ECON 121 Discussion: Week 9

Slides available here:

All discussion slides here:

Today’s Plan

  1. Review the financial system
  2. Review the Time Value of Money
  3. Practice Problems

Financial System Review

The Financial System

So how does investment spending and saving actually work? Via the financial system.


What does the financial system do?

  1. It’s a market for savers and borrowers to exchange funds

    • This reduces transaction costs: it’s usually easier for a company to call a bank for a loan than trying to raise funds from individual savers!

  2. Reduce risk: it makes it easier for savers to put money into a wide range of financial assets

    • Some loans won’t get paid back: financial market makes it easier to put money into many types of investment opportunities to spread this risk out

  3. Provide liquidity: savers would usually rather have their money in liquid types of savings

    • Liquidity: how easy it is to turn something into cash

      • Which is more liquid: money in a savings account or a loan you make to a company that will get 100% paid back in five years?

Major Types of Financial Assets/Instruments

  1. Deposit accounts: savings or checking accounts (or some other type of account) at a bank

  2. Loans: money borrowed from a bank (usually) with a promise to be paid back later

    • Banks use the money in deposit accounts to make loans

  3. Bonds: a type of loan where a (usually large) company borrows directly from lenders without using a bank

    • A company or government will sell a bond directly to savers, which comes with a promise to pay it back with interest

  4. Stocks: a portion of ownership (share) of a company which entitles the stockholder to a part of the company’s earnings

    • A company is not borrowing money when it issues shares and doesn’t pay interest on them like with a bond or a loan
    • A company may pay a dividend per share, which is a part of their profit
      • Companies aren’t obligated to pay a dividend (and might not if profits are low or the company doesn’t make a profit): Amazon and Tesla famously don’t pay dividends despite their profitability
    • A shareholder gets a say in how the company is run (depending on how many shares they own) - lenders and bondholders don’t have this right with loans and bonds

What Are These Assets Worth?

Notice that a key part of owning these financial assets is that they pay you money over time in the form of interest or dividends… would you rather have money now or in the future?


The present value of these assets is how much the money they pay you in the future is worth today, accounting for their rate of return and how long you have to wait to “realize” that return

  • “Realize:” when you actually earn real money from an asset


Why is getting money a month from now not worth the same as having that money today (aside from inflation)? Because you can save or invest a dollar today and earn a return, like interest, on it: you will have more than a dollar next month!


In general, the present value of an asset…

  1. …decreases with time (how far in the future you’ll realize the return on the asset)

  2. …decreases the higher the rate of return on the asset

Practice Problems

Practice Problem #1

Are the following scenarios describing stocks or bonds?

  1. Acme Inc. wants to start a new product research project. It pays for the project through debt financing.

  2. Jared buys a company’s financial asset secondhand (i.e., buys it from another investor). Later in the year he’s able to vote on who will be on the company’s board in the its annual shareholder meeting.

  3. Jared buys another financial asset. This time he buys it from a company but doesn’t get to vote on the company’s board members. He gets an interest payment from the company.

  4. Torie buys a Treasury bill, (which is basically lending money to the federal government). In ten years the government will pay her back, plus a little more.

Practice Problem #1

Are the following scenarios describing stocks or bonds?

  1. Acme Inc. wants to start a new product research project. It pays for the project through debt financing.

  2. Jared buys a company’s financial asset secondhand (i.e., buys it from another investor). Later in the year he’s able to vote on who will be on the company’s board in the its annual shareholder meeting.

  3. Jared buys another financial asset. This time he buys it from a company but doesn’t get to vote on the company’s board members. He gets an interest payment from the company.

  4. Torie buys a Treasury bill, (which is basically lending money to the federal government). In ten years the government will pay her back, plus a little more.

Answer

  1. Bond (the hint: “debt financing”)

  2. Stock (the hint: he votes for the board, so he has some ownership of the company)

  3. Bond (the hint: he earns interest)

  4. Bond (the hint: the “little more” the government pays back is an interest payment)

Practice Problem #2

Are the people/companies below buying/selling a financial asset from a financial intermediary or not?

  1. Rosie buys shares in a mutual fund from her investment broker.

  2. Microsoft needs money to fund a new data center. It issues bonds for investors to buy.

  3. Patricia buys a Treasury bill on the U.S. Treasury’s website.

  4. Terry gets a mortgage from his bank to buy a house.

Practice Problem #2

Are the people/companies below buying/selling a financial asset from a financial intermediary or not?

  1. Rosie buys shares in a mutual fund from her investment broker.

  2. Microsoft needs money to fund a new data center. It issues bonds for investors to buy.

  3. Patricia buys a Treasury bill on the U.S. Treasury’s website.

  4. Terry gets a mortgage from his bank to buy a house.

Answer

  1. Yes: a mutual fund contains many stocks and bonds pre-purchased from companies and Rosie is using a broker

  2. No: Microsoft is raising funds directly from investors

  3. No: Patricia is buying the bond directly from the government

  4. Yes: Terry is borrowing money from a bank

Practice Problem #3

Use the information below about the economy of Macronesia to answer the following questions:

  • GDP = $1 billion
  • C = $850 million
  • T = $50 million
  • G = $100 million
  • X = $100 million
  • IM = $125 million

What’s the value of government savings in Macronesia?

Practice Problem #3

Use the information below about the economy of Macronesia to answer the following questions:

  • GDP = $1 billion
  • C = $850 million
  • T = $50 million
  • G = $100 million
  • X = $100 million
  • IM = $125 million

What’s the value of government savings in Macronesia?

Answer

The government’s savings (or budget balance) is how much it brings in in revenue (taxes, T) minus how much it spends (government purchases, G):

\[ \$50 - \$100 = -\$50 \text{ million} \]

Practice Problem #3

Use the information below about the economy of Macronesia to answer the following questions:

  • GDP = $1 billion
  • C = $850 million
  • T = $50 million
  • G = $100 million
  • X = $100 million
  • IM = $125 million


  • GS = -$50 million

How much investment spending is there in Macronesia? How much private savings?

Practice Problem #3

Use the information below about the economy of Macronesia to answer the following questions:

  • GDP = $1 billion
  • C = $850 million
  • T = $50 million
  • G = $100 million
  • X = $100 million
  • IM = $125 million


  • GS = -$50 million

How much investment spending is there in Macronesia? How much private savings?

Answer

Use the GDP equation to solve for \(I\):

\[ \begin{align} GDP &= C + I + G + X - IM \\ 1,000 &= 850 + I + 100 + 100 - 125 \\ \$75 \text{ million} &= I \end{align} \]

Private saving is how much consumers don’t spend on consumption or taxes:

\[ \begin{align} S_{P} &= GDP - C - T \\ S_{P} &= 1,000 - 850 - 50 \\ S_{P} &= \$100 \text{ million} \end{align} \]

Practice Problem #3

Use the information below about the economy of Macronesia to answer the following questions:

  • GDP = $1 billion
  • C = $850 million
  • T = $50 million
  • G = $100 million
  • X = $100 million
  • IM = $125 million


  • GS = -$50 million
  • I = $75 million
  • Priv. Savings = $100 million

Think about imports and exports: how do you calculate net capital inflow and how does this relate to imports and exports? What’s Macronesia’s NCI?

Practice Problem #3

Use the information below about the economy of Macronesia to answer the following questions:

  • GDP = $1 billion
  • C = $850 million
  • T = $50 million
  • G = $100 million
  • X = $100 million
  • IM = $125 million


  • GS = -$50 million
  • I = $75 million
  • Priv. Savings = $100 million

Think about imports and exports: how do you calculate net capital inflow and how does this relate to imports and exports? What’s Macronesia’s NCI?

Answer

Think of imports like “buying” and exports like “selling:” if you buy more than you sell, you need to borrow to do that! This would be a positive NCI: capital is flowing into the country since you’re borrowing. The opposite is true for exporting more than you import.

Macronesia’s NCI:

\[ \begin{align} NCI &= IM - X \\ &= 125 - 100 = \$25 \text{ million} \end{align} \]

Practice Problem #4

What’s wrong with the tweet below? 🤨

Say you knew how long you were going to live and what interest rate you could save money at for the rest of your life. Given what you know about present value, how would you decide which option to pick?


Practice Problem #4

What’s wrong with the tweet below? 🤨

Say you knew how long you were going to live and what interest rate you could save money at for the rest of your life. Given what you know about present value, how would you decide which option to pick?


Answer

“Side Hustle King” isn’t thinking about how you could just save or invest the $1,000,000 today (and probably make a lot more than just $50 per month in interest!).

You could calculate the present value of the $50-per-month income stream and compare it to the $1 million you could have today: if the present value of Option B is greater than $1 million, then it would be a better option.

Practice Problem #4 (Hard Mode, Just For Fun)

Say you and Side Hustle King both have access to a savings account that pays 12% annual interest, compounded monthly. Both of you expect to live another 50 years. Side Hustle King takes option B ($50 per month) and puts their money into their account each month. At the end of 50 years, they’ll have $1,952,917 in their savings account. You pick option A ($1,000,000 now).


How much will be in your account at the end of 50 years? How does it compare to what’s in Side Hustle King’s account?


Use the present value formula to solve this

\[ \text{Present Value} = \frac{\text{Future Value}}{(1 + r)^n} \]

where \(r\) is the rate of return you earn and \(n\) is the number of periods.


This is just for fun: do not expect something like this to be on an exam (especially because this would require a calculator)!

Practice Problem #4 (Hard Mode, Just For Fun)

Answer

Notice we’re comparing future values here instead of present values. So rearrange the present value formula to solve for future value instead: \(\text{Future Value} = \text{Present Value} \times (1 + r)^n\).

\(r = 12\% / 12 = 1\%\) because interest is compounding monthly. \(n = 50 \times 12 = 600\) is the total number of periods (months) in the problem. Then do the calculation:

\[ \text{Future Value} = \$1,000,000 \times (1 + 0.01)^{600} = \$391,583,397 \]

You would have over $391 million in your account while Side Hustle King would have less than $2 million!

Another way to make this comparison: like the answer to the original question, we could compute the present value of the $50-per-month income stream (at 12% annual interest compounded monthly for 50 years) and compare it to the $1 million you could have now. This involves a slightly more complicated present value equation, but you can try it yourself: the present value comes out to just less than $5,000. That’s way less than a million bucks!