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Calculate the net present value (F) of projects
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Apply the payback period and internal rate of return methods
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Analyse the interactions between F, S, and E in projects
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Apply a balanced approach in integrated present value calculations
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Assess the advantages and shortcomings of the different investment decision rules
6.1 Calculating Financial Value by Means of NPV
Year | 2022 | 2023 | 2024 | 2025 | 2026 | 2027 | 2028 | 2029 |
Cash flow | –100 | 25 | 25 | 25 | 25 | 25 | 25 | 25 |
Discount factor | 1.00 | 0.91 | 0.83 | 0.75 | 0.68 | 0.62 | 0.56 | 0.51 |
PV(Cash flow) | –100.0 | 22.7 | 20.7 | 18.8 | 17.1 | 15.5 | 14.1 | 12.8 |
NPV | 21.7 |
Year | 2022 | 2023 | 2024 | 2025 | 2026 | 2027 | 2028 | 2029 |
Cash flow | –50 | 20 | 20 | 20 | 5 | 5 | 5 | 5 |
Discount factor | 1.00 | 0.91 | 0.83 | 0.75 | 0.68 | 0.62 | 0.56 | 0.51 |
PV(Cash flow) | –50.0 | 18.2 | 16.5 | 15.0 | 3.4 | 3.1 | 2.8 | 2.6 |
NPV | 11.65 |
Year | 2022 | 2023 | 2024 | 2025 | 2026 | 2027 | 2028 | 2029 |
Cash flow | –100 | 40 | 40 | 40 | 10 | 10 | 10 | 10 |
Discount factor | 1.00 | 0.91 | 0.83 | 0.75 | 0.68 | 0.62 | 0.56 | 0.51 |
PV(Cash flow) | –100.0 | 36.4 | 33.1 | 30.1 | 6.8 | 6.2 | 5.6 | 5.1 |
NPV | 23.3 |
Year | 0 | 1 | 2 | 3 | 4 | 5 |
Cash flow | –1200 | 50 | 50 | 500 | 500 | 500 |
Year | 0 | 1 | 2 | 3 | 4 | 5 |
Discount factor | 1.00 | 0.89 | 0.80 | 0.71 | 0.64 | 0.57 |
Year | 0 | 1 | 2 | 3 | 4 | 5 |
PV(Cash flow) | –1200 | 45 | 40 | 356 | 318 | 284 |
6.2 Other Investment Decision Rules
6.2.1 Payback Rule
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The pre-specified payback period is usually arbitrary
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The payback period does not account for the time value of money
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It makes cash flows beyond the cut-off point irrelevant, which does not stimulate long-term investment
6.2.2 IRR Rule
Year | 2022 | 2023 | 2024 | 2025 | 2026 | 2027 | 2028 | 2029 |
Cash flow | –100 | 25 | 25 | 25 | 25 | 25 | 25 | 25 |
Discount factor | 1 | \( \frac{1}{{\left(1+r\right)}^1} \) | \( \frac{1}{{\left(1+r\right)}^2} \) | \( \frac{1}{{\left(1+r\right)}^3} \) | \( \frac{1}{{\left(1+r\right)}^4} \) | \( \frac{1}{{\left(1+r\right)}^5} \) | \( \frac{1}{{\left(1+r\right)}^6} \) | \( \frac{1}{{\left(1+r\right)}^7} \) |
PV(Cash flow) | –100 | ? | ? | ? | ? | ? | ? | ? |
NPV | 0 |
Year | 2022 | 2023 | 2024 | 2025 | 2026 | 2027 | 2028 | 2029 |
CF project A | –200 | 110 | 110 | 110 | –60 | 110 | 110 | –300 |
CF project B | –150 | 30 | 30 | 30 | 30 | 30 | 30 | 30 |
Discount rate (%) | NPV |
---|---|
13 | –192 |
12 | –158 |
11 | –123 |
10 | –86 |
9 | –47 |
8 | –6 |
7 | 36 |
Year | 0 | 1 | 2 | 3 | 4 | 5 |
Cash flow | –1200 | 50 | 50 | 500 | 500 | 500 |
Positive CFs | 50 | 50 | 500 | 500 | 500 | |
Cumulative positive CFs | 50 | 100 | 600 | 1100 | 1600 | |
Investment outlay paid back? | No | No | No | No | Yes |
6.2.3 NPV Versus IRR and Payback
Method | Project X | Project Y | Project Y twice | Preferred project |
---|---|---|---|---|
NPV | 21.7 | 11.6 | 23.3 | Project Y twice |
IRR | 16.3% | 19.6% | 19.6% | Project Y or Project Y twice |
Payback rule | 4 | 3 | 3 | Project Y or Project Y twice |
6.3 Behavioural Effects on Investment Decisions
Unbiased assessment | Manager A assessment | Manager B assessment | Manager C assessment | |
---|---|---|---|---|
Project risk | 8% | 7.5% | 8% | 7.5% |
Perpetual CF | 200 | 200 | 220 | 220 |
-
Manager A: 200/0.075 = 2666.7
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Manager B: 220/0.080 = 2750.0
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Manager C: 220/0.075 = 2933.3
Unbiased assessment | Manager A assessment | Manager B assessment | Manager C assessment | |
---|---|---|---|---|
Unbiased project value | 2500 | 2500 | 2500 | 2500 |
Estimated project value (with bias) | 2500 | 2667 | 2750 | 2933 |
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The arrogance of its CEO, Jeff Skilling, was hard to miss: he boasted about his smartness; posted large pictures of himself in the Enron annual report; made wild claims (e.g., ‘perception is reality’). And he was known to be a compulsive gambler
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The company had a self-deceiving accounting system: Skilling introduced mark-to-market accounting, which was approved by the auditors and allowed Enron to basically make up its profits (‘hypothetical future value’)
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Group processes: employees evaluated each other on a scale of 1–5, where the 1s got huge bonuses and the 5s (15%) were fired—which gave unhealthy incentives in voting
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The company had a macho culture with wild motorcycle expeditions and parties with strippers at the office at night and
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There was no decent capital budgeting process. For example, the company built a power plant in India without seriously assessing local electricity demand
6.4 Integrated Investment Decision Rules
Method | Analysis | Example |
---|---|---|
Standard NPV | NPV on F gives FV | Projects from Sect. 6.1 |
Constrained PV | Add: S and/or E in their own units as a budget | E: Net zero CO2 emissions S: Positive health effects |
Expanded PV | Add: SV and/or EV in monetary terms | EV: CO2 emissions x price |
SV: Positive health effects x price | ||
Integrated PV | Add: FV + SV + EV all in monetary terms | IPV = FV + b * SV + c * EV, with b, c > 0 |
6.4.1 Constrained PV
Project | Investment, € millions | NPV F, € millions | CO2 emitted, millions | CO2 stored, millions | NPV ≥ 0? | Contribution to CO2 emissions ≤0? |
---|---|---|---|---|---|---|
A | 70 | –50 | 0 | 1 | No | Yes |
B | 100 | 200 | 0.2 | 0 | Yes | No |
C | 20 | 250 | 0.2 | 0 | Yes | No |
Project | Investment, € millions | NPV F, € millions | CO2 emitted, millions | CO2 stored, millions | NPV≥0? | Contribution to CO2 emissions ≤0? |
---|---|---|---|---|---|---|
A + B | 170 | 150 | 0.2 | 1 | Yes | Yes |
A + C | 90 | 200 | 0.2 | 1 | Yes | Yes |
Project | Quality life years added | Contribution to health effects ≥0? |
---|---|---|
A | – | Yes |
B | 2500 | Yes |
C | 4000 | Yes |
A + C | 4000 | Yes |
6.4.2 Expanded PV
Project | Investment, € millions | NPV F, € millions | E in own units net CO2 reduction, millions of tons | EV (€ millions) net CO2 reduction at 200 Euro/ton | S in own units quality life years added | SV (€ millions) quality life years added at 110k euro/life |
---|---|---|---|---|---|---|
A | 70 | –50 | 1.0 | 200 | – | 0 |
B | 100 | 200 | –0.2 | –40 | 2500 | 275 |
C | 20 | 250 | –0.2 | –40 | 4000 | 440 |
A + C | 90 | 200 | 0.8 | 160 | 4000 | 440 |
6.4.3 Integrated PV (IPV)
Project | FV | SV | EV | IPV = FV + SV + EV |
---|---|---|---|---|
A | –50 | 0 | 200 | 150 |
B | 200 | 275 | –40 | 435 |
C | 250 | 440 | –40 | 650 |
A + C | 200 | 440 | 160 | 800 |
Project | FV | SV | EV | IPV = FV + 0.5 * SV + 0.5 * EV | IPV = FV + SV + EV |
---|---|---|---|---|---|
K | 50 | –50 | –20 | 15 | –20 |
L | 30 | 30 | –40 | 25 | 20 |
M | 10 | 60 | –40 | 20 | 30 |
6.5 Internalisation
Project | FV | SV | EV | IPV = FV + 0.5 * SV + 0.5 * EV |
---|---|---|---|---|
X | 80 | –20 | –50 | 45 |
Y | –20 | –30 | 40 | –15 |
Z | –40 | –50 | 60 | –35 |
Project | FV (old) | SV | EV | FV (new) = FV (old) + 0.75 * EV | IPV with internalisation | IPV without internalisation |
---|---|---|---|---|---|---|
X | 80 | –20 | –50 | 42.5 | 7.5 | 45 |
Y | –20 | –30 | 40 | 10 | 15 | –15 |
Z | –40 | –50 | 60 | 5 | 10 | –35 |
IPV with internalisation | Probability of internalisation (%) | IPV without internalisation | Probability of no internalisation (%) | Expected IPV |
---|---|---|---|---|
15 | 0 | –15 | 100 | –15 |
15 | 10 | –15 | 90 | –12 |
15 | 20 | –15 | 80 | –9 |
15 | 30 | –15 | 70 | –6 |
15 | 40 | –15 | 60 | –3 |
15 | 50 | –15 | 50 | 0 |
15 | 60 | –15 | 40 | 3 |
15 | 70 | –15 | 30 | 6 |
15 | 80 | –15 | 20 | 9 |
15 | 90 | –15 | 10 | 12 |
15 | 100 | –15 | 0 | 15 |
6.6 Conclusions
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Constrained PV (present value) includes S (social) and E (environmental) factors in their own units as a budget constraint to the NPV on financial value
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Excessive optimism involves the overestimation of cash flows
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Expanded PV (present value) expresses S (social) and E (environmental) factors in monetary values (SV and EV) and shows these in addition to the NPV on financial value
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Integrated PV (IPV) calculates and explicitly balances FV, SV, and EV in a formula
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Internal rate of return (IRR) says that one should take any investment opportunity in which the IRR exceeds the opportunity cost of capital
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Investment decision rules are decision rules for investment projects; examples of such rules are NPV, IPV, payback rule, and IRR
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Materiality indicates relevant and significant information
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Materiality assessment aims to determine which S (social) and E (environmental) factors are sufficiently important for consideration in SV and EV
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Monetisation of social value (SV) and environmental value (EV) means to express them in monetary terms
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Net present value (NPV) is the present value of cash inflows and cash outflows
-
Payback rule states that one should only do an investment if its cash flows pay back its initial investment within a pre-specified period
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Payback period is the number of years needed to earn back the initial investment
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Overconfidence means that managers underestimate the risk involved in their investments
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Shadow prices reflect the ‘true scarcity’ of resources to stay within planetary boundaries or the ‘true price’ of human rights breaches to stay within social boundaries; shadow prices are based on welfare theory
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Quantification of social and environmental factors means to express them in their own units