Question

Setup A: Bill, a plumber, owns a bond with a $1,000 par value, a 7.00 percent coupon rate paid annually, three years remaining to maturity, and a 9.00 percent yield to maturity. When the government releases new economic numbers tomorrow, Bill believes the interest rate on this type of bond will fall 150 basis points and there will be a parallel shift in the yield curve.

1. What is the bond’s price to two decimal places?
2. What is the bond’s value in dollars and cents (if sold today, how much does Bill get)?
3. What is the bond’s duration to two decimal places?
4. What is the bond’s modified duration to two decimal places?
5. What is the bond’s current yield to two decimal places?

If Bill is correct and the yield to maturity falls 100 basis points tomorrow.

6.         What will be the bond’s new yield to maturity to two decimal places?
7.         Using modified duration, what will be the new bond price to two decimal places?

If Bill is wrong and the yield to maturity increases 75 basis points tomorrow.

8.         What will be the bond’s new yield to maturity to two decimal places?
9.          Using modified duration, what will be the new bond price to two decimal places?

Answer 1

Time (t)	CF	PV	PV x t
1	70	64.22	64.22
2	70	58.92	117.84
3	1070	826.24	2478.71
	Sum	949.37	2660.76
	Dur	2.80
	Mod Dur	2.57

Bond Price = Bond Value = Sum of PV = $949.37

PV = CF / (1 + ytm)^t

where, CF = Coupon + Principal, ytm = 9%, t - year

Duration = Sum of PV x t / Sum of PV = 2,660.76 / 949.37 = 2.80

Modified Duration = Duration / (1 + YTM) = 2.80 / 1.09 = 2.57

Current Yield = Coupon / Price = 70 / 949.37 = 7.37%

New YTM = 8%

% Change in Bond Price = - Mod Duration x Change in yield = - 2.57 x -1% = 2.57%

=> New Bond Price = 949.37 x (1 + 2.57%) = $973.78

New YTM = 9.75%

% Change = -2.57 x 0.75% = - 1.93%

=> New Bond Price = 949.37 x (1 - 1.93%) = $931.07