# What's the best payment?

#### Summary

After predicting which of two earnings streams has the highest currrent value, students use a discounted values table to compare the two earnings streams, discovering that earlier earnings has higher value and that the choice of earnings streams depends on the interest rate chosen.

## Learning Goals

Students will see the impact of time on future earnings, and discover the impact of interest rates on the present value of future earnings.

## Context for Use

Introductory or intermediate course in section on financial markets.

## Description and Teaching Materials

This activity follows the steps of an Interactive Lecture Demonstration

Student worksheet (Microsoft Word 44kB Aug2 09)

Student worksheet (Microsoft Word 44kB Aug2 09)

## Teaching Notes and Tips

In this activity students will work in pairs or in small groups (no more than four students per group) Learn more about using small groups in class.

The activity sheet (above in Teaching Notes) guides students through four steps:

Predict

1. Working individually, students predict which payment is best: $10,000 at end of 10 years or $1000 per year for 9 years. Student answers will likely vary, in part because students will be unable to distinguish the nearly equal present values and because the best choice depends on the discount rate. Students share their predictions with the class. The instructor should be careful not to express approval or disapproval of the predictions at this point.

2. Students students explain to one another why future earnings are valued less than current earnings. The list of reasons should include risk, inflation, and, most importantly for this activity, opportunity cost. The reasons are shared with the class and listed for later discussion.

Experience

3. Students, working in pairs or small groups, use the discounted present value table to calculate the present value of the two earnings streams. Although more cumbersome than a calculator or an online present value web site, the table helps students see the decline in value over time with different interest rates.

Students must choose a discount rate for which the activity deliberately does not provide directions. While students are working, the instructor should note which discount rates are used for step 4.

Reflection

4. Students compare their calculated present value with the choice in question 1.

Students compare answers across groups. If the class is large, if possible, call on one group with an interest rate 2% or lower, and one group with a higher interest rate. Note the reversal in choice between 2% and 3%. Student groups can be asked to explain their choice of discount rate.

To ensure transfer of understanding to new situations, ask students to answer the following context-rich problem: You and your sister just inherited a discount bond. The bond has a face value of $10,000 and matures in 5 years. You would like to hold onto the bond until maturity, but your sister wants her money now. She offers to sell you her half of the bond, but only if you give her a fair price. What is a fair price to offer her? How can you convince your sister it is a fair price?

The activity sheet (above in Teaching Notes) guides students through four steps:

Predict

1. Working individually, students predict which payment is best: $10,000 at end of 10 years or $1000 per year for 9 years. Student answers will likely vary, in part because students will be unable to distinguish the nearly equal present values and because the best choice depends on the discount rate. Students share their predictions with the class. The instructor should be careful not to express approval or disapproval of the predictions at this point.

2. Students students explain to one another why future earnings are valued less than current earnings. The list of reasons should include risk, inflation, and, most importantly for this activity, opportunity cost. The reasons are shared with the class and listed for later discussion.

Experience

3. Students, working in pairs or small groups, use the discounted present value table to calculate the present value of the two earnings streams. Although more cumbersome than a calculator or an online present value web site, the table helps students see the decline in value over time with different interest rates.

Students must choose a discount rate for which the activity deliberately does not provide directions. While students are working, the instructor should note which discount rates are used for step 4.

Reflection

4. Students compare their calculated present value with the choice in question 1.

Students compare answers across groups. If the class is large, if possible, call on one group with an interest rate 2% or lower, and one group with a higher interest rate. Note the reversal in choice between 2% and 3%. Student groups can be asked to explain their choice of discount rate.

To ensure transfer of understanding to new situations, ask students to answer the following context-rich problem: You and your sister just inherited a discount bond. The bond has a face value of $10,000 and matures in 5 years. You would like to hold onto the bond until maturity, but your sister wants her money now. She offers to sell you her half of the bond, but only if you give her a fair price. What is a fair price to offer her? How can you convince your sister it is a fair price?

## Assessment

Students should be able to explain discounted earnings to a peer.