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Bond Pricing Formula & Cash Flow Timeline | EasyCFA | Wall Street Uni

Fixed Income

Bond Pricing: Formula, Timeline & PV Decomposition

Interactive three-panel visualization connecting the bond pricing formula with cash flow timeline and present value decomposition. Hover over any payment to see its term in the formula and its contribution to bond price.

Subtopic: Fixed-Income Bond Valuation
Level: Applied
Status: Featured
Views: 330

Parameters

Payment Frequency

Formula

\begin{aligned}PV &= \sum_{t=1}^{T} \frac{C/2}{(1+r/2)^t} + \frac{FV}{(1+r/2)^T} \\[6pt] PV &= \sum_{t=1}^{10} \frac{\$25.00}{(1+0.0300)^t} + \frac{\$1{,}000}{(1+0.0300)^{10}} \\[6pt] PV &= \$957.35\end{aligned}

Interactive Chart

Bond pricing is the application of present value concepts to a stream of future cash flows. Each coupon payment and the final principal repayment is discounted back to today using the yield to maturity (YTM) as the discount rate. The bond price is the sum of all these present values. Mathematically: PV = C₁/(1+r)¹ + C₂/(1+r)² + ... + (Cₜ + FV)/(1+r)ᵀ where each term represents one discounted cash flow.

Interactive charts are desktop only

The sliders, formulas and analytics view need more room than a phone screen can give them. Open this chart on a desktop or larger tablet to use the full interactive experience.

Study aids

Working with this chart

The errors candidates make on this topic, and what to carry into the exam.

Common mistakes

Forgetting to adjust for payment frequency: Annual YTM must be divided by frequency
Using wrong number of periods: For semi-annual bonds over 5 years, n=10 not 5
Mixing up coupon rate and YTM: Coupon determines cash flow size, YTM determines discount rate
Not summing all terms: Bond price requires summing PV of EVERY cash flow including final principal
Assuming linear discounting: Discounting is exponential, not linear
Ignoring the pull to par: Bond price converges to face value as maturity approaches

Exam tips

Know the formula cold: PV = Σ [Cₜ/(1+r)ᵗ] + FV/(1+r)ᵀ
Calculator TVM functions: Use PV, FV, PMT, N, I/Y keys - much faster than manual calculation
Price-yield relationship: If YTM ↑ then Price ↓ (inverse)
Premium/discount/par rule: Coupon > YTM → premium; Coupon < YTM → discount; Coupon = YTM → par
Hovering technique: Use interactive hover to understand which cash flow contributes most to price
Duration connection: Low-coupon bonds (more principal-heavy) have higher duration
Semi-annual standard: Unless stated otherwise, assume semi-annual coupon payments
Common exam setup: Given FV, coupon rate, YTM, maturity → calculate price
Watch signs on calculator: PV and FV should have opposite signs (outflow vs inflow)

Parameters

Payment Frequency

CCoupon Rate (%)%

015

rYield to Maturity (%)%

0.515

nMaturity (Years)years

230

Formula

\begin{aligned}PV &= \sum_{t=1}^{T} \frac{C/2}{(1+r/2)^t} + \frac{FV}{(1+r/2)^T} \\[6pt] PV &= \sum_{t=1}^{10} \frac{\$25.00}{(1+0.0300)^t} + \frac{\$1{,}000}{(1+0.0300)^{10}} \\[6pt] PV &= \$957.35\end{aligned}

Interactive Chart

Face Value

$1000

Coupon Rate

5.0%

YTM

6.0%

Frequency

Semi-Annual

Bond Price: $957.35

Discount

5yr · 10 periods

Cash Flow Timeline

Pricing Formula (hover cash flows to highlight)

PV =25.00 / (1 + 0.0300)^1+25.00 / (1 + 0.0300)^2+25.00 / (1 + 0.0300)^3+25.00 / (1 + 0.0300)^4+25.00 / (1 + 0.0300)^5+25.00 / (1 + 0.0300)^6+25.00 / (1 + 0.0300)^7+25.00 / (1 + 0.0300)^8+25.00 / (1 + 0.0300)^9+(25.00 + 1000) / (1 + 0.0300)^10

Bond Price: $957.35

Value Breakdown

Bond Price

$957.35

PV of Coupons$213.26

22.3%

PV of Principal$744.09

77.7%

Student Instructions:

Hover over any payment bar to see its matching term in the pricing formula
Blue bars = coupon payments, Green bars = principal repayment at maturity
Increase YTM and observe how the bond price drops below par (discount)
Try Zero-Coupon mode to see a pure discount bond with no periodic payments
Compare how much of the bond's value comes from coupons vs principal