Present Value 2 | Interest and debt | Finance & Capital Markets | Khan Academy

Summary

This video script explores the concept of present value in financial decision-making, offering three hypothetical payment options. It explains the process of discounting future payments to their current value using a 5% risk-free rate. The script illustrates that receiving $100 today is more valuable than a promise of $110 in two years, due to the time value of money. It also demonstrates how to calculate the present value of a series of payments, concluding that option one is the most beneficial based on the given conditions.

Takeaways

• 💰 The script presents a choice between three different payment options, all involving receiving money at different times and amounts.
• 📅 Choice one offers immediate payment of $100 today, highlighted in magenta to indicate the time of payment.
• 🔢 Choice two proposes a payment of $110 in two years, with the payment time also marked in magenta.
• 📈 Choice three is a more complex arrangement, offering $20 today, $50 in one year, and $35 in three years, totaling $105 over the three years.
• 🏦 The speaker assumes a risk-free environment, comparing the payment options to lending money to the federal government at a 5% interest rate.
• 📉 The concept of present value is introduced to determine the worth of future payments in today's money, using a 5% discount rate.
• 🧮 A calculation is provided to show that the present value of $110 received in two years is $99.77, using the formula \( \frac{110}{(1.05)^2} \).
• 🤔 The comparison of choices reveals that taking $100 today and investing it at a 5% interest rate would yield more than the $110 to be received in two years.
• 💡 The importance of the discount rate in financial calculations is emphasized, as it can significantly affect the outcome of present value calculations.
• 📊 The present value of each payment in choice three is calculated individually and then summed up to compare with the other options.
• 📝 The final comparison shows that choice one, receiving $100 today, has the highest present value of approximately $99.37 when compared to the other options.
• 🔑 The takeaway is that understanding present value is crucial for making informed decisions about different payment options and financial investments.

Q & A

What are the two initial payment options presented in the script?

The two initial payment options are: Choice one, receiving $100 today, and Choice two, receiving $110 in 2 years.

Why does the presenter introduce a third payment option?

The third payment option is introduced to provide a more complex scenario and to illustrate the concept of present value more effectively.

What is the significance of circling the payment in magenta in the script?

The magenta circle is used to visually indicate when the payment is received, helping to differentiate between the timing of different payments.

What is the assumed risk-free rate used for discounting future payments in the script?

The assumed risk-free rate used for discounting future payments is 5%.

How does the presenter calculate the present value of $110 received in 2 years?

The presenter calculates the present value by dividing $110 by 1.05 (the factor for 5% growth over one year) twice, which represents discounting back two years.

What is the result of the present value calculation for $110 received in 2 years?

The present value of $110 received in 2 years, using a 5% discount rate, is $99.77.

Why is the present value of $110 in 2 years less than $100 today according to the script?

The present value of $110 in 2 years is less than $100 today because of the time value of money; money received in the future is worth less than the same amount today due to the potential earning capacity of money over time.

What does the script suggest about the comparison between receiving $100 today and $99.77 as the present value of $110 in 2 years?

The script suggests that it is more advantageous to receive $100 today rather than the present value equivalent of $110 in 2 years, which is $99.77.

How does the script handle the third payment option in terms of present value calculation?

The script calculates the present value of each payment in the third option separately: $20 today has a present value of $20, $50 in 1 year is discounted by dividing by 1.05, and $35 in 3 years is discounted by dividing by 1.05 squared.

What is the total present value of the third payment option as calculated in the script?

The total present value of the third payment option, which includes $20 today, $50 in 1 year, and $35 in 3 years, is $99.37.

What insight does the script provide about choosing between different payment options?

The script provides the insight that to make an informed choice between different payment options, one should calculate the present value of each option to determine which is worth more in today's terms.