Capital Budgeting and Investment Appraisal

FFM · Chapter 12

Capital Budgeting and Investment Appraisal

1 Capital investment

Capital investment (or expenditure) is an amount spent to acquire or significantly improve the capacity or capabilities of a long-term assets such as equipment or buildings. It should enhance the profit-making capabilities of the business. The cost is recorded in a statement of financial position (balance sheet) under non-current asset headings such as:

Land and buildings
Plant and machinery
Equipment
Motor vehicles

The assets' cost (except for the cost of freehold land) will then be depreciated (expensed) over the useful life of the asset.

In contrast to capital expenditure, revenue expenditure is for day-to-day running expenses of the business or to maintain the profit-earning capacity of the non-current assets (for example, repair, servicing, redecoration).

Capital investment expenditure is to acquire expensive items large and once the purchase of assets has begun it is usually difficult to stop the process. For example, if constructing a new factory, stopping half way through will probably leave the business with a useless shell or construction site. Furthermore, once an asset is purchased it is usually difficult to retrieve anything close to the amount spent as second hand values (other than for land and buildings) are often very low.

So, capital expenditure can irreversibly permanently remove large amounts of cash from a business. Therefore, it is vital that capital expenditure is carefully planned and budgeted for if the business is not to find itself with liquidity problems. It is also important that individual purchases of non-current assets are properly scrutinised before orders are placed to ensure that money is being spent properly on assets needed by the business and also that the best possible purchase deals are obtained.

When a business raises capital, it has two ways in which the amount raised can be invested:

Purchase of non-current assets
Increase in working capital (like cash balances or inventory).

Putting too much money into non-current assets can leave the business with insufficient working capital. Putting too much into working capital can mean that the business is not making good use of the cash raised (it is simply sitting in the bank or in inventory).

Businesses must carefully assess the volatility of their cash flows to try to ensure that capital raised is deployed in the best possible way and that a balance is achieved between prudence (lots of cash in working capital) and performance (lots of cash used to buy productive non-current assets).

1.1 Preparing and controlling a capital expenditure budget

Identify investment needs and collect proposals with cost, timing, relevant cash flows and expected benefits. Appraise projects, prioritise them within available funds and obtain approval before including them in the capital budget.
Set spending/authorisation limits and named responsibility. Monitor actual expenditure against budget, investigate variances and approve changes before further commitment.
Carry out a post-completion review of actual costs and benefits against the original appraisal. Use the findings to improve future estimates and decisions.

2 Capital investment appraisal - introduction

For the reasons stated above, the use of company funds for capital expenditure has to be carefully assessed. The funds are precious and the non-current assets bought may last for many years providing additional income. But is the income enough to justify the expenditure? What if there are several capital projects competing for funds - how does the company decide which project is best?

Several methods have been developed to address these problems:

The accounting rate of return
The payback period
The discounted payback period
Net present value
Internal rate of return.

3 The accounting rate of return

The accounting rate of return (ARR) is also known as the return on investment (ROI) and is defined as:

ARR

Illustration

A machine is bought for $24,000 and over the next four years is expected to produce pre-depreciation earnings as follows:

Year	Pre-depreciation earnings
1	$7,000
2	$8,000
3	$12,000
4	$8,000

The estimated scrap value of the machine at the end of 4 years is $4,000.

Calculate the ARR

Solution

The ARR is calculated as follows:

Total earnings = $35,000.

Total depreciation charge = $24,000 - $4,000 = $20,000

Average annual earnings after depreciation = ($35,000 - $20,000)/4 = $3,750

Average value of the investment (starts at $24,000 and falls to $4,000) =

($24,000 + $4,000)/2 = $14,000

ARR = 3,750/14,000 = 0.268 or 26.8%

The method draws an analogy with calculating an interest rate earned from a bank deposit where the rate = Interest earned/Amount invested.

So, 26.8% might look good, but whereas you are unlikely to lose the amount you invest in a bank, there is no guarantee that the company's expenditure of $24,000 will produce the income that is forecast. Capital investments always suffer from considerable risk and to compensate for this they should pay considerably more than could be earned in a bank deposit account. How much more depends on the company's owners because, ultimately they put up the money for the new investment either by forgoing dividends or by paying more capital into the company.

Therefore, companies establish a target rate of return that projects should meet or exceed. If in the example above the target rate had been 25%, because the ARR is above that the project would be accepted. If the target rate were 30%, the project would be rejected.

Sometimes the ARR is calculated using the initial capital employed instead of the average investment. In the above example the ARR on that basis would be:

$3,750/$24,000 = 0.156 or 15.6%

This doesn't mean that the project has suddenly become worse - it's just a different way of assessing it and it be compared to a different target rate to decide whether or not it was an acceptable project.

Advantages of the ARR:

Simple to understand and calculate
The accounting data used is readily available (assuming capital budgets have been prepared).
Tends to be accepted by managers

Disadvantages of the ARR:

Based on profits - which are susceptible to manipulation by adopting different accounting assumptions and policies.
Does not take into account the time value of money. Exactly the same ARR would be obtained if no profits were made for the first three years and all the earnings of $35,000 did not arrive until the fourth year. Obviously that would make the project less attractive and more risky.
There is not a standardised way of calculating the ARR.
Assessing the target rate can be difficult and rather arbitrary.

ARR is the one method in this chapter built on profit, so depreciation is deducted from the cash earnings before they are averaged, as in the example above. The denominator is the average investment, (initial cost + residual value) ÷ 2: the residual value is added, not deducted, and the total is halved, not divided by the life of the project as if you were working out depreciation. Use the initial investment only where the question asks for it, because it gives a different, lower rate (15.6% against 26.8% in the example). For an outlay of $100,000 with no residual value, a ten-year life and cash inflows of $14,500 a year, ARR on average investment is (14,500 − 10,000) ÷ 50,000 = 9%; 14.5%, which ignores depreciation and uses the initial outlay, was the most popular answer.

4 The payback period

This method calculated how long it takes the company to recoup its initial cash spent on the project. Note that it uses cash inflows not profits and the big difference is likely to be depreciation which is an expense but is not a cash flow. If income is termed as "profits after depreciation" then for each year depreciation has to be added back to get the cash inflow figures.

Taking the example above:

	Cash earnings ($)	Cumulative cash earnings ($)
Year 1	7,000	7,000
Year 2	8,000	15,000	(ie $7,000 + $8,000)
Year 3	12,000	27,000	(ie $15,000 + $12,000)
Year 4	8,000	35,000	(ie $27,000 + $8,000)

The original cash outlay was $24,000.

This has not been recouped by the end of year 2, but it is recouped part way r year 3 because at the end of that year $27,000 has been received in total - $3,000 more than needed. To get payback, therefore, only $12,000 - $3,000 = $9,000 of year 3's earnings have to be received. This represents 9,000/12,000 = 0.75 of the year's total earnings so should be received 9 months into year 3.

The payback period is therefore 2 years 9 months.

Companies will set targets for acceptable payback. If the company had a target payback period of 4 years then achieving a payback of 2 years 9 months is acceptable as money is recouped faster than it needs to be.

If the target payback had been 2 years, then 2 years 9 months is unacceptable.

Payback gives some information about risk as the longer the actual payback, the more risk there is as it is much more difficult to have confidence about cash flows 8 years away (say) than inflows expected to arise after only 3 years. Companies in different business sectors will have their own acceptable criteria. For example, a company whose business is drilling for oil in the middle of an ocean will be used to long payback periods whereas a company in retail will expect much shorter payback.

One of the main problems with payback is that it 'loses interest' after payback either is or is not reached by the target period. Say that in the above example the target payback was 2 years; the actual payback of 2 years 9 months means that the project would be rejected. But would that be a reasonable decision if the expected cash flows were as follows?

	Cash earnings ($)
Year 1	7,000
Year 2	8,000
Year 3	12,000
Year 4	80,000

The project now is massively profitable, but the payback period is still 2 years 9 months. However, it is unlikely that rejecting the project would be a good decision. Therefore, it is dangerous to use payback on its own as not all cash flows are considered.

Advantages of payback:

Easy to calculate and understand
Uses cash flows not profits. Cash flows are more difficult to manipulate than profits
Gives some information about project risk
Concentrated on cash flows and these are vital to liquidity

Disadvantages of payback

Largely ignores the timing of cash flows within the payback period
Total profits are ignored as the method does not consider earnings after payback has or has not been achieved in the target period.
Can be difficult and arbitrary to establish the target payback period.

5 The discounted payback period

Discounted payback accumulates the present values of the project’s cash flows until the initial outlay is recovered. Earlier receipts have a higher present value because they can earn a return sooner. The discount rate reflects the required return, including the assessed risk.

Taking the example above and a discount rate of 5%:

Time	Cash inflow ($)	5% discount factor from tables	Discounted cash flow ($)	Cumulative discounted cash inflow ($)
1	7,000	0.952	6,664	6,664
2	8,000	0.907	7,256	13,920
3	12,000	0.864	10,368	24,288
4	8,000	0.823	6,584	30,872

The initial cash outlay was $24,000, so cash break-even is obtained during Year 3 as before.

At the end of year 2, discounted receipts total $13,920. The unrecovered outlay is $24,000 − $13,920 = $10,080.

Year 3 discounted cash flow is $10,368. Assuming cash is received evenly within that year, the fraction required is 10,080/10,368 = 0.9722.

Discounted payback = 2.9722 years, approximately 2 years 11.7 months. If all receipts occur only at year ends, recovery is at the end of year 3.

For all practical purposes, and given the uncertainty relating to cash flows and an appropriate discount rate, payback is achieved at the end of year 3. This would be compared to the company's target discounted payback period.

Advantages and disadvantages

As for payback with the added difficulty of having to estimate a proper discount rate, but once that is done then the time-value of money has been taken into account.

5.1 Usefulness of payback and discounted payback

Payback is simple and emphasises liquidity and early recovery, useful where cash is constrained or forecasts far ahead are unreliable. It ignores cash after payback and uses an arbitrary acceptable period.
Ordinary payback ignores time value. Discounted payback recognises it, but needs a discount rate and still ignores later cash flows. Neither measures total value added as NPV does.

6 Net present value (NPV)

NPV is a technique that uses discounted cash flows and is one of the most theoretically sound ways of evaluating capital projects It converts all cash inflows and outflows arising from a project into their net present values and adds up the present value amounts to assess whether the project makes the investor richer or poorer after adjusting for the time value of money.

Outflows are shown as negative cash flows; inflows are positive. Time 0 = now

Illustration 1

A company is considering investing in a machine that costs $75,000 and which then produces inflows of $30,000, $50,000 and $20,000 at times 1,2 and 3. (Note: time 1 is 12 months from now etc and for simplicity cash flows are assumed to happen at the end of each 12 month period.)

If the discount rate is 10%, is the project worthwhile?

The analysis is as follows:

Time	Cash flow $	10% Discount factor	Discounted cash flow (= present value of the flow)
0	(75,000)	1	(75,000)
1	30,000	0.909	27,270
2	50,000	0.826	41,300
3	20,000	0.751	15,020
		Net present value	8,590

The NPV is $8,590 positive. This means that the investor would be the equivalent of $8,590 better off now if the project is undertaken even after allowing for the effect of the inflows not happening until some time in the future. The advice, therefore, is to ACCEPT this project.

If the NPV had been negative then this means that the investor is poorer by that amount if the project is carried out. That loss can be avoided by REJECTING the project.

Illustration 2

A company is considering in buying a machine for $250,000 to be spent at time 0 and $50,000 to be spent at time 1. The machine will produce annual income $35,000 for 10 years starting at time 2 and will be sold for $20,000 scrap value just as the final income is received.

Is the project worthwhile if the discount rate is 9%?

The analysis is as follows:

Time	Cash flow $	9% Discount factor	Discounted cash flow (= present value of the flow)
0	(250,000)	1	(250,000)
1	(50,000)	0.917	(45,850)
2 - 11	35,000	6.805 - 0.917 = 5.888 Year 1 - 11 cumulative factor less the year 1 factor leaving years 2 - 11	206,080
11	20,000	0.388	7,760
		Net present value	(82,010)

The NPV is −$82,010 ie heavily negative, so the project should be rejected.

7 Advantages and disadvantages of NPV as a method of investment appraisal

Advantages of NPV as a method of investment appraisal:

Uses cash flows - which are more difficult to manipulate than profits
The time value of money is taken into account
Higher discount rates can be used when assessing riskier projects giving them a higher hurdle to clear
More distant cash flows are more heavily discounted so that those far-off less certain flows have less importance in the calculation

Disadvantages

Requires training and practice to carry out and to interpret
A discount rate has to be estimated.

8 Relevant cash flows for NPV calculations

Relevant cash flows are future incremental cash flows which are caused by (or affected by) the decision to invest.

In particular, the following are not relevant cash flows:

Depreciation (not a cash flow at all)
Past (or sunk costs). Money already spent or committed should not affect the decisions about future cash flows
Reallocation of existing costs (not incremental)
Interest or capital repayments on loans These are already taken into account within the discounting procedure.

Illustration

A business bought leasehold land for $500,000⁽¹⁾ three years ago. It has a current market value of $750,000⁽²⁾ .

The business can erect an office for $800,000⁽³⁾ that would be depreciated at $20,000 ⁽⁴⁾ per year over the next 40 years. The office would be rented out for $150,000⁽⁵⁾ pa for 20 years. 10% of current administration costs of $50,000⁽⁶⁾ pa would be allocated to the project's budget.

Is the project worthwhile if the discount rate is 10%pa.

The amounts should be treated as follows:

The land was bought three years ago. This is a past (sunk) cost and is not relevant.
Building the office means that the land cannot be sold for $750,000 so the decision to proceed with the project reduces potential cash flows by $750,000. This figure is relevant.
The cost of the office is a simple future incremental cash flow, so is relevant.
Depreciation is not a cash flow so not relevant
This is future incremental income, so is relevant
This is not an incremental cost. It is simply an internal reallocation of an existing cost so it is not relevant.

The full appraisal is therefore:

Time	Cash flow	Discount factor	Discounted cash flow
0	(750,000 + 800,000)	1	(1,550,000)
1 - 20	150,000	8.513 (20 year 10% factor)	1,276,950
		Net present value	(273,050)

9 The internal rate of return (IRR)

9.1 Introduction

This is also a discounted cash flow technique. The internal rate of return is defined as:

IRR = the discount rate at which the net present value is zero

It can be regarded as a 'break-even' discount rate:

If IRR > actual discount rate, the NPV is > 0 and the project should be accepted.

Think of it as the project earning at a higher rate than is being used to discount the cash flows so undertaking the project will make the investor richer.

If IRR < actual discount rate, the NPV is < 0 and the project should be rejected.

Think of it as the project earning at a lower rate than is being used to discount the cash flows so undertaking the project will make the investor poorer.

9.2 The NPV in 'normal' projects

A 'normal' project is one where there is an outflow now and inflows in the future.

The initial outflow, happening now, is already the present value amount and is therefore not affected by discount rates. The future inflows are discounted and the higher the discount rate the lower the present value figures (you can see this by looking along any year in the discount tables: as discount rates increase, the discount factors decrease and so too will the present value of future flows.

Consider this project: Expenditure at Time 0 = $12,000. Income for times 1,2 and 3 = $5,000 pa.

Discount rate	Cumulative 3 year discount factor	NPV of inflows ($5,000 x cumulative discount factor	NPV
0	3.000	15,000	3,000
5.00%	2.723	13,615	1,615
10.00%	2.487	12,435	435
15.00%	2.283	11,415	(585)
20.00%	2.106	10,530	(1,470)

On a graph the results are:

You can see that the NPV crosses through zero between a discount rate of 10 and 15, perhaps around 12%. So, the internal rate of return (IRR) is about 12%.

If discount rate used for the NPV is less than 12%, ie to the left, all the NPV values are > 0 and the project should be accepted.

If discount rate used for the NPV is greater than 12%, ie to the right, all the NPV values are < 0 and the project should be rejected.

Therefore, IRR can be used as an accept/reject criterion instead of the NPV.

9.3 Calculation of the IRR

To estimate the IRR, two discount rates are used to find two NPVs. The discount rates are more or less randomly chosen but ideally they yield one positive and one negative NPV.

So, in the example above:

Discount rate = 5%, NPV = 1,615

Discount rate = 15%, NPV = -585

We know that the IRR is therefore between 5% and 15%

You may have noticed that the line on the graph, above, is not quite straight, but in this following estimation we have to pretend that is straight. A simplified view is therefore:

The IRR is a point F, so we need to find the length of OF.

The triangles ABF and ACE are similar, meaning that their sides have the same proportions.

So, BF/AB = CE/AC [base/perpendicular in each case]

BF/1,615 = (15 - 5)/(1615 - (-585)) = 10/2,200

BF = 1,615 x 10/2,200 = 7.3

If BF = 7.3 then OF = 5 + 7.3 = 12.3, close to what we estimated by eye using the graph.

IRR = 12.3 (approximately).

You can either use this type of diagram, or use a formula (not provided in the exam):

IRR = A + [N_A/(N_A - N_B)] x (B - A)

Where

A = lower discount rate tried

B = higher discount rate tried

N_A= NPV at A%

N_B= NPV at B%

So here A = 5, B = 15, N_A= 1,615, N_B= -585

IRR = 5 + [1615/(1615 - (-585))] x (15 - 5) = 12.3

There is one tricky part and that is the (N_A - N_B) term. If N_Bis negative then when to subtract this negative number you need to add it to N_A.You need the total distance A to C on the diagram and that is 1615 + 585.

The formula above has to be used if the cash flows are uneven, however, there are some situations where calculating the IRR is easier

IRR of an annuity

Illustration

In return for an investment of $5,000, $650 will be received for each of years 1 - 10. What is the IRR of this investment?

To solve this you have to remember the definition of IRR: it is the rate at which the NPV of the cash flows is zero. Therefore at IRR

Investment = PV of inflows (= the cumulative discount factor x annual inflow)

Here, 5,000 = Cumulative 10 year factor x 650

Cumulative 10 year factor = 5,000/650 = 7.7

So, look along the 10-year row of the cumulative discount table until you find a discount factor as near as possible to 7.7. The 10 year, 5% factor is very close to 7.7, so 5% is approximate IRR.

IRR of a perpetuity

The cumulative discount factor for a perpetuity at a discount rate of r is 1/r

So, at the IRR, NPV = 0 (by definition) and

Investment = PV of inflows (annual inflow x 1/r)

1/r = Investment/Annual inflow

r = Annual inflow/Investment, where r will be the IRR.

9.4 Problems with the IRR as a method of appraisal

Mutually exclusive investments

Illustration

A company owns a piece of land. It can either:

(i) Build an office for $3m which it would then rent out for $300,000 pa in perpetuity.

(ii) Lease to a charity incurring legal costs of $200 and from which it would receive $50 pa in perpetuity.

The discount rate used by the company is 8%

The two investment opportunities can be evaluated as follows:

	NPV	IRR
(i) Office	-$3m + $300,000 x 1/0.08 = $750,000	300,000/$3m = 10%
(ii) Charity	-$200 + $50 x 1/0.08 = $425	50/200 = 25%

Using IRR, option (ii) looks much better, paying 25% as opposed to only 10% from option (i).

However, the sums involved in option (ii) are trivial and the NPV shows that it enriches the company by an NPV of only $425. Option (i) makes the company $750,000 better off.

Here, the correct decision is to go for option (i). NPV shows in absolute terms how much a project enriches an investor. The IRR shows returns only in relative terms and says nothing about which project is more valuable.

Multiple yields

A 'normal' project has cash outflows now (the initial investment) then inflows in the future. Such a project has only one discount rate for which the NPV = 0: there is only one IRR.

However, some projects can have more complex cash flow patterns. For example:

Time	Cash flow	NPV sign
0	Build a chemical works for $50m	Negative
1 – 10	Receive inflows of $8m per year	Positive
11	Spend $15m on environmental clean-up after the factory closes	Negative

Mathematically, there is a discount rate where the NPV is zero every time the direction of the cash flow changes. For the chemical works the flows are -, +, - so there are two changes in flow direction so two IRRs. This obviously complicates using IRR to decide whether a project is acceptable. For example, if the two IRRs were 5% and 15% and the discount rate is 10% then one IRR is above the discount rate and the other below it.

There are ways in which this complication can be solved, but they are beyond your needs for this syllabus.

10 Advantages and disadvantages of IRR as a method of investment appraisal

Advantages of IRR as a method of investment appraisal:

Uses cash flows - which are more difficult to manipulate than profits
The time value of money is taken into account
For simple, non-mutually exclusive projects, gives a clear accept/reject indication
More distant cash flows are more heavily discounted so that those far-off less certain flows have less importance in the calculation
Many managers feel more comfortable with a % rate compared to an NPV

Disadvantages

Requires training and practice to carry out and to interpret
Can be time-consuming to calculate
Care needed when deciding between mutually exclusive projects: high IRRs do not mean the project is very valuable.
Complications (multiple yields) when project cash flows are complex.

11 Chapter 12 questions

Question 1

A machine costs $50,000 and will last for 5 years after which it has a scrap value of $10,000. Pre depreciation earnings over its life are:

Year	Pre-depreciation earnings ($)
1	10,000
2	15,000
3	20,000
4	15,000
5	10,000

(a) What is the accounting rate of return on this investment (using the average amount invested).

(b) If the target ARR is 15%, should the machine be purchased?

Question 1

(a)

Total pre depreciation earnings = $70,000

Depreciation = $40,000

Average post depreciation earnings per year = (70,000 – 40,000)/5 = 6,000

Average investment = (50,000 + 10,000)/2 = 30,000

ARR = 6,000/30,000 = 20%

(b) Yes, because 20% > 15%

Question 2

Using the data in the above question, what is the pay-back period of this investment?

If the target payback period is 4 years, should the investment be accepted?

Question 2

Year	Cumulative inflows
1	10,000
2	25,000
3	45,000
4	60,000

So, as expenditure was $50,000, payback occurs during year 4: another $5,000 has to be added to what was received at the end of year 3, ie 1/3 of the $15,000 earned during year 4.

Payback = 3 years 4 months

This investment therefore is acceptable because payback is achieved in a shorter time than required.

Question 3

Using the data from Question 1, above, what is the net present value of this investment if the discount rate is 10%?

Should the investment opportunity be accepted?

Question 3

NPV

Time	Description	$	Discount factor	DCF
0	Purchase	(50,000)	1	(50,000)
1	Pre-depreciation income = cash received	10,000	0.909	9,090
2	“	15,000	0.826	12,390
3	“	20,000	0.751	15,020
4	“	15,000	0.683	10,245
5	“	10,000	0.621	6,210
5	Scrap	10,000	0.621	6,210
NPV				9,165

This is a positive NPV so the investment should be accepted.

Question 4

At a discount rate of 7% a project has an NPV of 12,000. At 13%, the NPV is -6,000.

What is the IRR of the investment?

If the discount rate is 12%, should this project be accepted?

Question 4

IRR = 7 + 12,000/(12,000 – (-6,000)) x (13 – 7) = 11%

Because the IRR is less than the discount rate, this project should be rejected.

Question 5

Which of the costs should be brought into an NPV calculation with the following information?

A company bought patent rights for $20,000 three years ago. They could now be sold for $30,000 and have a book value of $25,000. The patent rights can be used to make a product that would need a production line costing $300,000 which would cost $200,000 pa to run. The $200,000 contains a depreciation charge of $30,000

Question 5

$30,000 = opportunity cost, so relevant as this cash flow is affected by the decision to use the patent.

$300,000 = an incremental cash outflow

$200,000 - $30,000 = $170,000. This is the incremental CASH outflow for running production

NB the employees are irrelevant: were paid $75,000 and are still paid $75,000.

Answer the questions one at a time. Your progress is saved so you can leave and come back.

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