Question

Suppose a seven-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading with a yield to maturity of 6.75%.

1. Is this bond currently trading at a discount, at par, or at a premium? Explain.

2. If the yield to maturity of the bond rises to 7.00% (APR with semiannual compounding), what price will the bond trade for?

**please list out step by step actions, please show the formulas used, please DONT USE excel**

Answer 1

Question a:

Par Value = $1,000

C = Semi annual coupon = $1000 * 8%/2 = $40

r = semi annual yeild to maturity = 6.75%/2 = 3.375%

n = 7*2 = 14 semi annual payments

Current Price of bond = [C * [1 - (1+r)^-n] / r] + [Par Value / (1+r)^n]

= [$40 * [1 - (1+3.375%)^-14] / 3.375%] + [$1,000 / (1+3.375%)^14]

= [$40 * 0.371677396/ 0.03375] + [$1,000 / 1.591539112]

= $440.5065428 + $628.3226045

= $1,068.829147

Therefore, Current Price of bond is $1,068.83

Bond is trading at premium since current price of bond is greater than par value.

Question b:

Par Value = $1,000

C = Semi annual coupon = $1000 * 8%/2 = $40

r = semi annual yeild to maturity = 7%/2 = 3.5%

n = 7*2 = 14 semi annual payments

Current Price of bond = [C * [1 - (1+r)^-n] / r] + [Par Value / (1+r)^n]

= [$40 * [1 - (1+3.5%)^-14] / 3.5%] + [$1,000 / (1+3.5%)^14]

= [$40 * 0.38221821 / 0.035] + [$1,000 / 1.618694522]

= $436.8208111 + $617.7817903

= $1,054.602601

Therefore, current value of bond is $1,054.60