This lesson extends TVM principles to streams of multiple equal cash flows (annuities) and perpetual cash flows (perpetuities). It covers the calculation of present and future values for ordinary annuities and annuities due, as covered in the NPTEL corporate finance syllabus .

• Definition of an Annuity: An annuity is a series of equal cash flows occurring at regular intervals. The NPTEL syllabus identifies annuities, amortization, and perpetuities as core TVM topics requiring mastery .

• Ordinary Annuity vs. Annuity Due: In an ordinary annuity, payments occur at the end of each period. In an annuity due, payments occur at the beginning of each period. Because payments are received or made earlier, an annuity due has a higher present and future value than an ordinary annuity, assuming the same cash flow and interest rate.

• Present Value of an Ordinary Annuity: The present value of an ordinary annuity is the sum of the present values of each individual payment. The formula is:

  • PV = PMT × [1 – (1 + r)^-n] / r.

• Future Value of an Ordinary Annuity: The future value of an ordinary annuity is the sum of the future values of each individual payment. The formula is:

  • FV = PMT × [(1 + r)^n – 1] / r.

• Perpetuities: A perpetuity is an annuity that continues forever. Its present value is a simple formula:

  • PV = PMT / r.

  • Perpetuities are conceptually important, although uncommon in practice. The valuation of non-callable perpetual preferred stock uses this exact formula, where the dividend is the perpetual payment and the required rate of return is the discount rate.

• Loan Amortization: A loan amortization schedule breaks down each loan payment into interest and principal components. This is a direct application of annuity calculations, as each payment is an annuity, and the present value of all payments equals the loan amount.