- Email: [email protected]
Cash Flow and Investment Analysis
C H A P T E R
3 Cash Flow and Investment Analysis
y3.1 INTRODUCTION The question of whether the costs of investing today are justified by the expected future benefits is fundamental to both public- and private-sector investment decisions. A widely-used approach is to express the costs and benefits in numerical, usually money, terms. A large part of this book deals with the financial, and to some extent the economic, aspects of PPPs and their effect on policy issues. It is therefore necessary for the reader to have a basic understanding of certain key concepts used in financial and economic analysis that are used in this book. This chapter is therefore aimed mainly at those not familiar with these concepts—those who are may omit the chapter. A PPP deals with cash flows over long periods of time, and the value of money is affected by the time that this money is received or paid. It is evident that a dollar today is worth more than a dollar in a year’s time, but is a dollar today worth more than two dollars in a year’s time? Two interlinked types of calculation are normally used to make this decision: • a discounted cash flow (DCF) calculation, which gives a value today, or ‘present value’ (PV), for a future cash flow (y3.2); and • an internal rate of return (IRR) calculation, which determines the overall rate of return on an investment based on its future cash flow (y3.3). Although both of these methods of calculation have some problems (y3.4), they are widely used in PPP projects in a variety of contexts (y3.5).
Public-Private Partnerships for Infrastructure DOI: https://doi.org/10.1016/B978-0-08-100766-2.00003-6
25
Copyright © 2018 E R Yescombe & Edward Farquharson. Published by Elsevier Ltd. All rights reserved.
26 | Chapter 3: Cash Flow and Investment Analysis
y3.2 PRESENT VALUE / DISCOUNTED CASH FLOW y3.2.1 Present Value The PV is the value today of a sum of money due in the future, discounted at the cost of money, i.e. a relevant interest rate.1 The formula for a PV calculation is PV 5
FV ; ð11iÞn
where PV 5 present value, i.e. the ‘money of today’, FV 5 future value, i.e. the ‘money of the future’, i 5 the discount rate, and n 5 the number of periods (e.g. annual or semi-annual with the discount rate adjusted accordingly) until FV is paid. Thus if the discount rate is 10% p.a., and a sum of $1,000 is due in a year’s time, the PV of that sum is 1;0004ð1 1 0:10Þ, or $909.1. To turn the calculation the other way around, if $909.1 is invested for a year at 10%, $1,000 (i.e. 909.1x1.10) will be repaid at the end of the year. Similarly the PV of a sum of $1,000 due in 2 years’ time at a discount rate of 10% p.a. calculated semi-annually (i.e. 5% per half year) is $1;0004ð110:05Þ4 , or $822.7.
y3.2.2 Discounted Cash Flow A DCF calculation is the PV of a series of future cash sums, the purpose of the calculation being to find what this stream of future cash flows is worth in money of today. It is calculated as the sum of the cash flow for each future period (usually semi-annually in PPP cash-flow calculations), each period’s cash flow being discounted to its PV as set out above. Typically the cash flow in a DCF calculation offsets, or ‘nets off’, the costs (such as investment and running costs) in a project against the stream of future revenues which the project produces. When this happens, the result is called the net present value (NPV). The term ‘net present cost’ (NPC) may be used when looking at the DCF from a contracting authority’s perspective (because the future cash flows are a series of payments by the contracting authority or users), but the calculation is the same as an NPV. Although DCF calculations can easily be done using the relevant spread-sheet software function, it is useful to understand the underlying formulæ and calculations as a way of checking and understanding the final result. The choice of discount rate is obviously crucial in determining the NPV of a project’s cash flow, and hence the value of the project as an investment: the higher the rate the lower the NPV, and vice versa. The discount rate used also depends on the context in which the DCF calculation is being performed, and by whom, as discussed at the end of this chapter. 1
This chapter looks at cashflows from an investment or financing perspective and hence the use of cost of money or interest rates as a discount rate. From an economic perspective, however, the discount rate may be based on different factors, such as a social time preference rate (cf. y8.6.2), but the principles of discounting are the same as described here.
y3.2: Present Value / Discounted Cash Flow | 27
y3.2.3 Using Discounted Cash-Flow Calculations The use of DCF calculations can be illustrated by the two contrasting investment cash flows set out in Table 3.1. Both involve an initial investment of $1,000, and cash flows over five years of $1,350, producing a surplus (net of the initial investment) of $350. The cash flow for each annual period has been discounted to its NPV at 10% p.a. Year 0 is the first day of the project, when the investment is made (the investment being shown as a negative figure in the cash flow); the remaining cash flows are received at annual intervals thereafter.
Table 3.1 DCF calculation Investment A ($) (c) Cash flow NPV ((c)4(b))
Investment B ($) (d) Cash flow NPV ((d)4(b))
(a) Year
(b) Discount factor ((1 1 0.1)(a))
0
1.0000
21,000
21,000
21,000
21,000
1
1.1000
340
309
200
182
2
1.2100
305
252
235
194
3
1.3310
270
203
270
203
4
1.4641
235
161
305
208
5
1.6105
200
124
340
211
350
49
350
22
Total
It will be seen that although the undiscounted cash flows produce the same net result over the five-year period, the NPV of Investment A is $49 (i.e. DCFs from years 1 to 5 of $1,049, less the original investment of $1,000), whereas that of Investment B is 2$2. Investment A is thus the better project. These differences in the DCF calculations illustrate the importance to investors of the timing of cash flows. The discount rate is often used as a ‘hurdle rate’, meaning that if the NPV is positive using this rate the investment is acceptable, whereas if it is negative the return is too low and therefore the investment is not acceptable. Thus if the same cash flows are discounted at 5% p.a., the NPV of Investment A is $184 and that of Investment B is $154; so, changing the hurdle rate does not affect the decision that Investment A is the better one, but it also turns Investment B from a doubtful into an attractive investment. If Investment B were the only choice, changing the hurdle rate from 10% to 5% would affect the decision whether to go ahead with it or not, which illustrates the importance of the choice of discount rate. A DCF calculation also provides a means of valuing an investment that is already held (in which case there is no initial investment cost outflow). If a PPP contract is expected to provide a stream of revenues of $1,000 a year for the next 20 years, the financial value of this business is determined by discounting this stream of revenues to its value today, i.e. its PV. The choice of discount rate again makes a substantial difference to the result: if this stream is discounted at 15% p.a., its value today is $6,259, but if discounted at 8% p.a., its
28 | Chapter 3: Cash Flow and Investment Analysis value is $9,818. As will be seen, investors have different views about the value of a stream of future revenues, and so use different discount rates—thus the same PPP project may have a different value for different investors.
y3.3 INTERNAL RATE
OF
RETURN
The IRR measures the return on the investment over its life. It is the discount rate at which the NPV of the cash flow (adding up both the outflows and the inflows) is zero. Thus using the examples in Table 3.1 as set out in Table 3.2, the IRR of Investment A is 12.08% and Investment B is 9.94%, so again showing that Investment A is the better of the two; the calculation can be checked by discounting the two cash flows at these respective rates. Again a minimum IRR can be used as a hurdle rate, so if the investor has an IRR hurdle rate of say 12%, Investment A will be acceptable but Investment B will not.
Table 3.2 IRR calculation End year
Investment A ($) Cash flow [email protected]%
Investment B ($) Cash flow [email protected]%
0
21,000
21,000
21,000
21,000
1
340
303
200
182
2
305
243
235
194
3
270
192
270
203
4
235
149
305
209
5
200
113
340
212
Total
350
0
350
0
y3.4 PROBLEMS WITH DISCOUNTED CASH FLOW AND INTERNAL RATE CALCULATIONS
OF
RETURN
Some caution must be exercised with DCF and IRR calculations, as both have defects or weaknesses which need to be understood.
y3.4.1 Single Discount Rate The use of a single discount rate or IRR to assess investments suggests that the risks involved in a project are the same throughout its life. In reality, of course this is not the case (cf. y20.3.1). Similarly, in a typical PPP, there is a construction period lasting several years, during which the project’s cash flow is of course negative, generally followed by positive cash
y3.4: Problems with Discounted Cash Flow and Internal Rate of Return Calculations | 29 flows for the rest of the project life, unlike the cash flows in the tables above, where all the investment is assumed to take place on day one of the project. If a high discount rate is used to calculate the NPV of the project, which is usually the conservative approach because a higher discount rate gives a lower NPV, the negative cash flows over an extended construction period are also being discounted at this high rate, which is not conservative: where future cash flows are negative, the conservative approach is to use a low discount rate. Arguably two different discount rates should be used for the initial negative and subsequent positive cash flows although this is not generally the case in the PPP market.
y3.4.2 Discounted Cash-Flow Calculations and Different-Sized Projects When comparing two different projects, account has to be taken of their relative sizes. This is illustrated in Table 3.3.
Table 3.3 DCF calculations and different-sized projects Investment C ($)
Investment D ($)
21,000
22,000
1,400
2,600
273
364
40%
30%
(c) PV of benefits (5PV of (b))
1,273
2,364
(d) PV of costs (5(a))
1,000
2,000
1.27x
1.18x
(a) Original investment (b) Cash flow 1 year later NPV@10% IRR Cost-Benefit Analysis
Benefit to cost ratio ((c)4(d))
Investment D has a higher NPV than Investment C, but this is merely because of its larger size. As is apparent from the IRR calculation, Investment C is the better investment; the incremental $1,000 invested in Investment D compared to Investment C gives a much poorer return. To better compare these investments the NPV comparison can be broken down into a comparison of the PV of the costs and the PV of the benefits, as shown in the second half of Table 3.3. This suggests that Investment C gives a better return, i.e. the value of benefits in relation to the amount of the investment, a point confirmed by the IRR calculation. The approach here is that any project with a benefit to cost ratio (BCR) over 1x is a sound one, but the project with the highest BCR is the one which should be chosen. On the other hand, if availability of funding is not a problem, and if there is no other use for the funds, it could be argued that Investment D is still worthwhile because it produces a greater absolute net benefit.
30 | Chapter 3: Cash Flow and Investment Analysis
y3.4.3 Internal Rate of Return and Cash Reinvestment A fundamental problem with IRR is the assumption in the calculation on what happens to interim cash flows. This is illustrated by Table 3.4.
Table 3.4 IRR and interim cash flows Investment E ($)
Investment F ($)
Year
Cash flow
Cash flow
Annual cash flow reinvested @15% to year 5
0
21,000
21,000
1
0
298
522
2
0
298
454
3
0
298
395
4
0
298
343
5
2,011
298
298
Total
1,011
492
2,011
NPV@12%
141
75
IRR
15%
15%
It is evident that Investment E gives a better return, and the DCF calculation supports this, but the IRRs of the two investments are the same. This is because the standard IRR calculation assumes that cash taken out of the project is reinvested at the IRR rate until the end of the calculation period. Thus as shown in the last column of Table 3.4, if the Investment F cash flow in years 1-4 is reinvested at 15% p.a. compounded, the total amounts to $2,011 at the end of year 5, the same as Investment E. Clearly, some account should be taken of Investment F generating cash more quickly, but the assumption that this cash can be reinvested at 15% is not correct unless this is the investor’s cost of capital (cf. y20.3.1), and so may double-count the return on another investment at that rate. The effect of an IRR calculation can be clearly seen in Table 3.4; it overvalues early cash flow— the longer the cash-flow period, the more the IRR is exaggerated by using a high reinvestment rate—and conversely undervalues cash flows further into the future. This is of particular relevance to PPP projects, which have very long cash flows. There are two ways of dealing with this type of distortion: Modified IRR (MIRR) The MIRR calculation assumes a lower reinvestment rate (e.g. the investor’s cost of capital, as assumed for the discount rate in a DCF calculation, instead of the IRR rate) for cash taken out of the project. This is a better representation of the real
y3.4: Problems with Discounted Cash Flow and Internal Rate of Return Calculations | 31 world. If we take the examples in Table 3.4, but the reinvestment rate is taken as 12% (i.e. the cost of capital used for the DCF calculation) as shown in Table 3.5, the MIRR of Investment F is 13.6%, while that of Investment E of course remains at 15% (as there is no interim cash flow to invest). This then makes it clear that Investment E is the better one. Surprisingly the use of MIRR by PPP investors is not widespread.
Table 3.5 IRR and MIRR Investment E ($)
Investment F ($)
Year
Cash flow
Cash flow
Annual cash flow reinvested @12% to year 5
0
21,000
21,000
21,000
1
0
298
469
2
0
298
419
3
0
298
374
4
0
298
334
5
2,011
298
298
Total
1,011
492
105
141
75
NPV@12% IRR
15.0%
MIRR
15.0%
15.0% 13.6%
Payback period An alternative (or at least supplementary) approach is to ignore the reinvestment issue in looking at IRR calculations but require that any investment also has a maximum payback period (i.e. the length of time that it takes to recover the original cash investment). This to a certain extent balances the exaggerating effect of IRR calculations on longer term cash flows, but it is a crude measure—in particular it does not take account of returns after the end of the payback period. Nonetheless, it may still provide a useful check. Thus besides requiring a minimum IRR level, a maximum payback period of not more than a certain number of years may be required as one of the criteria for making a new investment. The payback period for Investment F in Table 3.4 is 3-4 years, and that for Investment E is the full 5 years.
y3.4.4 Internal Rate of Return and Different Project Lives Another consequence of the over-valuation of early cash flow in the IRR calculation is that projects with different lives cannot be compared using their IRRs. This is illustrated in
32 | Chapter 3: Cash Flow and Investment Analysis Table 3.6, which shows the cash flow from two projects which have identical IRRs—but it is evident, and confirmed by the DCF calculation, that the longer Investment J is better than the shorter Investment G (assuming there is no greater risk in Investment J).
Table 3.6 IRR and different project lives Year
Investment G($)
Investment J($)
0
21,000
21,000
1
200
145
2
200
145
3
200
145
4
200
145
5
200
145
6
200
145
7
200
145
8
200
145
9
145
10
145
11
145
12
145
13
145
14
145
15
145
IRR
11.8%
11.8%
NPV@10%
67
106
y3.4.5 Internal Rate of Return and Positive / Negative Cash Flows More esoterically, IRR calculations may not be suitable where a cash-flow flips between negative and positive and back again in different periods (e.g. where an investment takes places in phases, with revenues building up between each phase of investment, or where there is a final cost to an investment, such as cleaning up a quarry after it is exhausted), as the same calculation may then give more than one answer. This is illustrated in Table 3.7, in which it can be seen that the same cash flow, in which amounts are negative at the beginning, then positive in year 1, then negative in year 2, can be discounted at both 10% and 20% to produce an NPV (i.e. adding up all the positive and negative PVs) of zero, i.e. the IRR can be either 10% or 20%.
y3.5: Uses in Public-Private Partnerships | 33
Table 3.7 IRR and negative / positive cash flows 10% discount rate
20% discount rate
Year
Cash flow($)
Discount factor
PV($)
Discount factor
PV($)
0
250,000
1.00000
250,000
1.00000
250,000
1
115,000
0.90909
104,545
0.83333
95,833
2
266,000
0.82645
254,545
0.69444
245,833
NPV
0
0
It should be noted that standard spread-sheet software will probably only give one of these answers, with no obvious indication that different answers are possible.2
y3.4.6 Cash Investment vs Risk DCF and IRR calculations are based only on investment of cash; they take no account of the risk involved in making a commitment to invest cash in the future (cf. y20.3.6), nor of the need (and hence the cost) of setting aside resources to make this future investment. This is of particular relevance in PPPs, where construction and hence investment may take place over several years, or where there may be investments of cash in later stages of a project.
y3.5 USES
IN
PUBLIC-PRIVATE PARTNERSHIPS
DCF and IRR calculations are used in a variety of different ways by the different parties to a PPP project. The following just summarises these and provides cross-references to the context in which they are used elsewhere in this book. However, one general point should be made—all these calculations involve estimates of future cash flows, and the calculations are thus only as good as the data used for these estimates. Financial models (cf. y23.8) often work to a spurious level of accuracy down to fine decimal points—such calculations may be correct arithmetically, but have limited use since the underlying data cannot be that accurate.
y3.5.1 By the Public Sector A DCF calculation may be used by the contracting authority: • when deciding whether to proceed or not with a project (cf. y7.4.2)—an ‘economic rate of return’ calculation (a form of IRR) may also be used in this case (cf. y7.4.4); • in a quantitative ‘value for money’ (VfM) assessment (cf. y8.3); and • to evaluate private-sector bids for a PPP project (cf. y10.6.5). 2
Excel can be forced to give one answer or the other, depending on the ‘guess rate’ entered into the formula.
34 | Chapter 3: Cash Flow and Investment Analysis
y3.5.2 By Private-Sector Investors The project IRR—i.e. the IRR of the cash flow before debt service or equity returns— may be used by investors to assess the general financial viability of a project without taking account of its financial structure (cf. y20.3.2). However, the main measure for investors is the equity IRR—i.e. the IRR of the equity cash flow versus the original equity investment (cf. y20.3.3). This is commonly used as a hurdle rate for PPP investments—i.e. in order for an investment to be justified the equity IRR must be x% or above. Investors also use an NPV calculation as a method of valuing the project company (cf. y26.3).
y3.5.3 In PPP Contracts The equity IRR may be used to calculate • the initial service fees (cf. y23.9.5); • revisions to service fees, or compensation for changes in circumstances during the life of the PPP contract (cf. y16.2.2); • refinancing-gain calculations (cf. y26.2.6); and • compensation to investors for early termination of the PPP contract, for which a DCF calculation may also be used (y17.3); and the project IRR may be used as a discount rate to calculate the payment due on termination for a default by the project company (cf. y17.2.4).
y3.5.4 By Lenders Lenders use the project IRR to calculate their loan-life cover ratio (cf. y23.3.3).
3 Cash Flow and Investment Analysis
y3.1 INTRODUCTION The question of whether the costs of investing today are justified by the expected future benefits is fundamental to both public- and private-sector investment decisions. A widely-used approach is to express the costs and benefits in numerical, usually money, terms. A large part of this book deals with the financial, and to some extent the economic, aspects of PPPs and their effect on policy issues. It is therefore necessary for the reader to have a basic understanding of certain key concepts used in financial and economic analysis that are used in this book. This chapter is therefore aimed mainly at those not familiar with these concepts—those who are may omit the chapter. A PPP deals with cash flows over long periods of time, and the value of money is affected by the time that this money is received or paid. It is evident that a dollar today is worth more than a dollar in a year’s time, but is a dollar today worth more than two dollars in a year’s time? Two interlinked types of calculation are normally used to make this decision: • a discounted cash flow (DCF) calculation, which gives a value today, or ‘present value’ (PV), for a future cash flow (y3.2); and • an internal rate of return (IRR) calculation, which determines the overall rate of return on an investment based on its future cash flow (y3.3). Although both of these methods of calculation have some problems (y3.4), they are widely used in PPP projects in a variety of contexts (y3.5).
Public-Private Partnerships for Infrastructure DOI: https://doi.org/10.1016/B978-0-08-100766-2.00003-6
25
Copyright © 2018 E R Yescombe & Edward Farquharson. Published by Elsevier Ltd. All rights reserved.
26 | Chapter 3: Cash Flow and Investment Analysis
y3.2 PRESENT VALUE / DISCOUNTED CASH FLOW y3.2.1 Present Value The PV is the value today of a sum of money due in the future, discounted at the cost of money, i.e. a relevant interest rate.1 The formula for a PV calculation is PV 5
FV ; ð11iÞn
where PV 5 present value, i.e. the ‘money of today’, FV 5 future value, i.e. the ‘money of the future’, i 5 the discount rate, and n 5 the number of periods (e.g. annual or semi-annual with the discount rate adjusted accordingly) until FV is paid. Thus if the discount rate is 10% p.a., and a sum of $1,000 is due in a year’s time, the PV of that sum is 1;0004ð1 1 0:10Þ, or $909.1. To turn the calculation the other way around, if $909.1 is invested for a year at 10%, $1,000 (i.e. 909.1x1.10) will be repaid at the end of the year. Similarly the PV of a sum of $1,000 due in 2 years’ time at a discount rate of 10% p.a. calculated semi-annually (i.e. 5% per half year) is $1;0004ð110:05Þ4 , or $822.7.
y3.2.2 Discounted Cash Flow A DCF calculation is the PV of a series of future cash sums, the purpose of the calculation being to find what this stream of future cash flows is worth in money of today. It is calculated as the sum of the cash flow for each future period (usually semi-annually in PPP cash-flow calculations), each period’s cash flow being discounted to its PV as set out above. Typically the cash flow in a DCF calculation offsets, or ‘nets off’, the costs (such as investment and running costs) in a project against the stream of future revenues which the project produces. When this happens, the result is called the net present value (NPV). The term ‘net present cost’ (NPC) may be used when looking at the DCF from a contracting authority’s perspective (because the future cash flows are a series of payments by the contracting authority or users), but the calculation is the same as an NPV. Although DCF calculations can easily be done using the relevant spread-sheet software function, it is useful to understand the underlying formulæ and calculations as a way of checking and understanding the final result. The choice of discount rate is obviously crucial in determining the NPV of a project’s cash flow, and hence the value of the project as an investment: the higher the rate the lower the NPV, and vice versa. The discount rate used also depends on the context in which the DCF calculation is being performed, and by whom, as discussed at the end of this chapter. 1
This chapter looks at cashflows from an investment or financing perspective and hence the use of cost of money or interest rates as a discount rate. From an economic perspective, however, the discount rate may be based on different factors, such as a social time preference rate (cf. y8.6.2), but the principles of discounting are the same as described here.
y3.2: Present Value / Discounted Cash Flow | 27
y3.2.3 Using Discounted Cash-Flow Calculations The use of DCF calculations can be illustrated by the two contrasting investment cash flows set out in Table 3.1. Both involve an initial investment of $1,000, and cash flows over five years of $1,350, producing a surplus (net of the initial investment) of $350. The cash flow for each annual period has been discounted to its NPV at 10% p.a. Year 0 is the first day of the project, when the investment is made (the investment being shown as a negative figure in the cash flow); the remaining cash flows are received at annual intervals thereafter.
Table 3.1 DCF calculation Investment A ($) (c) Cash flow NPV ((c)4(b))
Investment B ($) (d) Cash flow NPV ((d)4(b))
(a) Year
(b) Discount factor ((1 1 0.1)(a))
0
1.0000
21,000
21,000
21,000
21,000
1
1.1000
340
309
200
182
2
1.2100
305
252
235
194
3
1.3310
270
203
270
203
4
1.4641
235
161
305
208
5
1.6105
200
124
340
211
350
49
350
22
Total
It will be seen that although the undiscounted cash flows produce the same net result over the five-year period, the NPV of Investment A is $49 (i.e. DCFs from years 1 to 5 of $1,049, less the original investment of $1,000), whereas that of Investment B is 2$2. Investment A is thus the better project. These differences in the DCF calculations illustrate the importance to investors of the timing of cash flows. The discount rate is often used as a ‘hurdle rate’, meaning that if the NPV is positive using this rate the investment is acceptable, whereas if it is negative the return is too low and therefore the investment is not acceptable. Thus if the same cash flows are discounted at 5% p.a., the NPV of Investment A is $184 and that of Investment B is $154; so, changing the hurdle rate does not affect the decision that Investment A is the better one, but it also turns Investment B from a doubtful into an attractive investment. If Investment B were the only choice, changing the hurdle rate from 10% to 5% would affect the decision whether to go ahead with it or not, which illustrates the importance of the choice of discount rate. A DCF calculation also provides a means of valuing an investment that is already held (in which case there is no initial investment cost outflow). If a PPP contract is expected to provide a stream of revenues of $1,000 a year for the next 20 years, the financial value of this business is determined by discounting this stream of revenues to its value today, i.e. its PV. The choice of discount rate again makes a substantial difference to the result: if this stream is discounted at 15% p.a., its value today is $6,259, but if discounted at 8% p.a., its
28 | Chapter 3: Cash Flow and Investment Analysis value is $9,818. As will be seen, investors have different views about the value of a stream of future revenues, and so use different discount rates—thus the same PPP project may have a different value for different investors.
y3.3 INTERNAL RATE
OF
RETURN
The IRR measures the return on the investment over its life. It is the discount rate at which the NPV of the cash flow (adding up both the outflows and the inflows) is zero. Thus using the examples in Table 3.1 as set out in Table 3.2, the IRR of Investment A is 12.08% and Investment B is 9.94%, so again showing that Investment A is the better of the two; the calculation can be checked by discounting the two cash flows at these respective rates. Again a minimum IRR can be used as a hurdle rate, so if the investor has an IRR hurdle rate of say 12%, Investment A will be acceptable but Investment B will not.
Table 3.2 IRR calculation End year
Investment A ($) Cash flow [email protected]%
Investment B ($) Cash flow [email protected]%
0
21,000
21,000
21,000
21,000
1
340
303
200
182
2
305
243
235
194
3
270
192
270
203
4
235
149
305
209
5
200
113
340
212
Total
350
0
350
0
y3.4 PROBLEMS WITH DISCOUNTED CASH FLOW AND INTERNAL RATE CALCULATIONS
OF
RETURN
Some caution must be exercised with DCF and IRR calculations, as both have defects or weaknesses which need to be understood.
y3.4.1 Single Discount Rate The use of a single discount rate or IRR to assess investments suggests that the risks involved in a project are the same throughout its life. In reality, of course this is not the case (cf. y20.3.1). Similarly, in a typical PPP, there is a construction period lasting several years, during which the project’s cash flow is of course negative, generally followed by positive cash
y3.4: Problems with Discounted Cash Flow and Internal Rate of Return Calculations | 29 flows for the rest of the project life, unlike the cash flows in the tables above, where all the investment is assumed to take place on day one of the project. If a high discount rate is used to calculate the NPV of the project, which is usually the conservative approach because a higher discount rate gives a lower NPV, the negative cash flows over an extended construction period are also being discounted at this high rate, which is not conservative: where future cash flows are negative, the conservative approach is to use a low discount rate. Arguably two different discount rates should be used for the initial negative and subsequent positive cash flows although this is not generally the case in the PPP market.
y3.4.2 Discounted Cash-Flow Calculations and Different-Sized Projects When comparing two different projects, account has to be taken of their relative sizes. This is illustrated in Table 3.3.
Table 3.3 DCF calculations and different-sized projects Investment C ($)
Investment D ($)
21,000
22,000
1,400
2,600
273
364
40%
30%
(c) PV of benefits (5PV of (b))
1,273
2,364
(d) PV of costs (5(a))
1,000
2,000
1.27x
1.18x
(a) Original investment (b) Cash flow 1 year later NPV@10% IRR Cost-Benefit Analysis
Benefit to cost ratio ((c)4(d))
Investment D has a higher NPV than Investment C, but this is merely because of its larger size. As is apparent from the IRR calculation, Investment C is the better investment; the incremental $1,000 invested in Investment D compared to Investment C gives a much poorer return. To better compare these investments the NPV comparison can be broken down into a comparison of the PV of the costs and the PV of the benefits, as shown in the second half of Table 3.3. This suggests that Investment C gives a better return, i.e. the value of benefits in relation to the amount of the investment, a point confirmed by the IRR calculation. The approach here is that any project with a benefit to cost ratio (BCR) over 1x is a sound one, but the project with the highest BCR is the one which should be chosen. On the other hand, if availability of funding is not a problem, and if there is no other use for the funds, it could be argued that Investment D is still worthwhile because it produces a greater absolute net benefit.
30 | Chapter 3: Cash Flow and Investment Analysis
y3.4.3 Internal Rate of Return and Cash Reinvestment A fundamental problem with IRR is the assumption in the calculation on what happens to interim cash flows. This is illustrated by Table 3.4.
Table 3.4 IRR and interim cash flows Investment E ($)
Investment F ($)
Year
Cash flow
Cash flow
Annual cash flow reinvested @15% to year 5
0
21,000
21,000
1
0
298
522
2
0
298
454
3
0
298
395
4
0
298
343
5
2,011
298
298
Total
1,011
492
2,011
NPV@12%
141
75
IRR
15%
15%
It is evident that Investment E gives a better return, and the DCF calculation supports this, but the IRRs of the two investments are the same. This is because the standard IRR calculation assumes that cash taken out of the project is reinvested at the IRR rate until the end of the calculation period. Thus as shown in the last column of Table 3.4, if the Investment F cash flow in years 1-4 is reinvested at 15% p.a. compounded, the total amounts to $2,011 at the end of year 5, the same as Investment E. Clearly, some account should be taken of Investment F generating cash more quickly, but the assumption that this cash can be reinvested at 15% is not correct unless this is the investor’s cost of capital (cf. y20.3.1), and so may double-count the return on another investment at that rate. The effect of an IRR calculation can be clearly seen in Table 3.4; it overvalues early cash flow— the longer the cash-flow period, the more the IRR is exaggerated by using a high reinvestment rate—and conversely undervalues cash flows further into the future. This is of particular relevance to PPP projects, which have very long cash flows. There are two ways of dealing with this type of distortion: Modified IRR (MIRR) The MIRR calculation assumes a lower reinvestment rate (e.g. the investor’s cost of capital, as assumed for the discount rate in a DCF calculation, instead of the IRR rate) for cash taken out of the project. This is a better representation of the real
y3.4: Problems with Discounted Cash Flow and Internal Rate of Return Calculations | 31 world. If we take the examples in Table 3.4, but the reinvestment rate is taken as 12% (i.e. the cost of capital used for the DCF calculation) as shown in Table 3.5, the MIRR of Investment F is 13.6%, while that of Investment E of course remains at 15% (as there is no interim cash flow to invest). This then makes it clear that Investment E is the better one. Surprisingly the use of MIRR by PPP investors is not widespread.
Table 3.5 IRR and MIRR Investment E ($)
Investment F ($)
Year
Cash flow
Cash flow
Annual cash flow reinvested @12% to year 5
0
21,000
21,000
21,000
1
0
298
469
2
0
298
419
3
0
298
374
4
0
298
334
5
2,011
298
298
Total
1,011
492
105
141
75
NPV@12% IRR
15.0%
MIRR
15.0%
15.0% 13.6%
Payback period An alternative (or at least supplementary) approach is to ignore the reinvestment issue in looking at IRR calculations but require that any investment also has a maximum payback period (i.e. the length of time that it takes to recover the original cash investment). This to a certain extent balances the exaggerating effect of IRR calculations on longer term cash flows, but it is a crude measure—in particular it does not take account of returns after the end of the payback period. Nonetheless, it may still provide a useful check. Thus besides requiring a minimum IRR level, a maximum payback period of not more than a certain number of years may be required as one of the criteria for making a new investment. The payback period for Investment F in Table 3.4 is 3-4 years, and that for Investment E is the full 5 years.
y3.4.4 Internal Rate of Return and Different Project Lives Another consequence of the over-valuation of early cash flow in the IRR calculation is that projects with different lives cannot be compared using their IRRs. This is illustrated in
32 | Chapter 3: Cash Flow and Investment Analysis Table 3.6, which shows the cash flow from two projects which have identical IRRs—but it is evident, and confirmed by the DCF calculation, that the longer Investment J is better than the shorter Investment G (assuming there is no greater risk in Investment J).
Table 3.6 IRR and different project lives Year
Investment G($)
Investment J($)
0
21,000
21,000
1
200
145
2
200
145
3
200
145
4
200
145
5
200
145
6
200
145
7
200
145
8
200
145
9
145
10
145
11
145
12
145
13
145
14
145
15
145
IRR
11.8%
11.8%
NPV@10%
67
106
y3.4.5 Internal Rate of Return and Positive / Negative Cash Flows More esoterically, IRR calculations may not be suitable where a cash-flow flips between negative and positive and back again in different periods (e.g. where an investment takes places in phases, with revenues building up between each phase of investment, or where there is a final cost to an investment, such as cleaning up a quarry after it is exhausted), as the same calculation may then give more than one answer. This is illustrated in Table 3.7, in which it can be seen that the same cash flow, in which amounts are negative at the beginning, then positive in year 1, then negative in year 2, can be discounted at both 10% and 20% to produce an NPV (i.e. adding up all the positive and negative PVs) of zero, i.e. the IRR can be either 10% or 20%.
y3.5: Uses in Public-Private Partnerships | 33
Table 3.7 IRR and negative / positive cash flows 10% discount rate
20% discount rate
Year
Cash flow($)
Discount factor
PV($)
Discount factor
PV($)
0
250,000
1.00000
250,000
1.00000
250,000
1
115,000
0.90909
104,545
0.83333
95,833
2
266,000
0.82645
254,545
0.69444
245,833
NPV
0
0
It should be noted that standard spread-sheet software will probably only give one of these answers, with no obvious indication that different answers are possible.2
y3.4.6 Cash Investment vs Risk DCF and IRR calculations are based only on investment of cash; they take no account of the risk involved in making a commitment to invest cash in the future (cf. y20.3.6), nor of the need (and hence the cost) of setting aside resources to make this future investment. This is of particular relevance in PPPs, where construction and hence investment may take place over several years, or where there may be investments of cash in later stages of a project.
y3.5 USES
IN
PUBLIC-PRIVATE PARTNERSHIPS
DCF and IRR calculations are used in a variety of different ways by the different parties to a PPP project. The following just summarises these and provides cross-references to the context in which they are used elsewhere in this book. However, one general point should be made—all these calculations involve estimates of future cash flows, and the calculations are thus only as good as the data used for these estimates. Financial models (cf. y23.8) often work to a spurious level of accuracy down to fine decimal points—such calculations may be correct arithmetically, but have limited use since the underlying data cannot be that accurate.
y3.5.1 By the Public Sector A DCF calculation may be used by the contracting authority: • when deciding whether to proceed or not with a project (cf. y7.4.2)—an ‘economic rate of return’ calculation (a form of IRR) may also be used in this case (cf. y7.4.4); • in a quantitative ‘value for money’ (VfM) assessment (cf. y8.3); and • to evaluate private-sector bids for a PPP project (cf. y10.6.5). 2
Excel can be forced to give one answer or the other, depending on the ‘guess rate’ entered into the formula.
34 | Chapter 3: Cash Flow and Investment Analysis
y3.5.2 By Private-Sector Investors The project IRR—i.e. the IRR of the cash flow before debt service or equity returns— may be used by investors to assess the general financial viability of a project without taking account of its financial structure (cf. y20.3.2). However, the main measure for investors is the equity IRR—i.e. the IRR of the equity cash flow versus the original equity investment (cf. y20.3.3). This is commonly used as a hurdle rate for PPP investments—i.e. in order for an investment to be justified the equity IRR must be x% or above. Investors also use an NPV calculation as a method of valuing the project company (cf. y26.3).
y3.5.3 In PPP Contracts The equity IRR may be used to calculate • the initial service fees (cf. y23.9.5); • revisions to service fees, or compensation for changes in circumstances during the life of the PPP contract (cf. y16.2.2); • refinancing-gain calculations (cf. y26.2.6); and • compensation to investors for early termination of the PPP contract, for which a DCF calculation may also be used (y17.3); and the project IRR may be used as a discount rate to calculate the payment due on termination for a default by the project company (cf. y17.2.4).
y3.5.4 By Lenders Lenders use the project IRR to calculate their loan-life cover ratio (cf. y23.3.3).