True Discount Rate-Finance

Question

On January $1$, $2017$, you purchased a 10-year bond issued by Alpha Inc. at par. The bond features an $8\%$ coupon ($\$40$ every six months) and a par value of $\$1,000$. Within minutes of purchasing the bond, Alpha announced financial problems, and the terms of the bond were renegotiated overnight. Going forward, Alpha will only pay a $6\%$ coupon ($\$30$ every six months) and $\$800$ at maturity. The YTM rose to $24.43\%$ on January $2$, $2017$. What is the true discount rate (nominal annual rate with semi-annual compounding) investors are applying to the renegotiated cash flow?

Answer 1

Let that yield be r and thus

$ 0= -1000+\dfrac{30}{(1+\frac{r}{2})^{2*0.5}} + \dfrac{30}{(1+\frac{r}{2})^{2*1}}+\cdots+\dfrac{830}{(1+\frac{r}{2})^{2*10}}$

By goal seek in EXCEL such an r is equal to $4.3850542$ %