Question

Bond P is a premium bond with a coupon rate of 9 percent. Bond D is a discount bond with a coupon rate of 5 percent. Both bonds make annual payments, have a YTM of 7 percent, and have five years to maturity.

Requirement 1:

What is the current yield for bond P? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current yield

%

Requirement 2:

What is the current yield for bond D? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current yield

%

Requirement 3:

If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond P? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).)

Capital gains yield

%

Requirement 4:

If interest rates remain unchanged, what is the expected capital gains yield over the next year for bond D?(Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Capital gains yield

%

Answer 1

1) 8.32%

2) 5.45%

3) -1.32%

4) 1.55%

Let FaceValue of both bonds = $100

For Bond P: Coupon rate = 9% -> C= 9%*FV = 0.09*100=$9, YTM = 7%, n=5 years

where C = $9, i=7%, M=FV=$100

Bond Price of P = [9*(1-(1/1.07⁵))/0.07] + 100/(1.07⁵) = $108.20

Similarly, For bond D, Coupon rate = 5% -> C= 5%*FV = 0.05*100=$5, YTM = 7%, n=5 years

Bond Price of D = [5*(1-(1/1.07⁵))/0.07] + 100/(1.07⁵) = $91.80

1) Current Yield of the bond P = Bond's Annual Income/Current bond price

= Coupon payment / bond price

= 9/108.20

=0.0832

=8.32%

Current Yield of the Bond P = 8.32%

2) Current Yield of the bond D= Bond's Annual Income/Current bond price

= Coupon payment / bond price

= 5/91.8

=0.0545

=5.45%

Current Yield of the Bond D = 5.45%

3) Capital Gain Yield over the next year for the bond P =

(Current bond price - Original Bond Price) / Original Bond Price

= (Bond price at year 1- Bond Price at Year 0) / Bond Price at Year 0

Bond Price of P at year 1= PV of cash flows from Year 2-5

= [9*(1-(1/1.07⁴))/0.07] + 100/(1.07⁴)

=$106.77

Capital Gains Yield of Bond P over the next year = (106.77-108.20)/108.20 = -0.01318 = -1.32%

Capital Gains Yield of Bond P over the neext year = -1.32%

4) Bond Price of D at year 1= PV of cash flows from Year 2-5

= [5*(1-(1/1.07⁴))/0.07] + 100/(1.07⁴)

=$93.23

Capital Gains Yield of Bond D over the next year = (93.23-91.80)/91.80 = 0.01553 =1.55%

Capital Gains Yield of Bond D over the neext year = 1.55%