Question

Rearden Metal has just issued a callable, $1000 par value, twenty-year, 8% coupon bond with semiannual coupon payments. The bond can be called at par in five years or anytime thereafter on a coupon payment date. If the bond is currently trading for $1040.79, then its yield to call is closest to:

Group of answer choices

3.8%

7.0%

7.6%

8.0%

Answer 1

The answer is 7.0%

Step-by-step explanation:

The yield to call (YTC) is the return on bond that will bring total present value of all the coupon payments to bond's holders from the date they hold the bond to the earliest callable date and the call price equals to its current trading price.

In the question, we have:

Semi-annual coupon payments : 1,000 x 8%/2 = $40;

Discounting rate: Denote is i; which is equal to nominal annual YTC/2

Call price = par value = $1,000

Earliest callable date: 5 years, thus, 10 discounting period ( 5x2)

Current price: $1,040.79

Thus, we have:

1,040.79 = ( 40/ i) x [ 1 - (1+i)^-10 ] + 1,000/(1+i)^10 <=> i = 3.5%

=> YTC = 7.0%