Question $3(20$ marks$)$

You have been engaged by Alpha Corp. as a financial analyst to assist in determining their Weighted Average Cost of Capital $($WACC$).$ Your analysis relies on the following data points:

Debt: The corporation's outstanding, noncallable bonds have $15$ years remaining until maturity. They carry a $7\mathrm{.}00\%$ annual coupon rate, a face value of $1,000,$ and currently trade in the market at $980\mathrm{.}00$ per bond.

Taxes: Alpha Corp. is subject to a corporate tax rate of $30\%.$

Equity: The current risk$-$free rate is $4\mathrm{.}00\%.$ The expected market risk premium is $6\mathrm{.}00\%,$ and Alpha Corp.$\text{'}$s common stock has a beta of $1\mathrm{.}15.$

Capital Structure: The company aims to maintain a target capital structure comprising $40\%$ debt and $60\%$ common equity. Alpha Corp. does not plan to issue new common shares in the foreseeable future.

Required:

a$)$ Calculate Alpha Corp.$\text{'}$s WACC based on the provided information. $(12$ marks$)$

b$)$ Evaluate the accuracy of the following statement: $"$If market expectations shifted towards higher long$-$term inflation, the cost of equity capital would rise by a larger percentage amount than the yield on the company's long$-$term debt. $"(8$ marks$)$