A bond of face value Rs 100 pays Rs 10 at the end of the first year and Rs 110 at the end of the second year. The market rate of interest rises from 5 per cent to 10 per cent. Using present values, what happens to the price of the bond?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → It falls from Rs 109.29 to Rs 100.
A bond’s price equals the present value of what it pays. Each payment is divided by (1 + r) for each year of waiting.
\( \displaystyle \text{At 5\%: } \frac{10}{1.05} + \frac{110}{(1.05)^2} = 9.52 + 99.77 = 109.29 \)
\( \displaystyle \text{At 10\%: } \frac{10}{1.10} + \frac{110}{(1.10)^2} = 9.09 + 90.91 = 100 \)
The price falls from Rs 109.29 to Rs 100. A higher interest rate lowers the present value, so bond prices move opposite to the rate of interest. At 10 per cent the bond’s own rate equals the market rate, so it sells at its face value.
NCERT (2026-27): “The Speculative Motive … Calculation reveals that it is Rs 109.29 (approx.). It means that if you put Rs 109.29 in your savings bank account it will fetch the same return as the bond. But the seller of the bond is offering the same at a face value of only Rs 100. Clearly the bond is more attractive than the savings bank account and people will rush to get hold of the bond. Competitive bidding will raise the price of the bond above its face value, till price of the bond is equal to its PV. If price rises above the PV the bond becomes less attractive compared to the savings bank account and people would like to get rid of it. The bond will be in excess supply and there will be downward pressure on the bond-price which will bring it back to the PV. It is clear that under competitive assets market condition the price of a bond must always be equal to its present value in equilibrium. …” “It follows that the price of a bond is inversely related to the market rate of interest. …” |