Question

Harrison Co. issued 15-year bonds one year ago at a coupon rate of 7.6 percent. The bonds make semiannual payments. If the YTM on these bonds is 5.3 percent, what is the current dollar price assuming a $1,000 par value? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

Ans. The current dollar price of this bond is  $1,233.02  

Explanation:

Hi, assuming that 2 coupons were already paid, (since one year ago this bond was issued), we still have 14 years worth of coupons (28 coupon payments remaining) plus its face value 14 years from now.

So, the coupon (semi annual) to be paid is (0.076/2)*1,000=$38/semester, and the discount rate (YTM) in semi-annual terms is found as follows.

$YTM(semester)=(1+YTM(annual))^{\frac{1}{2} } -1=(1+0.053)^{\frac{1}{2} } -1=0.026158$

Therefore the YTM in semi-annual terms is 2.6158%.

Now, to find out the price of the bond, we have to use the following equation along with the information above.

$Price=\frac{Coupon((1+YTM)^{n}-1) }{YTM(1+YTM)^{n} } +\frac{FaceValue}{(1+YTM)^{n} }$

That is:

$Price=\frac{38((1+0.026158)^{28}-1) }{0.026158(1+0.026158)^{28} } +\frac{1,000}{(1+0.026158)^{28} }$

$Price= 747.73 + 485.29 = 1,233.02$

Best of luck.