Answer:
a-1. Percentage change in the price of Bond Bill = -8.07%
a-2. Percentage change in the price of Bond Ted = -21.12%
b-1. Percentage change in the price of Bond Bill = 8.94%
b-1. Percentage change in the price of Bond Ted = 30.77%
c. See the attached excel file for the graph.
d. It tells us that the longer the term of a bond, the greater will be its interest rate risk.
Explanation:
The price of each bond can be calculated using the following excel function:
Bond price = -PV(YTM, NPER, PMT, FV) ........... (1)
Where;
a-1. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Bill?
YTM = (6.2% + 2%) / Number of semiannuals in a year = 8.2% / 2 = 4.1%
NPER = Number of semiannuals to maturity = 5 * 2 = 10
PMT = Payment = Coupon rate * Face value = (6.2% / Number of semiannuals in a year) * 1000 = (6.2% / 2) * 1000 = $31
FV = Face value = Initial price of Bond Bill = $1,000
Substituting all the values into equation (1), we have:
New price of Bond Bill = -PV(4.1%, 10, 31, 1000)
Inputting =-PV(4.1%, 10, 31, 1000) in a cell in an excel file (Note: As done in the attached excel file), we have:
New price of Bond Bill = $919.29
Percentage change in the price of Bond Bill = ((New price of Bond Bill - Initial price of Bond Bill) / Initial price of Bond Bill) * 100 = (($919.29 - $1,000) / $1,000) * 100 = -8.07%
a-2. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Ted?
YTM = (6.2% + 2%) / Number of semiannuals in a year = 8.2% / 2 = 4.1%
NPER = Number of semiannuals to maturity = 25 * 2 = 50
PMT = Payment = Coupon rate * Face value = (6.2% / Number of semiannuals in a year) * 1000 = (6.2% / 2) * 1000 = $31
FV = Face value = Initial price of Bond Ted = $1,000
Substituting all the values into equation (1), we have:
New price of Bond Ted = -PV(4.1%, 50, 31, 1000)
Inputting =-PV(4.1%, 50, 31, 1000) in a cell in an excel file (Note: As done in the attached excel file), we have:
New price of Bond Ted = $788.81
Percentage change in the price of Bond Ted = ((New price of Bond Ted - Initial price of Bond Bill Ted) / Initial price of Bond Ted) * 100 = (($788.81 - $1,000) / $1,000) * 100 = -21.12%
b-1. If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Bill be then?
YTM = (6.2% - 2%) / Number of semiannuals in a year = 4.2% / 2 = 2.1%
NPER = Number of semiannuals to maturity = 5 * 2 = 10
PMT = Payment = Coupon rate * Face value = (6.2% / Number of semiannuals in a year) * 1000 = (6.2% / 2) * 1000 = $31
FV = Face value = Initial price of Bond Bill = $1,000
Substituting all the values into equation (1), we have:
New price of Bond Bill = -PV(2.1%, 10, 31, 1000)
Inputting =-PV(2.1%, 10, 31, 1000) in a cell in an excel file (Note: As done in the attached excel file), we have:
New price of Bond Bill = $1,089.36
Percentage change in the price of Bond Bill = ((New price of Bond Bill - Initial price of Bond Bill) / Initial price of Bond Bill) * 100 = (($1,089.36 - $1,000) / $1,000) * 100 = 8.94%
b-2. If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Ted be then?
rate = new YTM = (6.2% - 2%) / Number of semiannuals in a year = 4.2% / 2 = 2.1%
NPER = Number of semiannuals to maturity = 25 * 2 = 50
PMT = Payment = Coupon rate * Face value = (6.2% / Number of semiannuals in a year) * 1000 = (6.2% / 2) * 1000 = $31
FV = Face value = Initial price of Bond Ted = $1,000
Substituting all the values into equation (1), we have:
New price of Bond Ted = -PV(2.1%, 50, 31, 1000)
Inputting =-PV(2.1%, 50, 31, 1000) in a cell in an excel file (Note: As done in the attached excel file), we have:
New price of Bond Ted = $1,307.73
Percentage change in the price of Bond Ted = ((New price of Bond Ted - Initial price of Bond Bill Ted) / Initial price of Bond Ted) * 100 = (($1,307.73 - $1,000) / $1,000) * 100 = 30.77%
c. Illustrate your answers by graphing bond prices versus YTM.
Note: See the attached excel file for the graph.
d. What does this problem tell you about the interest rate risk of longer-term bonds?
It tells us that the longer the term of a bond, the greater will be its interest rate risk.