A bond has face value of ₹1000 matures in 4 years. Coupon rate 4% per annum. The bond makes annual coupon payments. If the yield to maturity is 4%, then the fair value of bond is :
(Given $(1.04)^{-4}=0.8551$)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → ₹1000
The fair value of a bond,
$P=∑\frac{C}{(1+r)^t}+\frac{F}{(1+r)^n}$
and,
$PV_{coupons}=C×\left(\frac{1-(1+r)^{-n}}{r}\right)$
$=40×\left(\frac{1-(1.04)^{-4}}{0.04}\right)$
$=40×3.63=142.5$
$PV_{face}=\frac{1000}{(1.04)^{4}}≃854.8$
$P=PV_{coupons}+PV_{face}$
$=145.2+854.8$
$=₹1000$