The Ministry of Defence could face a shortfall of more than £20bn in its equipment budget over the next decade, according to a National Audit Office report.

The MoD’s financial plan for equipment was unaffordable and did not provide a realistic forecast, according to the report, because the government failed to include a string of costs, including an extra £1.3bn for five Navy frigates.

The NAO said the cost of nuclear-related projects could destabilise the plan because of their size and complexity, noting that costs for the Dreadnought and Astute submarine projects had risen by £941m in one year.

The report will raise further questions about the MoD’s financial management, coming days after analysis of its deal on military housing found up to £4bn had been lost through the sale of property to an offshore private equity fund.

The MoD’s Eequipment plan covers the period from 2017 to 2027, with equipment and associated support projected to cost £179.7bn. The NAO said the department was relying on ambitious savings, and there was “a lack of transparency on the full amount of savings”.

Sir Amyas Morse, the head of the NAO, said: “The department’s equipment plan is not affordable. At present the affordability gap ranges from a minimum of £4.9bn to £20.8bn if financial risks materialise and ambitious savings are not achieved.”

According to the report, the MoD failed to factor in the falling value of the pound, which could result in costs being £4.6bn higher than anticipated. The ministry had also used the wrong exchange rate to calculate costs, using rates that were 24% higher than the dollar exchange rate and 2% higher than the euro rate.

An MoD spokesperson said it assessed exchange rates regularly and had measures in place to minimise the impact of fluctuations.

The NAO said the MoD had limited flexibility to use other budgets to cover the shortfall for equipment, because it had been unable to agree a balanced defence budget last year. As a result, the department was already trying to manage a significant projected overspend.

Meg Hillier, the chair of the public accounts committee, said: “The NAO has found that the Ministry of Defence simply doesn’t have enough money to buy all the equipment it says it needs and is facing a possible affordability gap of nearly £21bn.

“Until the MoD comes up with a realistic plan for funding new equipment, the MoD is bound to end up scrapping or delaying projects haphazardly. This is not a sensible way of looking after our national defence.”

Wayne David, a shadow defence minister, said the lack of budgeting for equipment such as the frigates “beggars belief”.

“You cannot do security on the cheap and it is time for ministers to get a grip and ensure that we have the investment in our nation’s defences that the public rightly expect.”

An MoD spokesperson said the modernising defence programme had just been launched almost £5bn had been saved in “efficiencies”.