Question

Wildhorse, Inc., has bonds outstanding that will mature in 8 years. The bonds have a face value of $1,000. These bonds pay interest semiannually and have a coupon rate of 4.6 percent. If the bonds are currently selling at $909.92, what is the yield to maturity that an investor who buys them today can expect to earn? What is the effective annual yield?

Answer 1

Data;

Par value/ Face value= $1000

Coupon rate per year=4.6%

Coupon rte per semi annual period= $\frac{4.6\%} {2}$ = 2.30%

Coupon payment= 0.023*1000=$23

Current price/ Present value=$909.92

Time= 8 years

Semi annual periods= 8*2=16

Calculation yield To Maturity

$YTM=\cfrac{C+\cfrac {(FV-PV)}{t}} {\cfrac{(FV+PV)} {2}}$

C=Coupon payment

FV= Face value

PV= Present value/ Price

t= No of years takes to maturity

$YTM=\cfrac{23+\cfrac {(1000-909.92)}{16}} {\cfrac{(1000+909.92)} {2}}$

$YTM=0.02998$

$YTM=2.998\%$

$YTM=0.02998$

$YTM=2.998\% * 2=5.996\%$

$YTM=\boxed{5.996\%}$

Calculation for Effective Annual Yield

$ENY=\lparen {1+\cfrac{r} {n}}\rparen ^{n} -1$

r= Interest rate

n=Number of payments per year

$ENY=\lparen {1+\cfrac{0.023} {2}}\rparen ^{2} -1$

$ENY=0.0231$

$ENY=2.31\%$

$ENY=2.31\% *2= 4.63\%$

$ENY=\boxed{4.63\%}$