To rank the companies from the most likely to the least likely to default, we calculate the Distance to Default (DD) for each company using the formula: $DD = \frac{\ln(A/L) + (\mu - \sigma^2/2)T}{\sigma \sqrt{T}}$

Company X: $A = 800,000$; $L = 500,000$; $\sigma = 25\%$; $\mu = 7\%$; $T = 3$ $Numerator = \ln(800/500) + (0.07 - 0.25^2 / 2) \times 3 = 0.4700 + (0.07 - 0.03125) \times 3 = 0.4700 + 0.11625 = 0.58625$ $Denominator = 0.25 \times \sqrt{3} = 0.25 \times 1.732 = 0.4330$ $DD_X = 0.58625 / 0.4330 = 1.354$

Company Y: $A = 1,000,000$; $L = 600,000$; $\sigma = 20\%$; $\mu = 5\%$; $T = 4$ $Numerator = \ln(1000/600) + (0.05 - 0.20^2 / 2) \times 4 = 0.5108 + (0.05 - 0.02) \times 4 = 0.5108 + 0.120 = 0.6308$ $Denominator = 0.20 \times \sqrt{4} = 0.400$ $DD_Y = 0.6308 / 0.400 = 1.577$

Company Z: $A = 900,000$; $L = 400,000$; $\sigma = 30\%$; $\mu = 6\%$; $T = 2$ $Numerator = \ln(900/400) + (0.06 - 0.30^2 / 2) \times 2 = 0.8109 + (0.06 - 0.045) \times 2 = 0.8109 + 0.030 = 0.8409$ $Denominator = 0.30 \times \sqrt{2} = 0.30 \times 1.414 = 0.4243$ $DD_Z = 0.8409 / 0.4243 = 1.982$

The lower the DD, the higher the probability of default. Ranking them from lowest DD to highest DD (most likely to least likely): Company X (1.354), Company Y (1.577), Company Z (1.982).