Annuity PV/FV & Break-Even / Margin / Markup

Annuity PV/FV, Break-Even, Margin & Markup — Quick Guide

Annuity PV discounts a stream of equal (or growing) payments to today; FV rolls them forward to the end. Choose ordinary for end-of-period payments or due for beginning. Growing annuities use a payment growth rate g. The tool converts your annual rates to effective per-period values based on your chosen period unit.

Break-even shows when you cover fixed costs: units = Fixed / (Price − Variable Cost). Margin is (Price − Cost)/Price, while Markup is (Price − Cost)/Cost. They’re related but not the same—25% markup equals 20% margin.

Annuity PV/FV and Break-Even / Margin / Markup — Plain-English Guide

Annuity PV/FV and Break-Even / Margin / Markup are everyday finance tools for planning payments, savings, and pricing. This guide explains what each term means, when to use it, and the key formulas our calculator applies. Examples use generic currency (apply £, $, € as needed).

Annuity Basics (PV & FV)

An annuity is a stream of equal payments at regular intervals (monthly, quarterly, yearly). You’ll meet two timing types:

• Ordinary annuity: payments at the end of each period (typical loan or savings deposit).
• Annuity due: payments at the beginning of each period (e.g., rent). Values are the ordinary result × (1 + r).

Present Value (PV) discounts future payments back to today; Future Value (FV) compounds payments forward. In our tool, you enter an annual rate; we convert it to an effective per-period rate based on your chosen unit (year/quarter/month).

• Level annuity PV: PV = P × [1 − (1 + r)⁻ⁿ] / r
• Level annuity FV: FV = P × [(1 + r)ⁿ − 1] / r
• Growing annuity PV (payment grows at g): PV = P × [1 − ((1 + g)/(1 + r))ⁿ] / (r − g)

Example: Pay 100 per month for 36 months at 8% annually. The tool converts 8% to an effective monthly rate and returns PV (today’s value of the stream) and FV (value at month 36). If you select “Annuity Due,” both results increase because cash arrives earlier.

Tips: If r ≈ g in a growing annuity, PV is very sensitive—try small adjustments to test robustness. For zero rates, the formulas simplify to arithmetic sums.

Break-Even, Margin, and Markup (Pricing)

Use this side of the tool to sanity-check pricing and volume goals.

• Contribution per unit: Price − Variable Cost
• Break-even units: Fixed Costs / (Price − Variable Cost)
• Break-even revenue: Fixed Costs / Contribution Margin Ratio, where CMR = (Price − Variable Cost) / Price
• Margin (%): (Price − Cost) / Price
• Markup (%): (Price − Cost) / Cost

Conversions: from margin m to markup u = m / (1 − m); from markup u to margin m = u / (1 + u).

Example: Price 50, Variable Cost 30, Fixed Costs 10,000 → Contribution = 20. Break-even units = 10,000 / 20 = 500. Margin = 20 / 50 = 40%. If you plan 700 units, expected profit ≈ 700 × 20 − 10,000 = 4,000.

When to Use Which

• Annuity PV/FV: valuing payment plans, leases, subscriptions, saving toward goals.
• Break-Even / Margin / Markup: setting prices, testing targets, and estimating how many units you need to sell to cover fixed overheads.

Common Pitfalls

• Margin ≠ Markup: 25% markup is only 20% margin. Use our conversion to avoid mispricing.
• Contribution ≤ 0: If price ≤ variable cost, break-even is impossible—raise price, cut cost, or rethink volume assumptions.
• Period mismatch: Enter an annual rate, then pick the correct period unit so discounting/compounding matches your cash-flow frequency.
• Tax/VAT note (UK/EU): Margin/markup are usually based on net (ex-VAT) prices. Use our VAT calculator if you need to separate VAT from price.

Pro tip: run quick sensitivities—nudge the rate, growth, price, or costs by ±5% to see how PV, FV, and break-even respond. Robust plans change slowly under small tweaks.