GHY is a company in a consumer goods industry. GHY$\text{'}$s capital structure is made up of $$1$Mil of short term corporate debt, and $$0\mathrm{.}1M$ of equity. Given a high leverage, the analysts are worried about company's default risk. For simplicity, assume that all the corporate debt has $1$ year to maturity, and is zero$-$coupon. Analysts estimate the default probability to be $10\%,$ and the recovery rate is $40\%.$ The default is believed to be systematic, and the estimated default risk premium is $4\%.$

The current one$-$year spot rate is $1\%.$ Assume annual compounding.

$($a$)$ Compute the expected return, the market price, and the yield on GHY$\text{'}$s corporate

debt. Explain why the yield is not equal to the expected return.

$($b$)$ Compute spread apainst 'Tressury, and Z$-$spread for GHY debt.

$($c$)$ Consider two independent events below $($asume everything else stays the same$).$Compare and contrast their impact on expected return, price, yield, and the corporate spread of the bond. Comment on similarities and differences.

$-$ A spot rate increases by $100$ bp from $1\%$ to $2\%$

$-$ The default risk premium increases by $100bp$ from $4\%$ to $5\%$

$($d$)$ Consider two independent events below $($assume everything else stays the same$).$Compare and contrast their impact on expected return, price, yield, and the corporate spread of the bond. Comment on similarities and differenoes.

$-$ The default probability increases from $10\%$ to $15\%,$ which triggers an increase in the default risk premium to $5\%$

$-$ The recovery rate decrenses from $40\%$ to $10\%,$ which triggers an increase in the default risk premium to $5\%$