The alternative land pricing mechanism proposed in this study seeks to address key issues that cause informal settlement including disparities between household income and land prices, transportation costs and tenure arrangements.
6.3.1 Derivation of the Formula to Calculate Affordable Land Price
Say a mortgagee borrows an amount ‘P’ at a monthly interest rate of ‘i’ and pays back the loan in monthly instalments ‘M’ in ‘n’ number of months.
The current monthly interest ‘H’ is calculated using H = Pi. The amount of the principal loan a mortgagee pays for the month is calculated using C = M – H. The new balance of the principal of the loan is calculated using Q = P – C. The study set P = Q and also set the affordable price of urban land
163 at a benchmark of 30 per cent of monthly mortgage repayment. An affordable land price is calculated using ALP= 0.3M.
For the first month n = 1:
H = Pi C = M – Pi
Q = P –
(
M – Pi)
= P + Pi – M = P
(
1 + i)
– M For the second month n = 2:H = Pi
(
1 + i)
– MiC = M –
(
Pi(
1 + i)
– Mi)
Q = P
(
1 + i)
– M –(
M – Pi(
1 + i)
– Mi)
= P
(
1 + i)
– M – M + Pi(
1 + i)
+ Mi = P(
1 + i)
2 – M(
1 + i)
– MFor the third month n = 3:
H =
(
P (1 + i)
2 – M(
1 + i)
– M)
iC = M –
(
Pi(
1 + i)
2 – Mi(
1 + i)
– Mi)
Q = P
(
1 + i)
2 – M(
1 + i)
– M –(
M – Pi(
1 + i)
2 – Mi(
1 + i)
– Mi)
= P
(
1 + i)
2 + Pi(
1 + i)
2 – M(
1 + i)
– Mi(
1 + i)
– M + Mi – M= P
(
1 + i)
3 – M(
1 + i)
2 – M(
1 + i)
– M [Equation #1]After ‘n’ number of months:
Q = P
(
1 + i)
n – M(
1+i)
n-1 – M(
1 + i)
n-2 – … – MWhere M
(
1 + i)
n-1 – M(
1 + i)
n-2 – … – M is a Geometric series with a first term – M and a common ratio(
1+i)
.Let one digress and consider the Geometric series:
164 Where r = is the common ration
(
1 + i)
a = is the first term – M n = is the number of terms One knows that:
Tn = arn -1
So assuming r is greater than 1, the sum of the series is expressed as:
Sn = a
(
1 – rn) (
r –1)
From P
(
1 + i)
3 – M(
1 + i)
2 – M(
1 + i)
– M one knows that M(
1 + i)
2 – M(
1 + i)
– M is a Geometric series with first term a = – M and r =(
1+i)
and greater than 1.Thus, the sum of this series is equal to:
Sn = a
(
1 – rn) (
r –1)
= – M
(
1 + i)
n – 1(
1 + i)
– 1= – M
( (1 + i)
n – 1)
[Equation #2]
i So
Q = P
(
1 + i)
n – M( (1 + i)
n – 1)
i
Now substitute – M
( (1 + i)
n – 1)
into P (
1 + i)
3 – M (
1 + i)
2 – M (
1 + i)
– M and set Q = 0,
i
The reason why the study set Q equal to zero is that when the mortgagee finishes paying the loan Q, the balance is reduced to 0.
So,
0 = P
(
1 + i)
n – M( (1 + i)
n– 1)
i
165 Solving for M, one gets
M
(
1 + i)
n –1 = P(
1 + i)
ni
M
(
1 + i)
n –1 = Pi(
1 + i)
n
M = Pi
(
1 + i)
n(
1 + i)
n – 1M = Pi
[Equation #3]
1 –
(
1 + i)
–nSo from [Equation 3], with the monthly mortgage repayment set at the affordability benchmark of 30 per cent of monthly household income, the study assumes that the price of land ought to be set also at an affordability benchmark of 30 per cent of monthly mortgage repayment. Thus, the price of urban land ought to be equal to 0.09 per cent of monthly household income. The formula for determining the annual repayment cost for affordable urban land based on 0.09 per cent of the annual household gross income is expressed as:
ALP = 0.09
y (1 – (
1 + i)
–n)
[Equation #4]
i
Where ALP = Affordable land price y = Gross household income i = Interest rate
n = Term of loan
If the intense demand for land in inner-city areas is contributing to rising prices for housing and limiting housing affordability among low-income households, it could be ideal to rescale the pricing mechanism of urban land. However, before rescaling the pricing mechanism of urban land it is important to know its market. Hence, the study determines the market value of the land occupied by the informal settlement on Lacey Road using the Comparative Method of valuation. The researcher derives the market value of the land using comparative values of residential properties in Sydenham, the township where the informal settlement on Lacey Road is located. An inspection of the land valuation register of eThekwini Municipality reveals that in Sydenham the value of a 200m2 plot is on average about R2,475 per square metre. The study prefers to use a 200m2 plot of land because it is the minimum size for a standard residential plot in South Africa.
166 It is difficult to derive the value of land occupied by an informal settlement by subtracting the construction cost from the value of the house and dividing by the size of the plot of land to obtain a per-square metre value of the land that is implied in the price of the house. Hence, the study conducted its own valuation of the land because an inspection of the land valuation register of eThekwini Municipality revealed that some land parcels that are part of the land occupied by the informal settlement on Lacey Road are not assigned a value because they are owned by the municipality. To cover this information gap, the researcher tasked valuation professionals from Rawson and the Real Estate Department of the municipality to derive a market value of the land. The valuation professionals estimate the value of the 2.37ha plot of land occupied by the informal settlement on Lacey Road at R49,177,500. Thus, it implies that on average a 200m2 plot of land cost about R415,000 or R2,075 per square metre, which makes this land unaffordable to low-income households in the settlement.
For purposes of comparison, the researcher uses the proposed pricing mechanism to determine a fair value for the land. Households in the informal settlement on Lacey Road that earn incomes between R38,400 and R76,800 can afford a mortgage for a house costing R140,000 at interest rates between 6 to 8 per cent as shown in Tables 5.26 and 5.27. For a house costing R140,000, the annual mortgage repayment is R10,952. Thus, the pricing mechanism proposed in this study sets the price of a 200m2 plot of land at R82,140 or R411 per square metre. The affordable price of this plot of land set at a benchmark of 30 per cent of the mortgage is calculated as follows:
ALP = 0.3M x 25 = 0.3 x R10,952 x 25 = R82,140
The land values calculated using this mechanism demonstrate that if the price of land is set at a benchmark of 0.09 per cent of income, it is more affordable to the urban poor. The market value of R2,075 per square metre for the plot of land occupied by the informal settlement on Lacey Road is 505 per cent more than the price calculated using the mechanism proposed in this study. The results of this research study demonstrate that it is possible to deliver AURL for low-income housing if the land price is scaled at a benchmark of 0.09 per cent of income. Hence, a 2.37ha plot of land if developed at a density of 50du/ha would yield 118 plots, each plot measuring 200m2; a yield that is adequate to accommodate 73 per cent of the households in the informal settlement on Lacey Road.
Based on these results, the mechanism could be strengthened through the following recommendations.
167 The study used its proposed pricing mechanism to deduce the affordable price of urban land. The model proposed in this study set the price of a 200m2 plot of land at R82,150 or R411 per square metre. The model proved that if land is priced at the benchmark of 0.09 per cent of income, it is affordable to the urban poor. The market value of R2,075 per square metre for the plot of land in Lacey Road for example, is 500 per cent more than the price proposed by this model. The results of this research study prove that it is possible to deliver AURL for low-income housing if the land price is scaled at a benchmark of 0.09 per cent of income. Thus, the study discovered that the first part of the interlinked hypotheses which states that pricing residential land in inner-city areas at a benchmark of 0.09 per cent of monthly household income ranging between R3,500 and R7,500 can improve overall housing affordability in eThekwini municipality, is accurate.