Haute Lumière

Commerce · III.05 · MMXXVI · daylight

La Bourse  /  Volume III  /  Nº III.05  /  Workbook — the executive

WORKBOOK — THE CORPORATE EXECUTIVE

Chapter III.05 · Interest, Time, and the Discount Rate

For the person who signs the capital paper. The premise is commercial and it is not softened: your organisation is almost certainly using one discount rate for two economically different classes of asset, and the arithmetic of that mistake is large enough to show up in your results.

---

THE PREMISE, STATED COMMERCIALLY

Three claims, each of which can be checked against your own numbers inside a month.

One. Your hurdle rate has no published construction. Ask the question in your next finance meeting and time the silence. The rate was set by somebody who has probably left, adjusted once for a bond issue, and carried forward. It is the most load-bearing parameter in your capital process and the only one that has never been through a review.

Two. Your horizon is set by a lease, a tenure or a budget cycle, and it is doing more damage than the rate. The rate gets all the attention. The horizon decides most of the outcomes. Both belong on the front page of the paper.

Three — and this is where the money is — you apply a pro-cyclical rate to counter-cyclical assets. Your hurdle rate embeds an equity risk premium. It is correct for a project that does well when the business does well. It is wrong, by construction, for an asset whose entire return is that it pays in the years you are having your worst results. Every protective, resilience and regenerative asset in your portfolio is in that second class, and every one of them has been appraised with the first class's rate. You have been systematically declining to buy insurance while simultaneously buying insurance, and the two decisions have never been on the same page.

None of this requires a new belief about the environment. It requires two rates instead of one, a published risk tolerance, and three extra lines on an appraisal form.

---

PART ONE — DISCOVERY

Days 1–30

Exercise 1.1 — The rate archaeology (one week, with your controller)

Establish four things and write them on one page.

Then write the rate as delta + eta · g even though it was not built that way. Working backwards from 11 or 12 percent to a pure time preference, a growth assumption and a risk premium is instructive precisely because the residual is large. The residual is the part nobody can defend, and naming its size is the whole of the first thirty days.

Exercise 1.2 — The counter-cyclical sweep (one week)

Go through the asset register and the last three capital plans and mark every item whose payoff is largest when results are worst. Candidates, in the order they usually appear:

1. Anything that reduces an insured loss — flood defence, fire suppression, water security, redundancy in a single-source supply.
2. Anything that reduces the variance of an input cost — on-site generation, long-term supply agreements, soil and watershed condition, storage.
3. Anything that shortens a recovery — spares, dual sourcing, cross-training, documented process.
4. Anything that reduces a regulatory or reputational tail.

For each, ask the evidentiary question rather than the intuitive one: in our own history, did this category's value rise in the years our results fell? Three cycles of data is enough to answer it. Where the data exists, you now have a beta estimate that came from your own accounts and will survive a challenge.

Exercise 1.3 — The insurer conversation (one meeting)

Your insurer and reinsurer already do this arithmetic professionally, every year, with money at stake. Ask your broker for the current submission: the modelled probability, the loss given event, and the premium for the layer. That document is the cleanest baseline available to you, because it was written by a counterparty with no incentive to flatter you.

Then ask the question that opens the whole instrument: what would we have to do physically to move this premium, and by how much? Underwriters answer this question readily. Almost nobody asks it.

---

PART TWO — THE ARITHMETIC

Days 31–50

Exercise 2.1 — The sensitivity that protects you (half a day)

Build the Ramsey table for your organisation. Hold your growth assumption fixed, vary delta across 0.1, 0.5, 1.0 and 1.5 percent and eta across 1.0, 1.5 and 2.0, and compute the present value of a £1m benefit at years 25, 50 and 100 in every cell.

The chapter's version, at g = 1.5 percent and year 100, runs from £204,470 to £12,257 — seventeen-fold across parameters nobody could call unreasonable. Yours will be similar.

Put three cells on the front page of every long-horizon paper, permanently: a central case and two adverse. A board that has seen the range once will never again accept a single number, and that is a durable improvement to your capital process obtained for the cost of one afternoon.

Exercise 2.2 — The two-rate policy, computed (one day)

Establish two published rates.

• The hurdle rate, for pro-cyclical revenue projects. Your existing WACC, now with a written construction.
• The protective rate, for counter-cyclical assets: r_f + beta · premium. With a risk-free rate of 2 percent, a market premium of 5 points and a beta of −0.3, that is 0.5 percent. At −0.5 it is −0.5 percent, and a pound in year fifty is then worth £1,284,831 per million — more than a pound today.

That last sentence will be the hardest to get through a finance committee and it is exactly correct. It is what a premium has always meant, written as a rate.

Take the sign of the beta from the theory and the size of the premium from a market that prices this risk — your own reinsurance quote, a catastrophe bond spread, a parametric premium. The consumption-CAPM's own estimate of the premium is 0.060 percentage points against an observed equity premium near six, which is Mehra and Prescott's puzzle of 1985 and the reason nobody should calibrate this from theory alone.

Exercise 2.3 — The three-line appraisal (one week)

Amend the capital appraisal template. Three new lines, mandatory:

Work the chapter's case to see the size of what you have been omitting. A plant loses £8.0m in a drought year with probability 0.15: expected loss £1.20m, variance 8.1600. A watershed restoration takes the probability to 0.12 and the loss to £3.0m: expected loss £0.36m, variance 0.9504. Mean saving net of operating cost, £0.64m. Variance removed, 7.2096. At a risk tolerance of £6.67m the certainty equivalent is £0.5407m a year — 84 percent as much again as the entire expected saving, and it currently appears on no line of your management accounts.

Exercise 2.4 — The reversal, and the honest caveat (2 hours)

Run the same project three ways over twenty-five years and put all three in the paper:

  mean only, at the 10% hurdle                        PV 5.81    NPV  -0.19
  mean only, at 3.5%                                  PV 10.55   NPV  +4.55
  mean at 0.5% risk-adjusted, plus variance at 2.0%   PV 25.56   NPV +19.56

Then shorten the horizon to ten years — the lease expires — and run it twice more: variance priced, NPV +£5.08m; mean only at 3.5 percent, NPV −£0.68m.

Two competent analysts, one project, opposite recommendations, and neither has done anything dishonest. Put that sentence in the paper. A board that has been shown the sensitivity of the method trusts the method; a board that discovers it later does not.

---

PART THREE — DESIGN

Days 51–70: the instrument

Exercise 3.1 — Draft the resilience facility (one week, with treasury)

Not a green bond. A facility that funds regenerative capital expenditure and is repaid out of the measured reduction in the cost of carrying the risk.

Exercise 3.2 — The audit and accounting conversation (one meeting, early)

Three treatments, and they must not be double-counted:

1. Insurance premium falls — operating expense, visible immediately.
2. Retained-loss provision falls — under IAS 37 this releases through the profit and loss account. Agree the release profile with your auditors in advance.
3. Certainty equivalent of the variance removed — not booked anywhere. It belongs in the appraisal and nowhere else. Say so explicitly in the paper, in those words, so that nobody later accuses the analysis of inventing income.

Capitalise the restored asset and depreciate over its regenerated life. Under IFRS S2 the resilience narrative and its quantified financial effects are now disclosable, which gives this arithmetic an external audience for the first time. A number that must be disclosed is a number that gets built.

Exercise 3.3 — Set the risk tolerance as a board parameter (one board meeting)

This is the single most important governance act in the chapter. Publish 1/a — the variability in a year the organisation is genuinely willing to carry — once, as policy, with a date and a review. Set it the way you already set an insurance retention, because it is the same quantity.

If each analyst chooses a, the method has a free parameter and will be gamed within two cycles. If the board owns it, the method has a constraint and becomes credible. This is the difference between a technique and a control.

---

PART FOUR — DESTINY AND DELIGHT

Days 71–90

Exercise 4.1 — The symmetry rule, written into policy (one paragraph)

Add one sentence to treasury policy: the same discount rate applies to liabilities as to benefits, in the same paper, always.

Show the board why. A £1bn decommissioning duty falling in year 100 requires a provision of £1.2m at 7 percent, £32.1m at 3.5 percent and £249.0m at 1.4 percent — two hundred and sixteen times more. Any team arguing a low rate for its project has argued it for the clean-up. That paragraph is what prevents the rate becoming the place every disagreement is quietly settled, which is the documented failure mode of every rate policy ever written.

Exercise 4.2 — Into the standing pack (one conversation)

Two numbers into the monthly pack: the variance of the operating cost line you are trying to reduce, and the current premium for the layer. Anything reviewed monthly persists. Anything reviewed by exception evaporates.

Exercise 4.3 — The second owner (before you need them)

The natural second owner is the risk function or the insurance manager, not the sustainability function. Their mandate already is variance, they already hold the loss model, and their credibility with the audit committee is already established. Recruit them by giving them the credit for the first result.

Exercise 4.4 — The board paper (day 90)

Title. One line, commercial. "Resilience facility: 24.4 percent on premium and avoided loss, £6.0m, repaid from the insurance line." Not "Nature-based solutions pilot."

1. The number. The decision inequality, computed, first paragraph.
2. The rate and the horizon. Both, together, on the front page.
3. Three cells of the sensitivity table.
4. The baseline. Probability, severity, premium — signed, by whom, when.
5. The structure. Facility, trigger, repayment, reversion, security.
6. What would make this fail. Three, honestly. This paragraph is why you will be believed.
7. The symmetry statement. The same rate applied to our own long-dated liabilities, with the number.
8. At ten times. One paragraph.

Length: two pages. If it is longer you have not decided what matters.

Exercise 4.5 — Delight, for a firm (ongoing)

The pleasure here is specific and worth naming because it is what makes the practice spread: the meeting where the rate is finally said out loud and a number that had been weather becomes a decision. Let the person who did the archaeology present it. They will not forget it, and neither will the room.

---

THE FAILURE MODES, NAMED

The rate becomes a lever. People discover that arguing the rate down is easier than arguing the benefit up. Defence: the symmetry rule, in policy.

The risk tolerance drifts. Each analyst picks a to suit the answer. Defence: board-owned parameter with a review date.

The horizon quietly shortens. A five-year template default kills thirty-year assets silently. Defence: horizon on the front page, justified from the asset rather than the calendar.

Double counting. Premium reduction, provision release and certainty equivalent all claimed as income. Defence: the three-treatment paragraph, agreed with audit before the first paper.

The beta is asserted rather than evidenced. Defence: three cycles of your own data, or say plainly that you could not find any and use zero.

---

THE NINETY DAYS ON ONE PAGE

---

APPRECIATIVE QUESTIONS FOR YOUR LEADERSHIP TEAM

1. Where have we already paid for something that only mattered in a bad year, and what made that decision possible at the time?
2. Which of our assets has demonstrably reduced how much our results move about?
3. What does our insurer know about our risk that our capital process does not use?
4. Where did we last approve a long-lived asset, and what rate and horizon did we use?
5. If every long-horizon paper carried three rates and a stated horizon, what would we approve next year that we would not approve this year?
6. What would it be worth to us to have our worst year be less bad, expressed as a number we would be willing to publish?
7. Who is the one signature that makes the two-rate policy real, and what do they need to see?
8. Which of our liabilities would we accept at the same low rate we want for our best project?
9. What would have to be true for the sensitivity table still to be in the template when everyone in this room has moved on?
10. What is the first sign we would see if the rate had become a negotiating position, and who would notice first?
11. Where are we currently reporting the liquidation of an asset as operating income?
12. If the operating unit kept the whole benefit after repayment, what would they attempt that they will not attempt today?