Question

Q1) A(n) 6.1% bond with 10 years left to maturity has a YTM of 9.1%. The bond's price should be $__________. You should assume that the coupon payments occur semiannually.

Q2) A 10-year 4.8% coupon bond was issued 2 years ago. Similarly risky bonds are yielding 6%. Assume semi-annual coupon payments. The bond's price should be $___________.

If you can, please complete both! Thank you so much.

Answer 1

Answer to Question 1:

Face Value = $1,000

Annual Coupon Rate = 6.10%
Semiannual Coupon Rate = 3.05%
Semiannual Coupon = 3.05% * $1,000
Semiannual Coupon = $30.50

Time to Maturity = 10 years
Semiannual Period = 20

Annual YTM = 9.10%
Semiannual YTM = 4.55%

Price of Bond = $30.50 * PVIFA(4.55%, 20) + $1,000 * PVIF(4.55%, 20)
Price of Bond = $30.50 * (1 - (1/1.0455)^20) / 0.0455 + $1,000 * (1/1.0455)^20
Price of Bond = $30.50 * 12.95176 + $1,000 * 0.41069
Price of Bond = $805.72

Answer to Question 2:

Face Value = $1,000

Annual Coupon Rate = 4.80%
Semiannual Coupon Rate = 2.40%
Semiannual Coupon = 2.40% * $1,000
Semiannual Coupon = $24

Time to Maturity = 8 years
Semiannual Period = 16

Annual YTM = 6.00%
Semiannual YTM = 3.00%

Price of Bond = $24 * PVIFA(3.00%, 16) + $1,000 * PVIF(3.00%, 16)
Price of Bond = $24 * (1 - (1/1.03)^16) / 0.03 + $1,000 * (1/1.03)^16
Price of Bond = $24 * 12.56110 + $1,000 * 0.62317
Price of Bond = $924.64