Interest calculations for PE instruments

The basic formula

All interest accrual on PE instruments — whether a shareholder loan or a preference share coupon — starts from the same foundation. For any period, interest is calculated as:

Each component has a precise meaning:

• Principal — the outstanding balance on which interest accrues. For a simple shareholder loan this is the original subscription amount. For a compounding instrument it increases over time as capitalised interest is added to the principal.
• Rate — the annual interest rate expressed as a decimal (e.g. 12% = 0.12). For variable-rate instruments the applicable rate may differ from one period to the next.
• Days — the actual number of calendar days in the period being calculated. This is counted from (and including) the start date up to (but not including) the end date, following standard financial market convention.
• Day Basis — the assumed number of days in a year used to normalise the rate. This is the source of the three principal day-count conventions described below.

Day-count conventions

The day basis is not a fixed number — it depends on the convention agreed in the instrument's legal documentation. The three conventions most commonly seen in European PE structures are Act/365, Act/360 and 30/360. The table below compares them:

The practical effect is that Act/360 produces slightly more interest than Act/365 for the same nominal rate and period — the denominator is smaller, so each day's accrual is larger. Over a £10m position held for several years, this difference is material.

Worked example: Q1 under each convention

Principal: £10,000,000. Annual rate: 12%. Period: 1 January to 31 March (Q1), which is 90 actual calendar days (31 Jan + 28 Feb + 31 Mar).

In this particular quarter Act/360 and 30/360 coincide because Q1 happens to contain exactly 90 days (3 months × 30 days = 90). The conventions diverge in months of 28, 29 or 31 days: Act/360 always uses the real day count, whereas 30/360 normalises each month to 30 days.

Simple vs compound interest

Simple interest accrues on the original principal only. Each period's interest is calculated on the same base amount; it does not itself earn interest. Simple interest is sometimes used for short-dated instruments or bridging positions.

Compound interest — the standard for PE shareholder loans and preference share coupons — works differently. At the end of each compounding period (typically the anniversary of the investment), the accrued interest is capitalised: it is added to the principal, and future interest is then calculated on this higher balance. This is the PIK (payment-in-kind) mechanic that drives the step-up in instrument value over the holding period.

The worked example below shows a £5,000,000 shareholder loan at 10% per annum, Act/365, compounding annually over three years:

Under simple interest the three-year total would be exactly £1,500,000 (£500,000 × 3). Compounding adds an additional £155,000 — the interest earned on previously capitalised interest. Over a typical five-to-seven year PE holding period, this compounding effect is a significant contributor to the total instrument value at exit.

Note that in practice, interest accrues daily throughout the year and is calculated and capitalised on each anniversary of the investment date, not on a fixed 31 December. This means intra-year accruals must be computed using the daily formula above, with the full annual amount capitalised on the anniversary.

Per-period rounding

The reason this matters is that floating-point arithmetic can produce fractional penny differences that compound invisibly over dozens of quarterly periods. Rounding once at the end — rather than per period — produces a total that does not agree with the sum of the individual line items that have been posted to the books.

Consider a simple illustration. An instrument accrues £333.333... of interest in each of three equal periods:

The one-penny difference is trivial here, but it breaks the audit trail: the three posted journal entries sum to £999.99, yet a round-at-end calculation says £1,000.00. Over a portfolio of 20 instruments accruing quarterly for six years, these discrepancies accumulate and create reconciliation work at every reporting date. Per-period rounding eliminates this entirely — the sum of all posted entries always equals the reported total.

Variable rates

Some instruments do not carry a fixed rate throughout their life. A shareholder loan may specify a base rate (such as EURIBOR or SONIA) plus a margin, or the fund documentation may provide for a step-up in rate after a defined period — for example, 8% for years one and two, rising to 10% thereafter.

Where rates vary, the instrument's life must be divided into windows, each with its own applicable rate. Each window is calculated independently using the formula above, and the results are summed. It is not valid to apply an average rate to the full period, because the per-period rounding step must be applied at the correct rate for each window separately.

In practice this means the calculation engine must hold a rate schedule for each instrument — not merely a single rate — and must correctly identify which rate is in force for any given calculation date. Errors here are a common source of discrepancy between a fund administrator's model and the legal instrument terms.

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