Question

Solve for the stock/bond problem. Show all of your work and equations. Hint: The correct answer is $1,097 if you round up. DO NOT USE EXCEL. HAND WRITTEN WORK PLEASE!

2. A bond with annual coupon rate of 5.10% and price of $1,090 just yesterday paid a coupon. A total of 23 coupons remain to be paid. Suppose you buy the bond at today's price, hold it and receive 8 coupons, and then sell the bond. If at the time you sell the bond its YTM has decreased a total of 50 basis points, find the selling price of the bond. (FYI; 0.01=1%=100 basis points; use semiannual compounding). Note that the number of coupons left is the same as "n" at the time of pricing.

Answer 1

	Pv	Current Price	$1,090
	Pmt	Annual Coupon amount=5.1%*1000	$51.00
	Nper	Number of Years	23
	Fv	Amount to be received at maturity	$1,000
	RATE	Yield to maturity(YTM)	4.47%	(Using RATE function of excel with Nper=23,Pmt=51,Pv=-1090,Fv=1000)
		YTM decreases by 50 basis point (0.5%)
	Rate	Decreased YTM after 8 years=4.47-0.5	3.97%
	Nper	Number of years to maturity (23-8)	15
	Pmt	Annual Coupon amount=5.1%*1000	$51.00
	Fv	Amount to be received at maturity	$1,000
	PV	Selling Price of the Bond	$1,126.39	(Using PV function of excel with Rate =3.97%, Nper=15,Pmt=-51,Fv=-1000)
		(Present Value of Future Cash Flows)
			H7 : fic =RATE(H5,H4,-H3, H6) E F I J K L M N O P H $1,090 $51.00 Current Price Annual Coupon amount=5.1%*1000 Number of Years Amount to be received at maturity Yield to maturity(YTM) Pmt Nper Fv RATE 23 $1,000 4.47%! (Using RATE function of excel with Nper=23,Pmt=51,Pv=-1090,Fv=1000) H15 =PV(H11, H12,-H13,-H14) H I J K L M N O P Q Pv Pmt Nper Current Price Annual Coupon amount=5.1%*1000 Number of Years Amount to be received at maturity Yield to maturity(YTM) $1,090 $51.00 23 $1,000 4.47% FV RATE (Using RATE function of excel with Nper=23,Pmt=51,Pv=-1090,Fv=1000) YTM decreases by 50 basis point (0.5%) Rate Nper Pmt FV PV Decreased YTM after 8 years=4.47-0.5 Number of years to maturity (23-8) Annual Coupon amount=5.1%*1000 Amount to be received at maturity Selling Price of the Bond (Present Value of Future Cash Flows) 3.97% 15 $51.00 $1,000 $1,126.39 Using PV function of excel with Rate =3.97%, Nper=15, Pmt=-51, Fv=-1000)