Formula

Fairhold separates the value of the house from the value of the land, and applies a discount to the land only. The Fairhold discount formula is used across both Fairhold Land Purchase and Fairhold Land Rent tenures.

Under Fairhold Land Purchase, the discount formula is applied directly to residual land value.

As for Fairhold Land Rent, the discount formula is applied to the imputed land rent portion of market rent.

Land value calculations

Residual land value

In the Fairhold Land Purchase model, the land is purchased upfront for a discounted price.

To calculate that price, we first work out the market value of the land (what it would cost if it didn’t have any buildings on it). That is called a residual land value calculation and is as follows:

Market value of the land = Market property price - development cost of a typical equivalent new building

Market property price is derived from the Land Registry Price Paid dataset. Outliers (first and last quartiles) have been removed to arrive at more accurate estimates for 'average' house prices in an area. The original dataset includes house type (eg flat, terrace, semi-detached or detached), but _does not_include number of bedrooms (in contrast to our private rental data and the social rent formula, which both do). We thus apply a weighting, determined by house type, to the house price to adjust for this. These figures are based on David Wilson Homes estimates for average house sizes by type.

Development cost of a typical equivalent new building is calculated using CostModelling's construction price estimates multiplied by the building's estimated square metrage, mapped from the number of bedrooms:

    1: 55,
    2: 70,
    3: 95,
    4: 110,
    5: 125,
    6: 135

Residual land value is arrived at by subtracting the development cost from the market property price.

Negative land values

Residual land value calculations may lead to negative land values in areas where housing costs are lower than the development cost of an equivalent home. So for instance, in an area where the average cost of a home is £100k and build costs £200k, that is a residual land value of -£100k.

For Fairhold purposes, as we cannot further discount an ostensibly negative land value, it will be treated as £1.

Rent

Market rent figures come from the Private rental market summary statistics in England ONS dataset, tables 2.3-2.6.

Imputed land rent is calculated by multiplying market rent by the same land value ratio (of residual land value to market property price).

The Fairhold formula

Land cost (either residual land value or imputed land rent) is discounted by a Fairhold multiplier, calculated using the following formula:

discount = 1 - max(multiplier * affordability + offset, plateau)

Affordability is calculated as what percentage of household income monthly housing costs take up. Median gross disposable household income data comes from IFS Median household incomes by region (2024) and is available at an ITL1 level.

So for market purchase (used to infer discount for Fairhold Land Purchase), that is monthlyMortgage / monthlyIncome, with the mortgage terms also assumed as constants: interest rate 6%, mortgage term 30 years, deposit 15%.

For market rent (used to infer discount for Fairhold Land Rent), affordability is similarly calculated as monthlyRent / monthlyIncome.

The multiplier, offset and plateau are constants:

multipler = -1.1
offset = 0.7
plateau = 0.15

Using affordability as in input means that the less affordable housing is in an area, the greater the discount.

The use of a max formula and plateau means that the discount will never exceed 85% off, and this would only be in areas where housing is highly unaffordable.