Question

A GM and a Ford bond both have 4 years to maturity. GM has a annual coupon rate of 0.066, while Ford has a annual coupon rate of 0.054. Both bonds are semiannual and have a face value of $1000.

The GM bond trades at 969.39. What is the yield to maturity (YTM)?

What is the price of the Ford bond?

Answer 1

(1) Without using Excel, we can compute semi-annual YTM for GM bond using following formula.

Semi-annual YTM = [C + {(F - P)/N}] / [(F + P)/2], where

C: semi-annual coupon payment = $1000 x 0.066 x (1/2) = $33

F: face value = $1000

P: Trading price = $969.39

N: Semi-annual compounding periods till maturity = 2 x 4 = 8

Therefore,

Semi-annual YTM = [33 + {(1000 - 969.39)/8}] / [(1000 + 969.39)/2]

= [33 + {(30.61)/8}] / [(1969.39)/2]

= (33 + 3.82625) / 984.695

= 36.82625 / 984.695

= 0.0374 (= 3.74%)

Annual YTM = 2 x Semi-annual YTM = 2 x 0.0374 = 0.0748 = 7.48%

(2) Ford's semi-annual coupon payment = $1000 x 0.054 x (1/2) = $27

Ford's Bond price ($) = Present value of future coupon payments + Present value of redemption price (face value)

= 27 x P/A(3.74%, 8) + 1000 x P/F(3.74%, 8)

= 27 x 6.8056** + 1000 x 0.7455**

= 183.75 + 745.5

= 929.25

**P/A(3.74%, 8) = [1 - (1.0374)^-8] / 0.0374 = (1 - 0.7455) / 0.0374 = 0.2545 / 0.0374 = 6.8056

**P/F(3.74%, 8) = (1.0374)^-8 = 0.7455