Question

Current yield, capital gains yield, and yield to maturity Hooper Printing Inc. has bonds outstanding with 9 years left to maturity. The bonds have an 9% annual coupon rate and were issued 1 year ago at their par value of $1,000. However, due to changes in interest rates, the bond's market price has fallen to $910.30. The capital gains yield last year was - 8.97%. a. What is the yield to maturity? Round your answer to two decimal places. % b. For the coming year, what is the expected current yield? (Hint: Refer to Footnote 7 for the definition of the current yield and to Table 7.1.) Round your answer to two decimal places. % For the coming year, what is the expected capital gains yield? (Hint: Refer to Footnote 7 for the definition of the current yield and to Table 7.1.) Round your answer to two decimal places. %

Answer 1

a.

Bond Price​= (Coupon  × (1−(1+YTM)^n)/YTM​​)+(Face Value  × 1/ (1+YTM)^n)​

910.3 = (90*(1-(1+YTM)^9/YTM)+ (1000*1/1+YTM)^9)

We have to solve this by trial and error method, given the current price is less than the face value the yield has to be greater then the coupon %. Consicering yield of maturity as 10% and applying to the above formula, the bond price comes to 942.40. Considering yield to be 11%, bond price comes to 889.25, interpolating gives the YTM as 10.6%

b. Value of the bond at the end of year two = (Coupon  × (1−(1+YTM)^n)/YTM​​)+(Face Value  × 1/ (1+YTM)^n)​

usnig n=8 and YTM =10.6% Face value = 1000, coupon =90

Bond price at end of year 2 = 926.38

current yield = Coupon/current price

= 90/926.38

=9.72%

c.

Capital yield = P1-P0 / P0

P0 = 910.3

P1=926.38

Capital yield = 1.77%

Capital Gain yield = 100