How does bond pricing actually work? I keep hearing 'present value of cash flows' but need a concrete example.
I'm studying CFA Level I Fixed Income and struggling with bond pricing mechanics. The textbook says a bond's price equals the present value of all future cash flows discounted at the yield to maturity, but when I try to apply it I get confused with the timing of coupons. Can someone walk me through it with real numbers?
Bond pricing is fundamentally about time value of money. You discount every future cash flow — each coupon payment and the final par repayment — back to today using the bond's yield to maturity (YTM) as the discount rate.
The Formula:
P = C/(1+r)^1 + C/(1+r)^2 + ... + C/(1+r)^n + FV/(1+r)^n
Where:
- P = Bond price
- C = Coupon payment per period
- r = YTM per period
- n = Number of periods to maturity
- FV = Face value (typically $1,000)
Worked Example: Consider a 3-year annual-pay bond with a 6% coupon rate and a YTM of 5%. Face value is $1,000.
- Annual coupon = 6% x 60
| Year | Cash Flow | Discount Factor (1/1.05^t) | Present Value |
|---|---|---|---|
| 1 | $60 | 0.9524 | $57.14 |
| 2 | $60 | 0.9070 | $54.42 |
| 3 | $1,060 | 0.8638 | $915.63 |
| Total | $1,027.19 |
The bond trades at a premium (1,000) because the coupon rate (6%) exceeds the YTM (5%). Investors pay extra for the above-market coupon stream.
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Key relationships to remember:
- Coupon rate > YTM --> Premium bond (price > par)
- Coupon rate < YTM --> Discount bond (price < par)
- Coupon rate = YTM --> Par bond (price = par)
For semiannual-pay bonds (the US standard), divide the coupon and YTM by 2, and double the number of periods. Practice this formula until it becomes second nature — it's tested heavily on the CFA Level I exam.
Explore our CFA Level I Fixed Income course for video walkthroughs of bond pricing problems.
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