Please explain with the number how to get the spread(%) Assuming a 10% risk-free

Question

Please explain with the number how to get the spread(%)

Assuming a 10% risk-free rate and a USD 110.00 debt due in one year, use the relationship between B, D, and R that we covered when discussing the Merton model to fill in the spread associated with the indicated level of the SPY investment in the table below. The spread values are obtained using the equation relating the risky rate R to the risk-debt value D and the owed amount B of exp(-Rt) = D/B and the relationship between the risk rate, the spread s and the risk-free rate rf of R = rf + s.

Explanation / Answer

exp(-Rt) = D/B, where t=1 and B=110 (i.e. owed amount)

So exp(-R) = D/110, which means R=-ln(D/110)

The spread in each case = R - rf, where rf=10%

So spread = -ln(D/110)-10%

In row 1, D=99.53, which means spread = -ln(99.53/110)-10% = 0%

In row 2, D=91.82, which means spread = -ln(91.82/110)-10% = 8.07%

In row 3, D=50, which means spread = -ln(50/110)-10% = 68.85%

In row 4, D=1, which means spread = -ln(1/110)-10% = 460.05%

Hope this helped ! Let me know in case of any queries.

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