Perpetuity and Annuity Derivations

Formula of perpetuity:

When you wish to prove on an account of this being a real statement, the divide it by C,

Multiplying the 3.5 equation by the factor which is (1 + r),

Subtracting the equation 3.5 from that of the equation given in 3.6,

This right hand side simplifies directly into the r/r that makes it a real statement.

Growing perpetuity on the other hand gives us a formula,

Returning to the original definition, a perpetuity (growing) will pull out a (1 + g) of the factor who is from the cash flows,

The f is replaced by  using the very first of the formula,

This can be further simplified into,

Annuity is considered as a perpetuity value which will pay a fixed amount of $10 always in the starting of the first year.

Another thing that must be considered is that the perpetuity begins in the five years & pays $10 that is beginning at the 6^th year. If you are to purchase a total of $10 every year for the duration of 5 years, then that would be so for $0 every year after that year.

This will show that $10 is the beginning of the next coming year and in the ending of the 5^th year. And this value must account to,

This is in fact the annuity determining formula.

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Links of Previous Main Topic:-

• Introduction of corporate finance
• The time value of money and net present value
• Stock and bond valuation annuities and perpetuities

Links of Next Financial Accounting Topics:-

• A first encounter with capital budgeting rules
• Working with time varying rates of return
• Uncertainty default and risk
• Risk and return risk aversion in a perfect market
• Investor choice risk and reward
• The capital asset pricing model
• Market imperfections
• Perfect and efficient markets and classical and behavioral finance
• Capital budgeting applications and pitfalls
• From financial statements to economic cash flows
• Valuation comparables financial ratios
• Corporate claims
• Capital structure and capital budgeting in a perfect market
• The weighted cost of capital and adjusted present value in an imperfect market with taxes
• What matters
• Equity payouts
• For value financial structure and corporate strategy analysis
• Capital structure dynamics firm scale
• Capital structure patterns in the united states
• Investment banking and mergers and acquisitions
• Corporate governance
• International finance
• Options and risk management