Question

Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas Bond Dave has 16 years to maturity.

a.	If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
b.	If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Requirement (a)-Percentage change in the price of Bond Sam and Bond Dave If interest rates suddenly rise by 2 percent

Percentage change in the price of Bond Sam = -5.16% (Negative)

Percentage change in the price of Bond Dave = -16.79% (Negative)

Percentage change in the price of Bond Sam

If the Bond is selling at Par Value, then the Yield to maturity (YTM) of the Bond will be equal to the Coupon Rate of the Bond

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $35 [$1,000 x 7% x ½]

Semi-annual Yield to Maturity = 4.50% [(7% + 2%) x ½]

Maturity Period = 6 Years [3 Years x 2]

The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $35[PVIFA 4.50%, 6 Years] + $1,000[PVIF 4.50%, 4 Years]

= [$35 x 5.15787] + [$1,000 x 0.76790]

= $180.52 + $767.90

= $948.42

Percentage change in the price of Bond = [(Current Price – Face Value) / Face Value] x 100

= [($948.42 - $1,000) / $1,000] x 100

= [-$51.58 / $1,000] x 100

= -5.16% (Negative)

Percentage change in the price of Bond Dave

If the Bond is selling at Par Value, then the Yield to maturity (YTM) of the Bond will be equal to the Coupon Rate of the Bond

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $35 [$1,000 x 7% x ½]

Semi-annual Yield to Maturity = 4.50% [(7% + 2%) x ½]

Maturity Period = 32 Years [16 Years x 2]

The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $35[PVIFA 4.50%, 32 Years] + $1,000[PVIF 4.50%, 32 Years]

= [$35 x 16.78889] + [$1,000 x 0.24450]

= $587.61 + $244.50

= $832.11

Percentage change in the price of Bond = [(Current Price – Face Value) / Face Value] x 100

= [($832.11 - $1,000) / $1,000] x 100

= [-$167.89 / $1,000] x 100

= -16.79% (Negative)

Requirement (b)-Percentage change in the price of Bond Sam and Bond Dave If interest rates suddenly fall by 2 percent

Percentage change in the price of Bond Sam = 5.51%

Percentage change in the price of Bond Dave = 21.85%

Percentage change in the price of Bond Sam

If the Bond is selling at Par Value, then the Yield to maturity (YTM) of the Bond will be equal to the Coupon Rate of the Bond

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $35 [$1,000 x 7% x ½]

Semi-annual Yield to Maturity = 2.50% [(7% - 2%) x ½]

Maturity Period = 6 Years [3 Years x 2]

The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $35[PVIFA 2.50%, 6 Years] + $1,000[PVIF 2.50%, 4 Years]

= [$35 x 5.50813] + [$1,000 x 0.86230]

= $192.78 + $862.30

= $1,055.08

Percentage change in the price of Bond = [(Current Price – Face Value) / Face Value] x 100

= [($1,055.08 - $1,000) / $1,000] x 100

= [$55.08 / $1,000] x 100

= 5.51%

Percentage change in the price of Bond Dave

If the Bond is selling at Par Value, then the Yield to maturity (YTM) of the Bond will be equal to the Coupon Rate of the Bond

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $35 [$1,000 x 7% x ½]

Semi-annual Yield to Maturity = 2.50% [(7% - 2%) x ½]

Maturity Period = 32 Years [16 Years x 2]

The Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $35[PVIFA 2.50%, 32 Years] + $1,000[PVIF 2.50%, 32 Years]

= [$35 x 21.84918] + [$1,000 x 0.45377]

= $764.72 + $453.77

= $1,218.49

Percentage change in the price of Bond = [(Current Price – Face Value) / Face Value] x 100

= [($1,218.49 - $1,000) / $1,000] x 100

= [$218.49 / $1,000] x 100

= 21.85%

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.   

FINAL ANSWERS

Requirement (a)-Percentage change in the price of Bond Sam and Bond Dave If interest rates suddenly rise by 2 percent

Percentage change in the price of Bond Sam = -5.16% (Negative)

Percentage change in the price of Bond Dave = -16.79% (Negative)

Requirement (b)-Percentage change in the price of Bond Sam and Bond Dave If interest rates suddenly fall by 2 percent

Percentage change in the price of Bond Sam = 5.51%

Percentage change in the price of Bond Dave = 21.85%