TERP Calculation: The Theoretical Ex-Rights Price Worked Step by Step

The theoretical ex-rights price is the share price that should prevail immediately after a rights issue, given the price before it and the terms on which new shares are offered. The TERP calculation is a weighted average, and almost every difficulty students have with it comes from applying the weights to the wrong quantities.

A rights issue offers existing shareholders the right to buy new shares in proportion to their holding, at a price below the current market price. The discount is not a gift. It is compensated for by the dilution the new shares cause, and the theoretical ex-rights price is the arithmetic that shows the two cancelling out.

The formula, and what each term means

For an issue of one new share for every N held:

TERP = [(N × cum-rights price) + issue price] ÷ (N + 1)

More generally, where the issue is n new shares for every N held:

TERP = [(N × cum-rights price) + (n × issue price)] ÷ (N + n)

Two definitions carry the whole calculation.

The cum-rights price is the market price while the shares still carry the right to participate. It is the price before the issue, and using a post-announcement price that has already partly adjusted is the most common source of a wrong answer.

The issue price is what a shareholder pays for each new share, set at a discount deep enough to make the offer attractive even if the market falls before the issue closes.

The formula is a weighted average of the two prices, weighted by the number of shares at each. Nothing more complicated is happening.

A worked TERP calculation

A company has 40 million shares trading at £4.50. It announces a 1-for-4 rights issue at £3.00 to raise £30 million.

Step 1 — check the terms. One new share for every four held. With 40 million in issue, 10 million new shares. At £3.00 each, that raises £30 million, which confirms the terms are consistent with the stated proceeds.

Step 2 — apply the formula.

TERP = [(4 × £4.50) + (1 × £3.00)] ÷ (4 + 1) TERP = (£18.00 + £3.00) ÷ 5 TERP = £21.00 ÷ 5 = £4.20

Step 3 — check it by market capitalisation, which is the version worth understanding.

Market value before: 40m × £4.50 = £180m Cash raised: £30m Total value after: £210m Shares after: 50m Price: £210m ÷ 50m = £4.20

The two routes agree because they are the same calculation. The capitalisation version is the one to use when the terms are awkward, and it is the one to show in an exam, because it demonstrates why the answer is what it is.

Why the shareholder is neither better nor worse off

Take a holder of 400 shares who takes up the rights in full.

Before: 400 × £4.50 = £1,800 Buys 100 new shares at £3.00: −£300 cash After: 500 × £4.20 = £2,100

The holding is worth £2,100 against £1,800 plus £300 of cash paid in, so wealth is unchanged. The discount was not a benefit; it was offset exactly by the fall in price from £4.50 to £4.20.

This is the point the calculation exists to demonstrate. A rights issue at a discount does not transfer value to participating shareholders, and the apparent bargain is arithmetic rather than opportunity.

The value of a right, and the shareholder who does not take up

A shareholder unwilling or unable to subscribe is not stranded, because the right itself has value and is usually tradeable.

Value of a right per new share = TERP − issue price = £4.20 − £3.00 = £1.20

Value of a right per existing share = £1.20 ÷ 4 = £0.30

Check it on the 400-share holder who sells the rights instead of taking them up:

Sells rights on 400 shares at £0.30 = £120 Holding after: 400 × £4.20 = £1,680 Total: £1,800

Unchanged again. The shareholder who sells the rights ends up with the same wealth as the one who takes them up, holding a smaller stake and more cash.

Only the shareholder who does nothing at all loses. Their holding falls from £1,800 to £1,680 and they receive nothing for the right they allowed to lapse — which is why companies arrange for unsubscribed rights to be sold in the market and the proceeds remitted, and why the calculation of a right's value is examined as often as TERP itself.

What the theoretical price does not include

The word theoretical is doing real work, and three factors move the actual price away from it.

The signal. A rights issue tells the market something about why the money is needed. Announcements associated with distress produce falls beyond the dilution; those funding an identified acquisition sometimes produce none. The calculation assumes the announcement conveys no information, which is rarely true.

The use of proceeds. TERP treats the cash raised as worth exactly its face value. If the market believes the funds will earn more than the cost of capital, the price settles above TERP; if it believes they will be wasted, below.

Issue costs. Underwriting, advisory and listing fees are real and are not in the formula. Net proceeds are lower than gross, so the theoretical price slightly overstates the outcome.

An exam answer that computes TERP and then notes that the actual price will differ for these reasons is doing what the question generally wants. Computing TERP and asserting the share will trade there is answering a simpler question than the one asked.

A second worked example with awkward terms

Examination questions rarely give round numbers, and the capitalisation route handles the awkward ones without any new formula.

A company has 18 million shares at £2.75 and announces a 3-for-8 rights issue at £1.90.

New shares. 18m × 3/8 = 6.75 million.

Cash raised. 6.75m × £1.90 = £12.825 million.

Value before. 18m × £2.75 = £49.5 million.

Total after. £49.5m + £12.825m = £62.325 million.

Shares after. 18m + 6.75m = 24.75 million.

TERP. £62.325m ÷ 24.75m = £2.5182, or £2.52 to the nearest penny.

Confirm with the weighted-average form: [(8 × £2.75) + (3 × £1.90)] ÷ 11 = (£22.00 + £5.70) ÷ 11 = £27.70 ÷ 11 = £2.5182. The two agree, as they must.

Value of a right per new share is £2.5182 − £1.90 = £0.6182, and per existing share held, £0.6182 × 3/8 = £0.2318.

Rounding is worth a word. Carry the unrounded TERP into the value of a right and round only at the end, because rounding to the penny first and then multiplying by a fraction introduces an error large enough to lose a mark on a calculation this short.

Where the calculation is used outside an exam

Underwriting decisions. The discount determines the probability that the market price falls below the issue price before the offer closes, which is what underwriters are being paid to bear. A deeper discount costs less in underwriting fees and produces a lower TERP, and the trade-off between the two is the practical question the arithmetic supports.

Index and derivative adjustments. Index providers and options exchanges use the theoretical ex-rights price to adjust strike prices and index divisors, so that a rights issue does not create a spurious jump in an index or a windfall for an option holder. The formula is the same one, applied mechanically.

Restating comparatives. Any per-share figure reported across the issue date has to be restated for the bonus element, and the adjustment factor comes from TERP. Earnings per share is the obvious case; dividend per share and net asset value per share are affected equally.

Why companies choose a rights issue at all

The arithmetic shows that the discount confers no benefit, which raises the obvious question of why the route is used.

Pre-emption. A rights issue offers the shares to existing holders first, preserving their proportionate stake and their voting weight. In the United Kingdom this is not merely a courtesy: pre-emption rights are statutory, and disapplying them requires a special resolution, so a placing to new investors needs shareholder permission that a rights issue does not.

Certainty. Underwritten rights issues raise a known sum on a known date, which matters when the money is committed to something.

Cost. For a large sum, a rights issue is usually cheaper than the alternatives per pound raised, because the buyers are already shareholders and require less marketing.

Against those sit the disadvantages the calculation makes visible. The process is slow, taking weeks during which the market can move below the issue price. It signals a funding need, and the market reads the signal. And it asks existing shareholders for cash they may not have, which is why the tradeability of the right matters so much to the fairness of the structure.

Related calculations that use the same figures

Bonus and scrip issues are the degenerate case: the issue price is zero, so a 1-for-4 bonus gives (4 × £4.50 + 0) ÷ 5 = £3.60, with no cash raised and no change in total value.

Earnings per share must be restated for the bonus element in a rights issue, using the TERP-based adjustment factor: cum-rights price ÷ TERP, here £4.50 ÷ £4.20 = 1.0714. Prior-period EPS is divided by this factor so the comparative reflects the same number of shares.

Deep-discounted issues stretch the same arithmetic. A very low issue price produces a very low TERP and a high value per right, and no change in the wealth conclusion — which is the argument for pricing an issue wherever underwriting is cheapest rather than worrying about the optics of the discount.