CGMA BA1

8. Investment appraisal

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Annuities, perpetuities, and investment methods

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Annuities

An annuity is a constant cash flow received or paid over several periods.

Present value of an annuity

Use this approach when the cash flow is the same each period.

$PV = Annual Cash Flow \times Annuity Factor$

Annuity factor formula:

$\frac{1 - ( 1 + r ) ^{- n}}{r}$

Example 4

Neymar will receive $$10, 000$ annually for $5$ years at $10%$ interest.

Using annuity tables:

$10, 000 \times 3.791 = 37, 910$

Solution:

(spoiler)

The present value of the annuity is $$37, 910$ .

Perpetuity

A perpetuity is a constant cash flow received forever.

Formula

$PV = \frac{Cash Flow}{r}$

Example 5

KTA invested $$50, 000$ to generate $$5, 000$ per year forever at $10%$ .

$\frac{5 , 000}{0.10} = 50, 000$

Solution:

(spoiler)

NPV = $0$ (break-even investment)

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Annuities, perpetuities, and investment methods

Annuities

An annuity is a constant cash flow received or paid over several periods.

Present value of an annuity

Use this approach when the cash flow is the same each period.

$PV = Annual Cash Flow \times Annuity Factor$

Annuity factor formula:

$\frac{1 - ( 1 + r ) ^{- n}}{r}$

Example 4

Neymar will receive $$10, 000$ annually for $5$ years at $10%$ interest.

Using annuity tables:

$10, 000 \times 3.791 = 37, 910$

Solution:

(spoiler)

The present value of the annuity is $$37, 910$ .

Perpetuity

A perpetuity is a constant cash flow received forever.

Formula

$PV = \frac{Cash Flow}{r}$

Example 5

KTA invested $$50, 000$ to generate $$5, 000$ per year forever at $10%$ .

$\frac{5 , 000}{0.10} = 50, 000$

Solution:

(spoiler)

NPV = $0$ (break-even investment)

Annuities

An annuity is a constant cash flow received or paid over several periods.

Present value of an annuity

Use this approach when the cash flow is the same each period.

$PV = Annual Cash Flow \times Annuity Factor$

Annuity factor formula:

$\frac{1 - ( 1 + r ) ^{- n}}{r}$

Example 4

Neymar will receive $$10, 000$ annually for $5$ years at $10%$ interest.

Using annuity tables:

$10, 000 \times 3.791 = 37, 910$

Solution:

(spoiler)

The present value of the annuity is $$37, 910$ .

Perpetuity

A perpetuity is a constant cash flow received forever.

Formula

$PV = \frac{Cash Flow}{r}$

Example 5

KTA invested $$50, 000$ to generate $$5, 000$ per year forever at $10%$ .

$\frac{5 , 000}{0.10} = 50, 000$

Solution:

(spoiler)

NPV = $0$ (break-even investment)