Corporate finance Chapter 2 Part 3

Introduction to Week Two Lecture Videos Part Three

In this video, the instructor introduces the concept of shortcuts for calculating present values and future values when cash flows are longer. The two shortcuts discussed are perpetuity and annuity.

Perpetuity Shortcut

• A perpetuity is an asset that pays a fixed sum each year for an indefinite period.

• The formula to calculate the return on a perpetual cash flow is periodic cash flow divided by the present value.

• To calculate the present value of a perpetual cash flow, divide the periodic cash flow by the discount rate.

• Example: What is the present value of $1 billion every year indefinitely if the discount rate is 10%? The present value would be $10 billion.

Perpetuity Starting at a Future Period

• Sometimes, a perpetuity may start at a future period instead of immediately.

• To calculate the present value of a perpetuity starting in some future time, use the same formula as before but multiply it by a present value factor.

• Example: If an investment starts making money after three years with a perpetual cash flow, we first calculate the present value of the cash flow three years from now using the formula. Then, we multiply it by a present value factor to get the present value at zero time period.

Annuity Shortcut

• An annuity is similar to a perpetuity but occurs for a specific number of periods.

• An annuity has equal cash flows occurring at regular intervals.

• The formula to calculate the present value of an annuity is periodic cash flow multiplied by 1 divided by interest rate minus 1 divided by interest rate into (1 plus interest rate) power T.

• This formula uses a present value annuity factor to simplify calculations.

Example - State Lottery Jackpot Prize

In this example, the instructor demonstrates how to calculate the present value of a series of cash flows using the annuity formula.

• The state lottery advertises a jackpot prize of $590.5 million paid in 30 years.

• To calculate the present value, use the annuity formula with the periodic cash flow as $590.5 million and the time period as 30 years.

• This will give us the present value of all the cash inflows over 30 years.

Timestamps are not available for this section.

Understanding Annuities

In this section, we learn about annuities and their characteristics. An annuity is a cash flow that provides the same amount of money at regular intervals for a specific period of time.

Types of Annuities

• Ordinary Annuity: The cash flow starts at the end of the first period.

• Annuity Due: The cash flow starts immediately at zero time period.

Present Value and Future Value Formulas

• Present Value of an Ordinary Annuity: Calculated using the formula we have seen earlier, multiplied by (1 + R).

• Future Value of an Ordinary Annuity: Calculated by multiplying the future value annuity factor with the periodic cash flow.

Examples

1. Investing annually with an interest rate: We calculate the future value of an annuity using the formula and find out how much our investment will be worth after a certain number of years.

2. Paying off a bank loan: We use present value calculations to determine the size of each installment payment for an annuity.

3. Purchasing a TV with annual installments: We solve for the periodic payment amount using present value calculations.

Future Value of Annuites

This section focuses on calculating the future value of annuities, which determines the value of a series of cash flows occurring over a specific time period in the future.

Future Value Formula

• Future Value = Periodic Cash Flow * (1 + Interest Rate)^T - 1 / Interest Rate

Example

Calculating future value: We determine the future value of $20,000 paid at the end of each year for five years with an 8% interest rate.

Perpetuity and Growing Perpetuity

Here, we explore the concept of perpetuity and growing perpetuity. Perpetuity refers to a series of cash flows that continue indefinitely with the same amount at regular intervals.

Growing Perpetuity

• A growing perpetuity is a perpetuity where the cash flow continues indefinitely but increases over time.

Conclusion

In this transcript, we learned about annuities and their characteristics, including ordinary annuities and annuities due. We also explored the formulas for calculating present value and future value of annuities. Additionally, we discussed examples of using these formulas for investment calculations and loan payments. Finally, we touched on the concept of perpetuity and growing perpetuity.

New Section Present Value Calculation with Growth Rate

In this section, the speaker discusses the calculation of present value when there is a growth rate involved in the cash flow. The example used is a perpetuity with a rate of return of 10% and a constant growth rate of 4%.

Present Value Calculation with Growth Rate

• The present value calculation involves dividing the cash flow by the interest rate.

• When there is a growth rate, an additional term (R - G) is added to calculate the present value.

• In the example given, the cash flow is $1 billion, the rate of return is 10%, and the growth rate is 4%.

• By subtracting the growth rate from the rate of return (10% - 4%), we get 6% as the effective discount rate.

• The present value of this growing perpetuity is calculated to be $16.667 billion.

New Section Comparison with No Growth Rate

This section compares the present value calculation with and without a growth rate in the cash flow.

Comparison with No Growth Rate

• In a previous example where there was no growth in the cash flow, only one divided by the interest rate was used to calculate present value.

• In that case, when there was no growth, the present value of that perpetual cash flow was $10 billion.

• However, when there is a growth rate in the cash flow, such as in our current example, where it grows at 4%, then we use (R - G) term to calculate present value.

• As a result, when there is a growth in cash flow, like in our current example, where it grows at 4%, then we use (R - G) term to calculate present value.

• Therefore, the present value of the growing perpetuity increases to $16.667 billion.

New Section Conclusion

This section concludes the discussion on annuity and perpetuity, highlighting the impact of growth rate on present value.

• The addition of a growth rate in the cash flow affects the calculation of present value.

• When there is no growth, only one divided by the interest rate is used to calculate present value.

• However, when there is a growth rate, an additional term (R - G) is added to account for it.

• The presence of a growth rate increases the present value of a perpetual cash flow.

• In our example, with a 4% growth rate, the present value increased from $10 billion to $16.667 billion.

The transcript provided was already in English language.