What minimum weighted average coupon does a distressed portfolio needs to achieve if wants to earn a return at least equal to the risk-free rate of 5% after defaults if expects a 25% default rate and a 50% recovery rate on any bonds that do default?

Please refer below

Step-by-step explanation

In this case, 75% of cash flows are not expected to default. Out of the balance 25% that defaults, 50% is recoverable and 50% is irrecoverable. Therefore, the irrecoverable component in total amounts to 12.5% (being 25% of default * 50% irrecoverable defaults)

This means that returns if any, can be earned from 87.5% of the proceeds (being 100% - 12.5%)

If a return of 5% is required, the minimum weighted average coupon to be achieved shall be as follows:

Minimum weighted average coupon = Risk free rate / (Recoverable component of portfolio)

Solving this;

Minimum weighted average coupon = 5% / 87.5%

Minimum weighted average coupon = 5.71429% (rounded off)