Question

You own two bonds, each of which currently pays semiannual interest, has a coupon rate of 6 percent, a $1,000 face value, and 6 percent yields to maturity. Bond A has 3 years to maturity and Bond B has 10 years to maturity. If the market rate of interest decreases unexpectedly to 5 percent, Bond _will be the most volatile with a price_of_percent.

Answer 1

Before change in interest rates

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of Bond A is calculated using PV function in Excel :

rate = 6%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 3 * 2 (3 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 6% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,000.00

X A1 A 1 ($1,000.00)! : B fo C =PV(6%/2,3*2,1000*6%/2,1000) D E F G

Price of Bond B is calculated using PV function in Excel :

rate = 6%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 10 * 2 (10 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 6% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,000.00

A1 X for =PV(6%/2,10*2,1000*6%/2, 1000) B C D I F G 1 ($1,000.00)!

After change in interest rates

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of Bond A is calculated using PV function in Excel :

rate = 5%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 3 * 2 (3 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 6% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,027.54

X foc =PV(5%/2,3*2,1000*6%/2,1000) B C D E F A ($1,027.54)

Price of Bond B is calculated using PV function in Excel :

rate = 5%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 3 * 2 (3 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 6% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $1,077.95

=PV(5%/2,10*2,1000*6%/2,1000) B C D E F G A ($1,077.95)

% increase in price of Bond B = ($1,077.95 - $1,000) / $1,000 = 7.795%

Bond B will be most volatile with a price increase of 7.795%