An emerging economy as a current GDP of $100 billion. It borrows $20 billion at a real interest rate of 5%, which it will repay next year. The costs of default are 25% of GDP. What is the country's repayment threshold level of GDP (i.e., the GDP at which it is indifferent between defaulting and repaying the loan)?

Question

Quizplus · Accepted Answer

The total repayment amount will be $20 billion * (1 + 5%) = $21 billion.
If the country doesn't default, its GDP will decrease by $21 billion to $79 billion ($100 billion - $21 billion). 
Defaulting will cost the country 25% of GDP, which is $25 billion ($100 billion * 25%), so it will only default if the cost of repaying the loan is higher than $25 billion.
Therefore, the repayment threshold level of GDP is $79 billion + $25 billion = $104 billion.
Since the country's current GDP is only $100 billion, it will default. 
To check, we can calculate the costs of defaulting: $100 billion * 25% = $25 billion, which is equal to the cost of repaying the loan. 
Therefore, the country is indifferent between defaulting and repaying the loan at a GDP of $84 billion ($79 billion + $25 billion - $20 billion).

An Emerging Economy as a Current GDP of $100 Billion