Present Value of Perpetuity

What is the Present Value of Perpetuity?

Perpetuity can be defined as the income stream that the individual gets for infinite time period and its present value is arrived by discounting the identical cash flows with the discounting rate. Here the cash flows are infinite but its present value amounts to a limited value.

Explanation

Perpetuity is a series of cash flowsCash FlowsCash Flow is the amount of cash or cash equivalent generated & consumed by a Company over a given period. It proves to be a prerequisite for analyzing the business’s strength, profitability, & scope for betterment. read more that have an infinite life, and such an income stream grows with a proportionate rate. The cash flows should be identical.

The formula is basically derived from the dividend growth model. The formula attempts to determine the terminal valueTerminal ValueTerminal Value is the value of a project at a stage beyond which it's present value cannot be calculated. This value is the permanent value from there onwards. read more of the identical cash flows. Therefore, the present value of the cash flows at basic expression can be derived as follows: –

Present value = D / (1+r) + D x (1 + g) / (1 + r) ^2 + D / (1+r) + D x (1 + g) ^2 / (1 + r) ^3……….

Present value = D / r

Present Value of Perpetuity Formula

The formula is expressed as follows: –

Present Value of Perpetuity

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Source: Present Value of Perpetuity (wallstreetmojo.com)

PV of Perpetuity = ICF / r

Here,

  • The identical cash flows are regarded as the CF.
  • The interest rate or the discounting rate is expressed as r.

If the perpetuity grows by a constant growth rate, then it would be expressed as described below: –

PV of Perpetuity = ICF / (r – g)

Here,

  • The identical cash flows are regarded as the CF.
  • The interest rate or the discounting rate is expressed as r.
  • The growth rate is expressed as g.

How to Calculate Present Value of Perpetuity?

To calculate it has a discount rate only, the following steps should be performed as displayed below: –

Step #1 –  Choose the financial instrument or asset that provides sustainable infinite cash flows for its entire life cycle. Such financial assetsFinancial AssetsFinancial assets are investment assets whose value derives from a contractual claim on what they represent. These are liquid assets because the economic resources or ownership can be converted into a valuable asset such as cash.read more or instruments could be rental residential property, rental commercial property, preferred stocks, and bonds.

Step #2 –  Next, Determine the identical cash flows or the income stream.

Step #3 –  Next, determine the discount rate.

Step #4 –  To arrive at the PV of the perpetuity, divide the cash flows with the resulting value determined in step 3.

To calculate the PV of the perpetuity having discount rate and growth rate, the following steps should be performed as displayed below: –

Step #1 – Choose the financial instrument or asset that provides sustainable infinite cash flows for its entire life cycle. Such financial assetsFinancial AssetsFinancial assets are investment assets whose value derives from a contractual claim on what they represent. These are liquid assets because the economic resources or ownership can be converted into a valuable asset such as cash.read more or instruments could be rental residential property, rental commercial property, preferred stocks, and bonds.

Step #2 – Next, Determine the identical cash flows or the income stream.

Step #3 –  Next, determine the discount rate.

Step #4 – Next, determine the growth rate, if any, corresponding to the infinite cash flows.

Step #5 – Next, determine the difference between the discount rate and the growth rate.

Step #6 – To arrive at the present value of the perpetuity, divide the cash flows with the resulting value determined in step 5.

Examples

Example #1

Let us then take the example of a trading business. The business intends to receive an income of $120,000 for infinite tenure. The cost of capital for the business is at 13 percent. The cash flows grow at the proportionate basis of 3 percent. Help the management to determine it.

Solution

Calculation of PV of Perpetuity 

Present Value of Perpetuity Example 1
  • = $120, 000 / (13% – 3%)
  • = $1,200,000

Example #2

Let us then take the example of an individual investor who owns preferred stocks in company ABC. The business intends to distribute preferred dividends of $20 per share for infinite tenure. The required rate of return for the investor is at 8 percent. The cash flows grow at the proportionate basis of 2 percent. The investor currently holds 200 shares of the company ABC. Help the investor to determine it. Compute the total value of dividend income as displayed below: –

Solution

Total Value of Dividends

Present Value of Perpetuity Example 2

The total value of dividendsDividendsDividend is that portion of profit which is distributed to the shareholders of the company as the reward for their investment in the company and its distribution amount is decided by the board of the company and thereafter approved by the shareholders of the company.read more= Preferred dividend per share x number of shares

  • = $20 x 200
  • Total Value of Dividends = $4,000

Calculation of PV of Perpetuity 

Present Value of Perpetuity Example 2.1
  • = $4, 000 / (8% – 2%)
  • = $66,666.67

Example #3

Let us then take the example of the endowment scheme. The scheme intends to provide an income of $320,000 for infinite tenure. The required rate of return is 10 percent. Help the investor to determine it?

Solution

Calculation of Present Value of Perpetuity 

Present Value of Perpetuity Example 3
  • = $320, 000 / 10%
  • = $3,200,000

Uses

Conclusion

The perpetuity is identical cash flows that are received for infinite tenure. The PV of such income streams is derived by dividing through a discount rate and is termed as the present value of a perpetuity. The perpetuity determined through the discount rate may vary if the financial analyst modifies the discount rate at periodic levels.

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