The business case practice II: investment appraisal

Lesson 2 compared Ridgeline Water's options on weighted criteria and found that the result depended on how much the organization valued the benefits. Investment appraisal answers that question in money. It compares the costs and benefits of each option over time, so that the board can see which option offers the best value and how confident it can be in that answer. PRINCE2 does not prescribe a particular appraisal method; it expects the business case to include an appraisal suited to the organization and the decision. This lesson applies the common methods to the running example. FIN-201 covers the finance in more depth, including the theory behind discount rates and the cost of capital.

Costs and benefits over time

An appraisal starts with a table of cash flows for each option, year by year, measured against the do nothing baseline. Costs include the project costs and the ongoing costs of operating and maintaining the outputs. Benefits are the measurable improvements expressed in money where that is reasonable. Some benefits, such as customer satisfaction, are hard to convert to money; they should still be recorded and measured, and lesson 4 discusses how.

The figures show a typical pattern. The cheaper option starts saving sooner but saves less; the more expensive option takes a year longer to install and starts paying back later, but its larger annual benefit may outweigh the higher cost over the life of the assets. Investment appraisal makes this trade-off explicit. The appraisal period should match the useful life of the main assets, here about 15 years for the meters.

Simple payback

Payback is the time it takes for cumulative net benefits to recover the initial cost. It is easy to explain and is a useful measure of liquidity and exposure: a short payback means the money is at risk for less time. Its weaknesses are that it ignores benefits after the payback point and ignores the time value of money.

The time value of money and net present value

A dollar received in ten years is worth less to an organization than a dollar today, because money today can be invested or used to avoid borrowing. Discounting converts future cash flows into their present value at a chosen discount rate. The net present value (NPV) of an option is the sum of its discounted cash flows. A positive NPV means the option creates value at that discount rate; between options, a higher NPV is preferred if risks are similar.

Here \(C_t\) is the net cash flow in year \(t\), \(r\) is the discount rate and \(n\) is the final year of the appraisal. The discount rate is usually set by the organization, not by the project. Utilities and other public bodies often use a lower rate than private companies, and governments publish rates for public appraisals.

In Canada, the Treasury Board's Policy on Cost-Benefit Analysis, used for federal regulatory proposals, has long specified a real discount rate of 7 % as the base case, with sensitivity analysis at other rates. Provinces and municipalities set their own rates for capital decisions; a municipal utility might use its borrowing rate or a rate set by council. Check the current policy before relying on any figure.

Ridgeline Water's finance department has told the project to use a real discount rate of 5 % for its base case and to test 7 %. The code below computes NPV, a benefit–cost ratio and payback for both options.

def npv(rate, flows):
    return sum(cf / (1 + rate) ** t for t, cf in enumerate(flows))

def payback(flows):
    cum = 0.0
    for t, cf in enumerate(flows):
        prev = cum
        cum += cf
        if cum >= 0 and t > 0:
            return t - 1 + (-prev / cf)
    return None

years = 15
# incremental cash flows against do nothing, $000
dmin = [-4200] + [520 - 60] * years
dsom = [-5000, -4600] + [1420 - 180] * (years - 1)
for name, f in [("do minimum", dmin), ("do something", dsom)]:
    pv_costs = -sum(cf / 1.05 ** t for t, cf in enumerate(f) if cf < 0)
    pv_ben = sum(cf / 1.05 ** t for t, cf in enumerate(f) if cf > 0)
    print(f"{name:13} NPV@5% {npv(0.05, f):6.0f}  NPV@7% {npv(0.07, f):6.0f}  "
          f"BCR {pv_ben / pv_costs:4.2f}  payback {payback(f):4.1f} yr")

do minimum    NPV@5%    575  NPV@7%    -10  BCR 1.14  payback  9.1 yr
do something  NPV@5%   2309  NPV@7%    836  BCR 1.25  payback  8.7 yr

At 5 %, the smart-meter option has an NPV of about 2.3 million, four times that of the drive-by option, and a benefit–cost ratio of 1.25 against 1.14. At 7 %, the drive-by option's NPV falls to roughly zero while the smart-meter option still shows about 0.8 million. On these figures, do something is preferred at both rates. The payback periods are similar, about 8.7 and 9.1 years, which shows why payback alone would not distinguish the options well.

Internal rate of return

The internal rate of return (IRR) is the discount rate at which an option's NPV is exactly zero. It is often quoted because it is a single percentage that can be compared with the organization's required rate. For the smart-meter option the IRR is about 8.4 %; for the drive-by option it is about 7.0 %. Both exceed the 5 % base rate, so both have positive NPVs at that rate. IRR has known pitfalls: options with unusual cash flow patterns can have several IRRs, and IRR does not show the scale of value created. When options are mutually exclusive, NPV at the organization's rate is the safer basis for choice.

Sensitivity analysis

Every figure in an appraisal is a forecast, and some forecasts matter more than others. Sensitivity analysis changes one assumption at a time to see how much the result moves. It identifies which assumptions the decision really rests on, so that the board can focus scrutiny and risk management there. A related idea is the break-even value: how far an assumption can move before the option stops creating value.

def npv(rate, flows):
    return sum(cf / (1 + rate) ** t for t, cf in enumerate(flows))

base = {"reading": 380, "billing": 150, "leaks": 640, "energy": 250}
op_cost, capex = 180, [-5000, -4600]

def flows(ben, capex=capex, delay=0):
    net = sum(ben.values()) - op_cost
    return capex + [0] * delay + [net] * (14 - delay)

print("case                         NPV@5% ($000)")
print(f"{'base':28} {npv(0.05, flows(base)):8.0f}")
low = dict(base, leaks=base["leaks"] * 0.5)
print(f"{'leak benefit halved':28} {npv(0.05, flows(low)):8.0f}")
print(f"{'capital cost +20 %':28} {npv(0.05, flows(base, [c * 1.2 for c in capex])):8.0f}")
print(f"{'benefits start 1 yr late':28} {npv(0.05, flows(base, delay=1)):8.0f}")
print(f"{'all benefits -20 %':28} {npv(0.05, flows({k: v * 0.8 for k, v in base.items()})):8.0f}")
lo, hi = 0.0, 1.0
for _ in range(50):
    mid = (lo + hi) / 2
    if npv(0.05, flows({k: v * mid for k, v in base.items()})) < 0:
        lo = mid
    else:
        hi = mid
print(f"break-even benefit level: {hi:.0%} of forecast")

case                         NPV@5% ($000)
base                             2309
leak benefit halved              -708
capital cost +20 %                433
benefits start 1 yr late         1184
all benefits -20 %               -368
break-even benefit level: 83% of forecast

The results are sobering. The option survives a 20 % capital cost overrun and a one-year delay in benefits, but it turns negative if the leak saving is only half what is forecast, or if all benefits come in 20 % low. The break-even point is about 83 % of forecast benefits, which leaves little margin. The leak saving is the largest single benefit and the one most dependent on customers acting on alerts, so it is where the board should focus. Possible responses include a pilot in one district to measure leak savings before full rollout, or staging the rollout so that later stages can be stopped if the benefit does not appear.

This is where the business case connects to the plans and organizing practices. A pilot stage changes the plan; tight cost tolerance shapes the stage plans; and the benefit owners named by the senior user become accountable for the leak saving. Investment appraisal is not an end in itself; it tells the project where its control effort will matter most.

Risk-adjusted appraisal

Sensitivity analysis changes one thing at a time. A risk-adjusted appraisal weighs scenarios by their likelihood. In the simplest form, the expected NPV is the probability-weighted average of scenario NPVs. Suppose the board judges a 60 % chance that the base case holds and a 40 % chance that the leak saving is only half the forecast. The expected NPV is then 0.6 × 2,309 + 0.4 × (−708) ≈ 1,102 thousand.

An expected NPV of about 1.1 million is still positive, but the 40 % chance of a loss matters to an organization that cannot absorb one easily. Expected value does not capture the organization's appetite for risk, which is why PRINCE2 links the business case to the risk practice and to the risk appetite set by the business layer. PRIN-131 covers risk in detail.

Non-financial benefits and qualitative factors

Not everything can sensibly be converted into money. Ridgeline Water's smart meters may improve customer trust, support water conservation targets and give planners better data. These benefits should still appear in the business case with measures, even if they are not in the NPV. Equally, some dis-benefits, such as privacy concerns about detailed consumption data, are qualitative. The board must weigh them alongside the numbers. A business case that presents only an NPV hides judgments that the board should make openly.