Imagine your the person who lent the company money. You lent them £100m. They have assets of £50m. So you could go to court, declare them bankrupt, confiscate the assets, and sell them. It takes time, you have to pay the administrators so you might end up with £40m in a year’s time.
Or Mike might come to you and say “I will pay you 60p for each £1 of debt” this would give you £60m in a month’s time.
If you agree the administration is all agreed before hand so they can go into it, pay the agreed debts and come out of it quickly (to carry on trading).
To you the benefit is getting more money quicker than forcing them into administration, the negative is you don’t get all the money you were owed and other companies that owe you money might want to use it as a precedent for their own debts.
Edit to add:
Regarding the government there are rules on loans written off to connected parties, so if you owned company A and B and A owed B £100m and B wrote it off then B wouldn’t be allowed to include the £100m write off as an expense when calculating their taxable profits.
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