Question

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Bond P is a premium bond with a coupon rate of 8 percent. Bond D has a coupon rate of 3 percent and is selling at a discount. Both bonds make annual payments, have a YTM of 5 percent, and have seven years to maturity. 1.58 points eBook a. What is the current yield for Bond P and Bond D? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P and Bond D? (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.) Hint Print References a. Bond P Bond D Bond P Bond D

Answer 1

First, we will calculate the current bond price of Bond P and D.

- Calculating Bond Price of Bond P

Price =- +.... + Coupon Payment (1 + YTM Coupon Payment Coupon Payment (1 + YTM) 2 (1+YTM) FaceValue (1 + YTM

Where, Coupon payment = $1000*8% = $80

YTM =0.05

Face Value = $1000 (assuming it to be)

n = 7 years

80 80 1000 Price = (1 +0.05)1 + (1 +0.05)2 + .... + (1+0.05)3 + (1 +0.05)

Price = $ 1173.59

- Calculating Bond Price of Bond D

Price =- +.... + Coupon Payment (1 + YTM Coupon Payment Coupon Payment (1 + YTM) 2 (1+YTM) FaceValue (1 + YTM

Where, Coupon payment = $1000*3% = $30

YTM =0.05

Face Value = $1000 (assuming it to be)

n = 7 years

30 30 1000 Price = (1 +0.05)1 + (1 +0.05)2 + .... + (1+0.05)3 + (1 +0.05)

Price = $ 884.27

a). Now, calculating Current Yield:

Current Yield = Annual Coupon Payment/Current Bond Price

Current Yield of Bond P = 80/1173.59

= 6.82%

Current Yield of Bond B = 30/884.27

= 3.39%

b). As interest rate remain unchanged, to calculate capital gain yield we will calculate first the bond price of both bonds over the next year

- Calculating Bond Price of Bond P over the next year with maturity year left is 6 years

Price =- +.... + Coupon Payment (1 + YTM Coupon Payment Coupon Payment (1 + YTM) 2 (1+YTM) FaceValue (1 + YTM

Where, Coupon payment = $1000*8% = $80

YTM =0.05

Face Value = $1000 (assuming it to be)

n = 6 years

80 80 1000 Price = (1 +0.05)1 + (1 +0.05)2 + .... + (1+0.05)6 + (1 +0.05)

Price = $ 1152.28

- Calculating Bond Price of Bond D over the next year with maturity year left is 6 years

Price =- +.... + Coupon Payment (1 + YTM Coupon Payment Coupon Payment (1 + YTM) 2 (1+YTM) FaceValue (1 + YTM

Where, Coupon payment = $1000*3% = $30

YTM =0.05

Face Value = $1000 (assuming it to be)

n = 6 years

1000 Price = 710 05)1*(1 + 0.05)2 005)2 +...+(1+0.05)6(1 + 0.05) 30 30

Price = $ 898.49

a). Now, calculating Capital gain Yield:

Current Yield = (Closing Price-Beginning Price)/Beginning Price

Current Yield of Bond P = ($1152.28-$1173.59)/$1173.59

= -1.82%

Current Yield of Bond D = ($898.49-$884.27)/$884.27

= 1.61%

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