The extra gross revenue of £202,800 could be used to increase salaries for staff and cut costs for parents, or 'a combination of the two', the Department for Education says.
For example, the nursery could cut fees for parents by 12 per cent, from £4 an hour to £3.49 and increase salaries.
If the extra revenue were used solely to reduce costs for parents, savings of 28 per cent could be made.
However, in the example given where fees are cut by 28 per cent for parents staff wages would remain the same, except for an increase in the wages of one of the graduates from £16,850 to £33,250.
In the scenario given, the planned changes to ratios would enable a nursery to offer 25 more places, increasing its number of places to 73.
However, the figures are based on an assumption that the nursery is operating at full occupancy with all the places filled on a full-time basis, 39 hours a week 52 weeks a year, and charges £4 an hour.
Most nurseries currently have around 20 per cent of places vacant, National Day Nurseries Association research shows.
The internal analysis by the DfE uses the example of a full-daycare setting which employs 11 full-time staff: three childcare workers and eight supervisory level staff, two of whom are graduates.
The analysis, made in response to a Freedom of Information request, claims that in a scenario where ratios are relaxed for under-threes and the setting moves from a ratio of 1:8 to 1:13 for over-threes, the number of full-time places could be expanded by 73, equivalent to a 52 per cent increase.
Around 60 per cent of the increase in revenue comes from using the 1:13 ratio for three-and four-year-olds with the nursery employing two graduates, it says.
The increase in revenue would also allow the nursery to raise staff wages, so that salaries for three childcare workers would rise from the average of £13,300 in England to the average wage of a French nursery worker, which the DfE says is £16,300.
Pay for six supervisory staff would rise from the average in England of £16,850 to £23,950, the average in France.
Pay for employing the two graduates would rise from £16,850 (the average of a supervisor or manager in England) to £33,250, the equivalent of a qualified primary teacher.
Early years organisations said that the figures were unrealistic and did not reflect the everyday reality of running a nursery.
The DfE itself acknowledges that the example is 'stylised' and that most nurseries do not operate at full child occupancy and that there are 'other constraints.'
It states, 'However, this serves to illustrate how the regulatory framework sets the conditions under which providers operate, with greater flexibility in the adult to child ratios providing considerable potential for expansion and investment.'
Neil Leitch, chief executive of the Pre-School Learning Alliance, said, 'We are appalled by the cynicism of the We are appalled by the cynicism of the Department for Education document. The model they have put forward is so far from reality, I’m surprised they saw fit to publish what reads like a work of fiction.
'Firstly, it relies on the assumption that day nurseries will remain open for 52 weeks of the year, with a 100 per cent occupancy rate. This, quite frankly, is nonsense. The Department itself acknowledges in the small print.'
Mr Leitch also pointed out that the report's economic model assumes that the ratios will be used on an all-day full daycare basis, which is at odds with the Department's More Great Childcare consultation, which states that the staff-to-child ratio for under-twos would 'most likely be for shorter periods of time, rather than for full-day sessions.'
He added, 'The Government’s model also states that the majority of supposed savings would be derived from providers moving from a 1:8 to a 1:13 ratio for three- to four-year-old children. To be clear, this is an option they already have under current law. If providers can benefit from such a substantial increase in gross revenue using ratio flexibility already available to them, why is it that no-one in the sector seems to have done so?
'The fact is that the majority of childcare providers choose not to work to a 1:13 ratio for over-threes because they do not believe it is in the best interests of the children. And for the Government to imply that these supposed savings would come as a result of the new ratios is disingenuous in the extreme.'
Purnima Tanuku, chief executive of the NDNA said, 'Economic models need to be used with care and we will be scrutinising these workings. The Department for education itself says that the model is based on a "stylised example" and the assumptions made to demonstrate savings do not reflect the realities of running a nursery that people on the front line in the sector would recognise. The model assumes full occupancy and full-time use of places by children.
'In reality nurseries currently have on average a fifth or more places vacant and a 'majority of places are used flexibly on a sessional basis by parents.
'The model also makes no allowance for non-contact time for staff, a vital part of good practice to allow for planning, training and working with other agencies - particularly to support children with additional needs. In addition, while we fully agree with the need to support more highly-qualified and better rewarded staff, the model does not address the need to get graduates working with under-threes - as highlighted by Professor Nutbrown in her review of the early years workforce for the Department for Education.'
She added, 'Modelling of provision is a useful exercise. We need a model of early years provision that takes quality of provision as its starting point, focusing first on providing for the right numbers of staff with the right qualifications to meet the needs of children. Any model needs to reflect the real life scenario in nurseries. There has been an overwhelming message from NDNA members that relaxing the childcare ratios is a risk to the quality of care for children. NDNA has been asking Government to stop, rethink and listen to evidence from the sector and academics.'
Anand Shukla, chief executive of the Family and Childcare Trust, said the analysis was helpful but raised questions about the model.
'What would parents actually save?' he said. 'The model assumes a 50 per cent increase in the number of childcare places nationally. If the number of childcare places were to jump overnight by 50 per cent, there would not be the demand to fill the places. Much of the extra money the analysis suggests could be distributed to parents via reduced costs does not in practice exist.'
He added that full occupancy was 'extremely rare', with surveys showing occupancy typically ranging from 70-80 per cent or lower, meaning that potential savings would drop.
'What would the impact of higher capital spending be on costs to providers? A 50 per cent increase in places would almost certainly require one off costs that the analysis does not appear to have factored in. What is the true impact on staff cover requirements of higher ratios? Caring for higher numbers of children has a range of consequences for staff - stress, lunch breaks, sick leave - that increase costs to providers. The analysis does not address these factors.'
He added, 'The overwhelming weight of evidence is that the more time that staff are able to spend with children, the higher the quality of care. Where utilised, the new ratios would significantly reduce the time available for staff to spend with each child. This is particularly important for the youngest children - those up to 36 months - whose welfare and development are closely linked to social interaction with adults and secure attachment relationships with carers.'
Catherine Farrell, joint chief executive, Professional Association for Childcare and Early Years, said, 'For months, both parents and childcare professionals have voiced concerns that changing ratios will damage the quality of care children receive, regardless of the qualification level of staff. In simple terms the more children you have to look after, the less individual attention you can give to them.
'To date, PACEY has not seen any evidence that the proposed changes to ratios will increase quality and continue to maintain that they will have a detrimental effect on the quality of care our youngest children receive.'
She added, 'PACEY also recognise that across the sector, providers are already struggling to deliver Government initiatives due to a lack of adequate funding, therefore any assumption that increased revenues will automatically result in fee reductions is a risky one. Government need to demonstrate more clearly how they intend to deliver a joined up strategy for quality improvement in childcare whilst at the same time tackling childcare costs.'
Claire McCarthy, director of public affairs at 4Children said, 'A realistic calculation on occupancy rates – which tend to be nearer to 75 per cent than 100 per cent, the inclusion of the additional costs associated with taking more children and the requirements of higher Ofsted demands on quality are just some of the things that need to be factored in. None of these are easy calculations given the multitude of delivery models in the sector and regional variation of both costs and fees but given some of these factors it is likely that this estimate is at the top of the likely savings that could accrue to providers.
'Clearly the Government will not base its decisions on a single, theoretical example, so it is important that childcare providers share their analysis on these numbers with the Department for Education to ensure that their decision making is as informed as possible.
'Finally, when making decisions on its response to the More Great Childcare consultation, the Department will need to ensure it furthers its ambition to improve the quality of childcare as well as reduce cost.'