FRM: Cash-flow timing

Explanations, applications and practice for cash-flow timing.

• Discrete and continuous compounding conventions

  Compare mathematical growth factors without treating a benchmark as an investment product.

  Comparisons

• A level perpetuity and its convergence condition

  Use the infinite-stream formula only with the required timing and positive discount rate.

  Concepts

• Discounting with a negative periodic rate

  Explain why a future fixed payment can have a present value above its amount.

  Concepts

• Annuity-due values at a common date

  Use the annuity-due values at a common date relationship with its timing and rate conditions.

  Formulas

• Continuous-compounding value of a single amount

  Use the continuous-compounding value of a single amount relationship with its timing and rate conditions.

  Formulas

• Effective annual rate from a nominal quotation

  Use the effective annual rate from a nominal quotation relationship with its timing and rate conditions.

  Formulas

• Effective rate for a shorter or longer interval

  Use the effective rate for a shorter or longer interval relationship with its timing and rate conditions.

  Formulas

• Payment for a fully amortizing level-payment model

  Use the payment for a fully amortizing level-payment model relationship with its timing and rate conditions.

  Formulas

• Future value of dated cash flows at a common time

  Use the future value of dated cash flows at a common time relationship with its timing and rate conditions.

  Formulas

• Present value of a level perpetuity

  Use the present value of a level perpetuity relationship with its timing and rate conditions.

  Formulas

• Future value of an ordinary annuity

  Use the future value of an ordinary annuity relationship with its timing and rate conditions.

  Formulas

• Present value of an ordinary annuity

  Use the present value of an ordinary annuity relationship with its timing and rate conditions.

  Formulas

• Single-sum present and future value

  Use the single-sum present and future value relationship with its timing and rate conditions.

  Formulas

• Ordinary annuity and annuity-due timing

  Place equal payments at the correct dates before applying the value factor.

  Lessons

• Nominal and effective interest rates

  Compare quoted annual rates only after identifying the compounding convention.

  Lessons

• Choosing a common date for cash-flow values

  Move differently dated cash flows to the same date before adding their values.

  Lessons

• Why dividing an effective annual rate by twelve changes the model

  Use the annual growth factor to obtain an equivalent monthly rate.

  Common mistakes
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  Equal-payment annuity value calculator

  Compare end-period and beginning-period payment patterns at defined dates.

  Tools
• 

  Effective annual rate calculator

  Convert a nominal annual quotation and inspect its periodic rate.

  Tools
• 

  Single-sum present and future value calculator

  Move one amount backward or forward over a stated count of equal periods.

  Tools

• Decomposing an uneven stream into an annuity and an extra payment

  Check cash-flow additivity using two representations of the same dated stream.

  Worked examples

• A finite annuity compared with the perpetuity limit

  Compare a bounded payment stream with an infinite stream under the same positive rate.

  Worked examples

• A level-payment amortization model

  Derive a payment from an annuity factor and separate interest from principal.

  Worked examples

• Comparing ordinary and due annuity values

  Shift each payment one period earlier while preserving the valuation date.

  Worked examples

• Quarterly and annual discounting of the same payment

  Check that an effective annual conversion preserves the value of a dated single sum.

  Worked examples

• Future value of end-quarter deposits

  Use a quarterly rate, quarterly payment count and a defined final date.

  Worked examples