Use variable names from the panel above (e.g. FV, r, n) โ or type numbers directly: 10000 / (1 + 0.08)^10
coupon
Annual coupon payment ($)
coupon = 50
face
Face (par) value at maturity ($)
face = 1000
y% as decimal
Yield to maturity (decimal)
y = 0.06
price
Current market price of bond ($)
price = 950
duration
Modified duration (years)
duration = 4.5
delta_y% as decimal
Change in yield (decimal)
delta_y = 0.01
๐ก You can also enter values directly in the formula: 10000 / (1 + 0.08)^10
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โฌ Export Calculation
Exports a plain .txt file with your expression, formula, all variable values, result, and educational notes โ ready to paste into any report, Word doc, Notion, or Google Docs.
The exported file includes the formula in standard mathematical notation โ you can paste it directly into Excel, Google Sheets, or back into FinanceSheep.
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Learn: Bond Mathematics
PART IX โ MATHEMATICAL FINANCE ยท Educational Guide
The Core Idea
A bond is a stream of future cash flows โ coupon payments and a final principal repayment. Its price is simply the present value of those cash flows discounted at the market yield. When market yields rise, bond prices fall โ this is the most important inverse relationship in fixed income and it directly affects WACC and discount rates in equity valuation.
How It Works
Price = ฮฃ [C / (1+y)^t] + [F / (1+y)^T]. YTM is the internal rate of return โ the yield making PV of cash flows equal the market price. Duration measures price sensitivity: a 1% yield rise drops price by approximately Duration%. Modified duration = Macaulay Duration / (1+y). Convexity is the second-order correction โ actual price change is slightly better than duration predicts because of curvature in the price-yield relationship.
๐ก
Real-World Example: 3-year bond, $1,000 par, 5% coupon, YTM = 6%: Price = 50/1.06 + 50/1.06ยฒ + 1,050/1.06ยณ = 47.17 + 44.50 + 881.68 = $973.35 (trading at a discount because coupon rate 5% < market yield 6%). Current yield: $50/$973.35 = 5.14%. If modified duration = 2.83 and yield rises 1%: ฮPrice โ โ2.83% ร $973.35 = โ$27.55 new price โ $945.80. Long duration bonds (30-year Treasuries, duration โ 18) are hit far harder by rising rates than short-duration bills.