Question

You intend to purchase a 5-year, $3,000 face value bond. The coupon rate of this bond is 10%. If your nominal annual required rate of return (nominal market interest) is 8 percent and the bond pays coupon semiannually, how much should you be willing to pay for this bond at the end of the second year? (Answer is rounded)

Answer 1

Answer :

Value of Bond = (Coupon * PVAF @ r% for n years) + (Face Value * PVF @ r% for nth years)

Coupon = 3000 * 10% = 300 / 2 = 150 (Divided by 2 as semiannual coupon payment)

r is the yield to maturity i.e 8% / 2 = 4% (Divided by 2 as semiannual coupon payment)

n is the number of years to maturity i.e (5-2) * 2 = 6 (As price is calculated at the end of year 2 therefore number of years remaining to maturity is 3 and Multiplied by 2 as semiannual coupon payment)

Value of Bond = (150 * PVAF @ 4% for 6 times) + (3000 * PVF @ 4% for 6th)

= (150 * 5.24213685661) + (3000 * 0.7903145257)

= 786.3205 + 2370.94356

= $3157.2641 or 3157

Note :

PVF can be calculated using [1 / (1 + 0.04)^6 ] = 0.0.7903145257

PVAF can be calculated as {[1 - (1 + 0.04)^16 ] / 0.04} = 5.24213685661