The purchase price P of a ₹50,000, 6% bond, dividends payable semi-annually, redeemable at par in 10 years, if the yield is to be 5% compounded semi-annually. Then P is equal :
[Given $(1.025)^{-20}=0.61027094]$
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹53897.29
Face Value = 50,000
Coupon Rate = 6% per annum → Semi-annual coupon = 3%
Semi-Annual component payment = $0.03×50,000=1,500$
Redemption value = 50,000
Time to maturity = 10 years → 20 Semi-annual periods.
$PV_{Coupons}=C×\left(1-\frac{1}{(1+r)^n}\right)÷r$
$=1500×\left(1-\frac{1}{(1+0.25)^{20}}\right)÷0.025$
$=1500×\frac{0.3898}{0.025}=23,388$
$PV_{Redemption}=\frac{50,000}{(1.025)^{20}}≃30,515$
∴ Purchase Price = $PV_{Coupons}+PV_{Coupons}$
$=23,388+30,515$
$=₹53897.29$