respondents were of the opinion that the WACC becomes irrelevant in high risk situations, as only equity capital can be used in such instances.

Those of you interested in this study can find it in:

Paulo, S.  1991.  The Weighted Average Cost of Capital:  Theory and South African Empirical Evidence.  Journal for the Study of Economics and Econometrics, vol 15, no 2.



Let’s return to how the WACC is calculated:


  • Step 1 is to determine the market value of the capital of the company.
  • Determine the market value of the equity of the company by multiplying the current market price of the share with the total issued shares.
  • Determine the market value of the debt of the company.  In this regard a company’s debt frequently has a price in the market.  If bonds are involved, you can use your knowledge of chapter 6 to determine the PV of the bonds.
  • We then say:

Value of company = Market value of debt plus market value of equity

V        =        D + E

1      =        D/V + E/V


•         We frequently say the D/E ratio is 1/3.  This means that the D/V = 1/4  and the E/V is 3/4 .  If we say the debt ratio is 25 %, we know the D/V is 0.25 and the E/V is 0.75.

•         Furthermore, note how debt is expressed.  If we speak of capital structure, we speak of long-term debt.  Some institutions use a wider approach in determining debt.  Brigham and Gapenski, and Gitman and Mercurio, show that only long-term debt should be used.  It is possible, however, to add the current portion of long-term debt (which is shown under current liabilities) to the long-term debt.


•         Now that we’ve determined the weights, we can use the formula of WACC:


WACC = (E/V) x RE + [(D/V) x RD x (1 – TC)]


RE = use SML

RD = observable in market

TC = after tax cost of debt is used.


Let’s consolidate all of this bmo an example:


Boats Ltd has 1.4 million shares, with the market price per share at R20 per share.  Its debt trades in the public and has a face value of R5 million.  Coupons are paid annually and the coupon rate is 12%.  The remaining life is 10 years while the YTM is 16%.  The riskfree rate is 14%.  The market risk premium is 10.6%, while Boats has a β of 0.74.  The tax rate is 35%.



•         Step 1:  Market value of debt:


•         FV                =        5 000 000

•         PMT             =        600 000 (12 % of 5 000 000)

•         N                  =        10

•         I/YR              =        16

•         Ask for PV    =        R4 033 354.50



•         Step 2:  Market value of equity:


•         1 400 000 shares

•         R20 market price

•         Equity =        R28 000 000

•         Step 3:  Value of Company:  R32 033 354.50


•         Step 4:  Determine RE


RE = rf + β (Mrp)

= 14 + 0.74 (10.6)

= 21.84 %


•         Step 5:  RD = 16 % (given)


•         Step 6:  Determine WACC


WACC = (E/V) x RE + [(D/V) x RD x (1 – TC)]

= 19,09 + 1,309

= 20,399 % = 20,4 %


Always remember to use the β that reflects the risk of the project.  You can only use the company’s β if the project is a replica of the company’s current operating activities.




Up till now we assumed that the issue of debt and equity was free.  This is not the case.  It costs money to issue loans as well as shares.  There are 2 approaches in treating the issue costs of debt and equity.

•         There are those that adjust the WACC upward to provide for issue costs.  This is not a good method as the RRoR is a function of the use of the funds and not of the source.

•         The best approach is to determine the weighted average of the issue costs of equity and debt and to inflate the costs of the project with it.


Let’s explain the process bmo an example:


Accept a target capital structure of 60% equity and 40% debt.  The issue costs of equity is 10% of funds obtained from shares, and the issue costs of debt is 5% of funds obtained from debt.  The project cost is R100 million – typically the capital outlay in year 0, plus the installation costs.

fa = (E/V) x fe + (D/V)x fd


= 0,6 x 10 % + 0,4 x 5 %

= 8 %


Project cost after issue costs       :    R100 million / (1 – fa)

=        100 000 000 / 0.92

=        R108 695 652,17





There will be circumstances when the company’s WACC is not suitable as RRoR because the risks differ.  If you use the company’s WACC in such a case:


•         You can reject projects while you should’ve accepted it.

•         Accept projects while you should’ve rejected it.


What happens if the company has 2 divisions?  Say a company has the following:


•         A transport division with low risk.

•         An electronics division with high risk.


The company’s WACC is therefore a mixture of 2 different costs of capital – one for each division.  If the 2 divisions compete for funds and the company uses a single WACC as hurdle rate, who is going to get more funds?

Remember:   high risk – high return!

Therefore the electronics division will be the “winner.”  Large companies are aware of this problem and work at developing separate divisional costs of capital.

What do you do if you cannot determine the β of the project, but you know that the project’s risk differs from that of the company?  Here we talk of the “pure play approach.”  You look at other investments outside the company that are the same risk class as the project under consideration.  You then use the market required returns on these investments as the discount rate.  The principle is that you must find companies that focus exclusively on the type of project we are interested in.

The third way of getting a discount rate is to use the “subjective approach.”  It entails that you make subjective adjustments to the company’s WACC.

•         You determine 3 to 4 categories of risk.

•         An adjustment factor for each category is determined.

•         The company’s WACC is adjusted upward or downward with the adjustment factor.

The effect of this is that you assume that all projects fall into 1 of 4 sectors.  The risk still remains that a project can be mistakenly accepted or rejected.

In principle it is better to determine the required return for such projects separately in an objective manner.  In practice it is not always possible to go much further than subjective adjustments due to the fact that the necessary information is missing, or it is not worth the cost and effort.



Someone one day said companies suck a hurdle rate from their thumbs and even couple it to a payback period.  This is not far off the mark.  I spoke to the financial manager of a large listed company in the 1980’s.  His answer was that they decided on a discount rate of 27 % – there were no grounds for this figure other than the feeling that if a project cannot give a 27 % return, it wasn’t worthwhile.  Furthermore, it was coupled to a payback period of 3 years.  We can indeed speak of a discounted payback method.