Question

A 100 par value 6% bond with semi-annual coupons is purchased at 110 to yield a nominal rate of 4% convertible semi-annually. A similar (with the same par and maturity date) 3% bond with semi-annual coupons is purchased at P to provide the buyer with the same yield rate. Calculate P.

(A) 90
(B) 95
(C) 100
(D) 105
(E) 110

Answer 1

To calculate the value of the 3% bond, we apply the present value formula and find that it is approximately $90.50.

Step-by-step explanation:

To calculate the value of the 3% bond, we need to use the present value formula. The bond pays semi-annual coupons, so the formula becomes:

P = C(1 - (1+r)^-n) / r + F(1+r)^-n,

where P is the price of the bond, C is the coupon payment, r is the yield rate, F is the face value of the bond, and n is the number of periods until maturity.

In this case, the coupon payment of the 3% bond is C = 3/2 = 1.5, the yield rate is r = 4%/2 = 2%, the face value is F = 100, and the number of periods until maturity is n = 2*2 = 4. Plugging these values into the formula:

P = 1.5(1 - (1+0.02)^-4) / 0.02 + 100(1+0.02)^-4

P ≈ 90.50.

Therefore, the correct option is (A) 90.