Question

Both Bond Sam and Bond Dave have 7.3 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave

Answer 1

-5.14 for sam

-18.01% for dave

Step-by-step explanation:

We first calculate for Sam

R = 7.3%

We have 2% increase

= 9.3%

We calculate for present value of coupon and present value at maturity using the formula for present value in the attachment

To get C

1000 x 0.073/2

= 36.5

time= 3 years x 2 times payment = 6

Ytm = rate = 9.3%/2 = 0.0465

Putting values into the formula

36.5[1-(1+0.0465)^-6/0.0465]

= 36.5(1-0.7613/0.0465)

36.5(0.2385/0.0465)

= 36.5 x 5.129

Present value of coupon = 187.20

We solve for maturity

M = 1000

T = 6 months

R = 0.0465

1000/(1+0.0465)⁶

= 1000/1.3135

Present value = 761.32

We add up the value of present value at maturity and that at coupon

761.32 + 187.20

= $948.52

Change in % = 948.52/1000 - 1

= -0.05148

= -5.14 for sam

We calculate for Dave

He has 20 years and payment is two times yearly

= 20x2 = 40

36.5 [1-(1+0.0465)^-40/0.0465]

Present value = 36.5 x 18.014

= 657.511

At maturity,

Present value = 1000/(1+0.0465)⁴⁰

= 1000/6.1598

= 162.34

We add up these present values

= 657.511+162.34 = $819.851

Change = 819.851/1000 -1

= -0.1801

= -18.01%