Mistakes in the calculations for the Ministry of Defence's plans for new military equipment have left a multi-billion pound black hole, the government's spending watchdog has said.

The National Audit Office (NAO) says in coming up with its 10-year plan to modernise the military, the MoD did not include the price tag of a new fleet of frigates and failed to take into account currency fluctuations between sterling and the dollar.

Other problems besetting the MoD included a failure to include £9.6bn in forecast costs for equipment, a £1bn increase in the cost of replacing Trident submarines and attack boats as well as a lack of clarity on how to save £16bn required. This has led to a black hole of up to £21bn.

Meg Hillier, chair of the Public Accounts Committee, said the MoD "simply doesn't have enough money to buy all the equipment it says it needs".

"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."

Amyas Morse, the head of the NAO, said the MoD needed to take urgent action to deal with the shortfall or delay its purchase of equipment.

"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."

Guto Bebb, defence procurement minister, said: "We aim to use this work to deliver better military capability and value for money in a sustainable and affordable way, and to ensure that defence capabilities complement other national security capabilities in the most effective way," the Times reported.