16. Engineering Economic Analysis 3 - Cashflow Analysis Techniques

Time value of money

Risk expects appropriate return

How do we use these fundamentals as a basis for engineering economic analysis?

How do we ensure we make decisions that are economically justified?

By comparing cash flows of alternatives.

Systematic Economic Analysis Technique (SEAT)

Identify the investment alternatives (doing nothing may be a valid option)
Define the planning horizon
Specify the discount rate
Estimate the cash flows
Compare the alternatives
Perform supplementary analyses (e.g. break-even, risk, sensitivity to discount rate)
Select the preferred alternative

3. Specify the Discount Rate

Example: 2019 Exam

$1.1 million dollars in capital required. 200K sitting in a bank account at 2% interest per annum (personal opportunity cost), 500K from the bank at 4% interest (debt cost), 400K from rich aunt in return for 50% ownership, expecting an average rate of return of at least 25% (equity cost).

a. What fundamental principle of economic analysis is behind aunt’s rate of return? What assumption is she making? ~~Discount rate?~~ risk expects appropriate return

b. Weighted cost of capital

~~1.02 * 200/1100 - 1.04 * 500/1100 - 1.25 * 400/1100 = -0.74~~

-\mathrm{WCC} = \frac{200 \cdot 2\% + 500 \cdot 4\% + 400 \cdot 25\%}{1100} = 11.27\%

4. Estimate the Cash Flows

Engineering economic decisions usually involve:

Lump sum payments/costs
- At the beginning of the project (initial cost)
- At the end of the project (sold, salvage or remediation)
Streams of cash benefits as a result of the investment over future years (operating revenues)
Ongoing regular outgoings (operating/maintenance costs)

Cash Flows:

Be consistent with inflation
- A cash flow can be in real or nominal dollars
- If the cash flow is real, the discount rate must be real
Cash flow is after tax
When considering cash flows, focus on the difference between alternatives, not the absolute value
Consider all relevant criteria
Be clear regarding uncertainty: how risk is treated (be consistent in use of best/worst/most likely scenarios)
Cash flow != accounting profit

Sunk costs: disregard money already spent as a result of past decisions.

4. Compare the Alternatives

Analyze future cash flows considering:

Payback period
Net present value
Internal rate of return

Method 1: Payback

Time it takes for incremental benefits to pay back the initial investment.

Often used as part of an initial screening process when evaluating investments.

Basic method is to establish is payback period is less than some period of time defined by management policy (could be set completely arbitrarily). If it is within the acceptable range a formal evaluation can be done.

When calculating, assuming cashflow in each time period (e.g. year) is constant in order to get a fractional payback period.

Downsides:

Simple version does not account for time value of money
Does not consider cash flows past the payback period
Biased against long-term projects
Arbitrary cut-off point

Method 2a: Net Present Value

Discounted future value (future cash flows) minus present value (initial cost):

\text{NPV} = \sum_0^t\frac{C_t}{(1 + r)^t}

Where $r$ the discount rate/minimum acceptable rate of return (MARR).

NPV provides an estimate of a project’s net contribution to the value of the firm by giving proper treatment to the time value of money and the riskiness of the investment.

Steps:

Determine the initial cost of the project $C_0$ - $t = 0$ so no discounting is required to get the present value
Estimate the project’s future cash flows (nominal or real?)
Determine the riskiness of the project and hence the discount rate
- Risk free? Use the risk free rate
- Risky? Discount rate will be higher
Calculate the NPV
Choose the option with the highest NPV (or if there is only one option, if it is positive)

Advantages:

Uses discounted cash flow - considers time value of money
Is a direct measure of the ‘value’ of the project to the firm
Is robust as a comparative tool

Disadvantages:

Difficult to understand without accounting/finance background
Difficult to estimate discount rate

If payback and NPV contradict each other, always use NPV.

Example: Power Plant

900 million dollar power plant with cash flows of 300 million a year for 4 years, after which it will be decommissioned at a cost of 90 million.

 -900   300/r   300/r^2  300/r^3 300/r^4  -90/r^5
---|-------|-------|-------|-------|-------|
t  0      1      2      3      4      5

At 6% discount rate, NPV is 72 million.

At 16% discount rate, NPM is -1 million.

Example: Solar Panels

$13,204 system cost with estimated annual savings of $1,478 (real cost). Assuming a 20 year system life and 7% discount (real) rate (average after tax rate of return for stock market):

\begin{aligned} \mathrm{NPV} &= C_0 + \mathrm{PV}_\text{annuity} \\ &= C_0 + C\left[\frac{1}{r} - \frac{1}{r(1 + r)^t} \right] \\ &= -\text{\textdollar}13,\!204 + \text{\textdollar}1,\!478 \cdot 10.59 \\ &= \text{\textdollar}2,\!454 \end{aligned}

Method 2b: Net Future Value

Calculate the future value of an investment undertaken. This can be any time in the future, not necessarily at the end of the project.

It is typically used to measure the worth of an investment at the time of commercialization.

NFV Example

Site purchased for 1.5 million, building costing 4 million at end of year 1 and 6 at the end of year 2. On project termination building/land will be sold for 8 million.

Manufacturing equipment installed in year 2 at a cost of 13 million.

Estimated revenues over six year life: 6, 8, 13, 18, 14, 8.

MARR is 15%. Calculate the equivalent worth at the start of operations (end of year 2).

               -13                                  8
  -1.5   -4    -6     6     8     13    18    14    8
    |-----|-----|-----|-----|-----|-----|-----|-----|
    -2    -1    0     1     2     3     4     5     6

$\text{NFV} = -\frac{1.5}{1.15^-2} + \dots + \frac{8}{1.15^7} = 18.4$ . Alternatively, you can calculate $\text{NPV} \cdot (1.15)^3$ .

Method 3: Internal Rate of Return (IRR)

Find discount rate at which the net present value (NPV) is zero.

Let $\mathrm{NPV} = 0$ and solve for $r$ .

\text{NPV} = \sum_0^t\frac{C_t}{(1 + \text{IRR})^t} = 0

Do this via direct solution, trial and error, graphically, by Excel, etc…

If the IRR is greater than the cost of capital or the MARR, then accept the project.

IRR is easier to understand but harder to establish with confidence (IRR can get things wrong - NPV will be right).

Pitfalls of IRR:

Unconventional cash flows can mess things up - $\text{NPV} = 0$ can occur at different discount rates (multiple solutions)
- Conventional means an initial outflow followed by inflows
- e.g. when there is a large cost at the end of the project
No solution to the equation
Lending and borrowing give different NPV but identical IRR
- e.g. $1,000 cost in year 0 then $1,500 revenue in year 1; switching costs and revenues still gives $\text{\textdollar}0 = \mp1000 \pm \text{\textdollar}1,\!500/(1 + r)$ so a IRR of $r = 50\%$
Mutually exclusive projects can cause IRR to erroneously favour fast payback (NPV works fine)
- In this case, incremental analysis required - find the IRR for the difference between the two options
- Fine for independent projects - costs and benefits of one project do not depend on whether another is chosen
- Contingent projects: related but not mutually exclusive

IRR Example

Installing new windows to save $4,000 per year over the building’s remaining 30 year life.

The windows have an initial cost of $80,000 and no salvage value.

The organization has a MARR of 8%.

This cannot be solved symbolically.

In Excel, put all the yearly costs in a row and use IRR(range) to get the estimate.

Comparing Projects Where Option Lives Differ from Analysis Period

Economic Analysis Fundamentals:

Money has time value

Risks and returns tend to be positively correlated

Make investments that are economically justified

Consider only differences in cash flows among investment alternatives

Compare investment alternatives over a common period of time

The last point is important to consider and can be done through two different but equally good methods:

Option 1: Lowest Common Multiple

Use lowest common multiple: assume you can repeat the same decision after the end of each project period.

e.g. If one option is five years and the other ten years, then $\text{NPV}_{10y} = \text{NPV}_{5y} + \text{NPV}_{5y}/(1 + r)^5$ .

TODO Example?

Assume 7% opportunity costs, maintenance costs for $$ options $()$ , $()$

Option 2: Equivalent Annual Cost

Dividing the PVA by annuity factor to get average annual cost in terms of present value.

\text{EAC} = \frac{\text{present value of costs}}{\text{annuity factor}}

Where the annuity factor is the present value annuity factor:

\begin{aligned} \mathrm{PVA} &= C \cdot \frac{1 - \frac{1}{(1+i)^t}}{i} \\ &= C \cdot \frac{1}{i} - \frac{1}{i(1+i)^t} \\ \end{aligned}

EAC Example 1

Two alternatives with annual costs of $(-15, -4, -4, -4)$ and $(-10, 6, -6)$ . Assuming $r = 6\%$ , NPVs are $-25.69$ and $-21.00$ respectively (first value is the initial cost).

Calculating the annuity factor for $r = 6\%$ for three years, we get $\mathrm{PVA} = 1/0.06 - 1/(0.06(1.06)^3) = 2.67$ . We can then divide the NPV by this to get $-25.67/2.67 = -9.61$ .

Repeating with the second option and $r = 6\%$ for two years, we get $-21.00/1.83 = -11.45$ .

Hence, the first option has a lower EAC so should be chosen.

EAC Example 2

25K in maintenance every 10 years. What is the total perpetuity?

Assuming 6.00% rate, we can calculate the equivalent annual cost:

\begin{aligned} \mathrm{PVA} &= \frac{1}{i} - \frac{1}{i(1+i)^t} \\ &= \frac{1}{0.06} - \frac{1}{0.06(1.06)^{10}} \\ &= 7.36 \end{aligned}

So the EAC is $\text{\textdollar}25,\!000/7.36 = \text{\textdollar}3,\!397$ . Using the perpetuity formula, $\text{perpetuity} = C/r = \text{\textdollar}3,\!387/0.06 = \text{\textdollar}56,\!612$ .

EAC Example 3: Replacement Machine

Operating machine costing $12,000 per annum to run with two years of life left. Scrap value will cover the cost of removal.

New machine costs $25,000 and $8,000 per annum to run, will last five years.

Assume OCC is 6.00%.

Options: replace now or in a year.

If replacing now:

\begin{aligned} \text{NPV} &= -25 - 8\left[ \frac{1}{0.06} - \frac{1}{0.06 (1.06)^5}\right] \\ &= -25 - 8 \cdot 4.21 \\ &= 58.70 \end{aligned}

If replacing next year, cost is shifted forwards one year, so $58.70/1.06 = 55.37$ . Add on the cost of operating for the current year to get a total cost of $67.37$ .

If replacing this year, EAC is $58.70 / 4.21 = 13.94$ . If replacing next year, annuity factor is $4.92$ (six years, not five years, at 6%) and hence the EAC is $13.69$ .

Hence, replacing next year is the cheaper option.

NB: can simply by just assuming EAC is $12,000 if not replacing.

EAC Example 4: Replacement Machine 2

Pressure vessel with operating costs of 60K, can operate for five more years. Sell now, can probably get 30K value, sell in five years = zero salvage value.

New pressure vessel costs 120K, can sell for 50K in five years time. Annual operating costs of 30K.

Use MARR of 20%, determine if pressure vessel should be replaced.

Annuity factor for five years at 20%: $\frac{1}{0.2} - \frac{1}{0.2(1.2)^5} = 2.99$ .

Keep: because you did not sell it, you take a 30K ‘loss’, making $\text{EAC} = (-30 -60 * 2.99)/2.99 = -70.04$ .

Buy: $\text{EAC} = \text{NPV}/\text{annuity} = (-120 - 30 * 2.99 + 50/1.2^5)/2.99 = -189.62/2.99 = -63.41$ . The two options are not mutually exclusive: buying the new machine does not necessarily mean you sell the old one, so the 30K from selling the machine should not be considered.

Cost Benefit Analysis (CBA)

Commonly used in public sector projects.

The discounted costs and benefits of a development for all stakeholders over its lifespan must be evaluated.

The CBA assigns values to all direct and indirect outcomes of an independent project with future costs discounted.

Use the benefit-cost ratio (BCR):

\frac{B}{C} = \frac{\text{PV benefits}}{\text{PV costs}} = \frac{\text{FV benefits}}{\text{FV costs}}

If the BCR is greater than 1, the project should proceed (assuming there is no capital rationing - there’s enough money for the project).

Placing dollar values on environmental impacts are difficult
Discount rate needs to be chosen
Cash flow estimates can be flawed
Social costs are difficult to value

Three types of benefits/costs should be considered:

Benefits/costs with monetary values derived from the marketplace (e.g. vehicle operating costs, remediation costs)
Benefits that have been given a standard monetary value (e.g. statistical value of a human life)
Benefits that have not been given a standard monetary value (e.g. cultural, visual, ecological impact)

When considering the BCRs of mutually exclusive alternatives, incremental analysis methods are required.