Question

QUESTION 1

(a). Five years ago, XYZ Company issued 10,000 (Ten Thousand) 20-year, K1,000 par value bonds at par. At that time the market rate for such bonds was at 8%. The coupon is paid annually. Today the actual market value of all the bonds together is K11,942,450. What is the yield to maturity of these bonds today?

 (b). What should be the price of a K1,000 par value, 10% annual coupon rate (coupon interest paid semi-annually) bond with 8 years remaining to maturity, assuming a discount rate of 12%?

(c). You have just discovered a K1,000 par value corporate bond with a maturity of 10 years. The bond’s yield to maturity is 9% and the bond is currently selling for K743.29. What is the bond’s annual coupon rate (the bond pays coupon payments annually)?

Answer 1

(a)we'll find it in one bond. let the coupon rate be 10%

С=100

$YTM=\frac{C+\frac{N-P}{t}}{\frac{N+P}{2}}$

$YTM=\frac{100+\frac{1000-1194.245}{20}}{\frac{1000+1194.245}{2}}$

YNM=0.082295

(b)

$P=\frac{\frac{C}{m}}{(1+\frac{r}{m})}+\frac{\frac{C}{m}}{(1+\frac{r}{m})^2}+...+\frac{\frac{C}{m}}{(1+\frac{r}{m})^{n\times m}}+\frac{N}{(1+{r})^n)}$

$m=2$

$C=1000\times0.1=100$

$P=\frac{\frac{C}{m}}{(1+\frac{r}{m})}+\frac{\frac{C}{m}}{(1+\frac{r}{m})^2}+...+\frac{\frac{C}{m}}{(1+\frac{r}{m})^{n\times m}}+\frac{N}{(1+{r})^n)}=\frac{50}{(1+\frac{0.12}{2})}+\frac{50}{(1+\frac{0.12}{2})^2}+...+\frac{50}{(1+\frac{0.12}{2})^{16}}+\frac{1000}{(1+{0.12})^8)}=909.178$

(c)$P=\frac{C}{(1+r)}+\frac{C}{(1+r)^2}+...+\frac{C}{(1+r)^n}+\frac{N}{(1+r)^n}=C(\frac{1}{(1+r)}+\frac{1}{(1+r)^2}+...+\frac{1}{(1+r)^n})+\frac{N}{(1+r)^n}$

$743.29=\frac{C}{(1+r)}+\frac{C}{(1+r)^2}+...+\frac{C}{(1+r)^n}+\frac{N}{(1+r)^n}=C(\frac{1}{(1+0.09)}+\frac{1}{(1+0.09)^2}+...+\frac{1}{(1+0.09)^{10}})+\frac{1000}{(1+0.09)^{10}}$

C=49.9992

$C=N\times r(c)$

$49.9992=1000\times r(c)$

r(c)=0.04999