Question

Ron Rhodes calls his broker to inquire about purchasing a bond of Golden Years Recreation Corporation. His broker quotes a price of $1,140. Ron is concerned that the bond might be overpriced based on the facts involved. The $1,000 par value bond pays 12 percent annual interest payable semiannually, and has 15 years remaining until maturity. The current yield to maturity on similar bonds is 10 percent.   

a. Compute the new price of the bond. (Use a Financial calculator to arrive at the answers. Do not round intermediate calculations. Round the final answer to 2 decimal places.)

New price of the bond           $

b. Do you think the bond is overpriced?

• No

• Yes

Answer 1

Solution:
a.	New price of the bond            $1153.72
b.	No
Notes:	Since actual bond price quoted is $1,140   but its theoretical value of the bond calculated below is $1,153.72 which is higher than $1,140 by $13.72 . Hence, the bond is not overpriced. it is underpriced by $13.72
Working Notes:
	New price of the bond           $1153.72
	We are using Excel method , you will able to get same answer by using financial calculator by same inputs.
	No. of period= years to maturity x no of coupons in a year = 15 x 2 = 30 =nper = N = 30
	Face value of bond = FV=    1000 par value
	Price of the bond = PV =??
	Semi -annual Coupon amount = PMT = coupon rate x face value x 1/2 = 12% x $1,000 x 1/2 = $60
	rate = YTM =semi annual yield to maturity = YTM/2 = 10%/2 = 5%
	For calculation price of the bond [PV] by excel
	type above data in below format
	=PV(rate, nper,pmt,fv)
	=PV(5%, 30,60,1000)
	-1153.724510	-ve sign shows it’s the bond price paid to get cash inflows during the life bond cash flows
	=1153.72
Please feel free to ask if anything about above solution in comment section of the question.