A company has issued a bond of face value Rs. 90,000 carrying an annual dividend of 7% and maturing in 15 years. If the prevailing market rate of interest is 9% , the value of bond redeemed at par is: (given \( (1.09)^{-15}\approx 0.3 \))
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 76,000
The value of a bond is the present value of all the annual dividends plus the present value of the redemption amount, both at the market rate i = 9%.
\( \displaystyle \text{Annual dividend}\ R=7\%\ \text{of}\ 90000=6300 \)
\( \displaystyle \text{Redemption value}\ F=90000\ \text{(at par)},\ n=15 \)
\( \displaystyle V=R\cdot\frac{1-(1+i)^{-n}}{i}+F(1+i)^{-n} \)
\( \displaystyle V=6300\times\frac{1-0.3}{0.09}+90000\times 0.3 \)
\( \displaystyle =6300\times\frac{70}{9}+27000 \)
\( \displaystyle =49000+27000=76000 \)
So the value of the bond is Rs. 76,000.
CBSE Applied Mathematics (Class XII):
Valuation of Bonds
