Question

Bond P is a premium bond with a coupon rate of 8 percent. Bond D has a coupon rate of 3 percent and is currently selling at a discount. Both bonds make annual payments, have a YTM of 5 percent, and have seven years to maturity.

  

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.)

Answer 1

a)

Bond P:

Assuming face value to be $1,000

Coupon = 0.08 * 1000 = 80

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 80 * [1 - 1 / (1 + 0.05)⁷] / 0.05 + 1000 / (1 + 0.05)⁷

Price = 80 * [1 - 0.70681] / 0.05 + 710.68133

Price = 80 * 5.786373 + 710.68133

Price = $1,173.5912

Current yield = (Coupon / Price) * 100

Current yield = (80 / 1,173.5912) * 100

Current yield of bond P = 6.82%

Bond D:

Assuming face value to be $1,000

Coupon = 0.03 * 1000 = 30

Price = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price = 30 * [1 - 1 / (1 + 0.05)⁷] / 0.05 + 1000 / (1 + 0.05)⁷

Price = 30 * [1 - 0.70681] / 0.05 + 710.68133

Price = 30 * 5.786373 + 710.68133

Price = $884.2725

Current yield = (Coupon / Price) * 100

Current yield = (30 / 884.2725) * 100

Current yield of bond D = 3.39%

b)

Bond P:

Price in 1 year = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price in 1 year = 80 * [1 - 1 / (1 + 0.05)⁶] / 0.05 + 1000 / (1 + 0.05)⁶

Price in 1 year = 80 * [1 - 0.746215] / 0.05 + 746.215397

Price in 1 year = 80 * 5.075692 + 746.215397

Price in 1 year = $1,152.2708

Capital gains yield = [(1,152.2708 - 1,173.5912) / 1,173.5912] * 100

Capital gains yield of bond P = -1.82%

Bond D:

Price in 1 year = Coupon * [1 - 1 / (1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price in 1 year = 30 * [1 - 1 / (1 + 0.05)⁶] / 0.05 + 1000 / (1 + 0.05)⁶

Price in 1 year = 30 * [1 - 0.746215] / 0.05 + 746.215397

Price in 1 year = 30 * 5.075692 + 746.215397

Price in 1 year = $898.48616

Capital gains yield = [(898.48616 - 884.2725) / 884.2725] * 100

Capital gains yield of bond D = 1.61%