Present value
Also called: PV, discounting · Topic: Financial Markets, Instruments, Insurance and Pensions · NCERT: Class 12, Ch 3 "Money and Banking"
Meaning
Present value (PV) is the sum you would need today, at the market interest rate, to earn a given amount in the future. Money in the future is worth less than money today, so future amounts are "discounted". For an amount A received after n years at market rate r:
PV = A ÷ (1 + r)ⁿ
In competitive equilibrium, a bond's price equals the PV of all its future payments. If the price is below PV, buyers rush in. If it is above PV, people sell.
Example
A bond pays Rs 10 after year 1 and Rs 110 after year 2 (NCERT example). At a 5% market rate, PV = 10/1.05 + 110/(1.05)² ≈ Rs 109.29. At 6%, PV ≈ Rs 107.33. A higher interest rate gives a lower PV and so a lower bond price.
Don't confuse with
- Face value: face value is the fixed amount repaid at maturity (Rs 100 here). Present value is what all the payments are worth today, and it changes with the interest rate.
Related concepts
- Bonds
- Coupon rate
- Bond price and interest rate inverse relation
- Capital gain
- Zero-coupon bond
- Floating rate bond
- Mark-to-market
- Yield curve
- Inverted yield curve
- Credit rating