Macroeconomics: Financial Economics

1. CHAPTER 36
Financial Economics

2. Financial Investment
Present Value
Some Popular Investments
Risk and Return
Chapter Contents

3. Financial Investment
Financial investment: The purchase of a financial asset or real
asset in the expectation of financial gain.
• Financial assets include stocks, bonds, and derivatives.
• Real assets include houses and lands.
• Securities: Financial assets that are tradable in organized financial
market.
 Apple stocks traded in New York Stock Exchange
 U.S. Treasury bonds traded in the over-the-counter market.
• Financial investment involves cashflows now and future. Its performance
and financial gains are assessed by comparing cashflows.

4. Time Value of Money
• Ex. Your boss tells you that you get a $1,000 bonus for your hard work.
Would you like to get the bonus today or next month? Your answer may
be “today.”
• Ex. You borrowed $2,000 from your mom to pay for the tuition and fees
and promised to pay back all one day. Would you like to pay back today or
next year? Your answer may be “next year.”
• As these examples illustrate, people want one cash flow over another.
Why? The reason is as everyone knows
A dollar today worth more than a dollar tomorrow.
• This implies that the same $1 has different values for you today, depending
on when you receive or pay it.

5. Implication of Time Value of Money
• Since a dollar today is different from a dollar tomorrow, we
cannot directly compare today’s cash flow with past or
future cash flows, nor simply add one cash flow in one year
and another cash flow in another year.
• Use a different weight on each cash flow (i.e., giving more
weight on today’s one dollar than tomorrow’s one dollar),
so that they are comparable.
• This weighing scheme is called “present value method.”

6. Future Value – Example 1
• Example: If you deposit $100 today at 8% annual interest
rate, how much will you get back in total one year later?
• Computation:
$100 + $100 x 8% (principal plus interest)
= $100 x (1+0.08) (8% = 0.08)
= $100 + $8 ($8 interest)
= $108

7. Future Value – Example 2
• Example: If you deposit $100 today at 8% annual interest rate,
how much will you get back in total two years later?
• Computation:
• Today to one year later: your principal will grow to
$100 + $100 x 8% = $108.
• One year later to two years later: let new principle grow one more year
$108 + $108 x 8% = $116.64 (new principal $108 plus interest of $8.64)
• This is equivalent to
$100 x (1+0.08) x (1+0.08) = $100 x (1+0.08)2 = $116.64

8. Compound Interest
• On the previous example, if you get an answer of “total of $116
two years later” (i.e., $100 + $8 x2) rather than $116.64, then
the difference must come from the concept of compound
interest.
• Compound interest means that the interest accrued in the first
year will be added to the principal at the beginning of the
second year, so that in the second year you will get an interest
on the original principal ($100) as well as the first-year interest
($8) – that is, interest is compounded.
• In real business world, we always use “compound interest”!

9. Future Value Formula
You may use the following formula to find the future value of
cash flow:
Future Value Formula: FV = PV x (1+i)n
• FV (Future value): A future amount in $.
• PV (Present value): A present amount in $.
• i: Annual interest rate (in decimals)
• n: Number of years
• Example: You keep your $100 at 8% for three years.
FV = $100 x (1+0.08)3 = $125.97

10. How to Compute Future Value on My Calculator?
• The future value formula involves a “power” (i.e., raised by n).
You can use your scientific calculator to perform this task.
• Suppose you want to compute 100 x (1+0.08)3. Look for a key
marked as “x^y” or “xy” on your calculator. First, calculate 1+0.08,
that is 1.08 (that is, x). Next, push this key (“x^y” or “xy”) and type
3 (that is, y). Then, push “=” or “Enter” key. Presto! You got
1.2597... Now, multiply by 100 to get the final answer, 125.97 
• Try to calculate FV if you leave $100 at 8% annual interest rate for
17 years.

11. Compounding: $100 at 8 Percent Interest
(1)
Years of
Compounding
(2)
Compounding
Computation
(3)
Value at
Year’s End
1 $100 (1.08) $108.00
2 100 (1.08)2 116.64
3 100 (1.08)3 125.97
4 100 (1.08)4 136.05
5 100 (1.08)5 146.93
17 100 (1.08)17 370.00
Practice: If you invest $10,000 and earn 12% annual interest
rate for 45 years, then how much will you get 45-years later?
Answer: $1,639,876.

12. Present Value
• Present value of a future amount of money: How much is a
future cashflow worth today?
 An IOU promises to pay you $108 next year. How much is it worth
today? At 8%, $100 today.
• Calculate what you should pay for an asset today.
 To purchase the IOU, you will not pay more than its present value
today. Buyer does not want to pay more than $100, nor seller wants
to sell at less than $100. What price do they negotiate today?
• Asset’s price today should be equal to total present value
of future payments.

13. Present Value – Example 1
• Example: If you want to receive $108 one year later, if you
can earn 8% annual interest rate from your bank, then how
much should you deposit today?
• Computation: You deposit $X today, then
$X x (1+0.08) = $108
$X = $108/1.08 = $100

14. Present Value – Example 2
• Example: If you want to receive $116.64 two years later, if you
can earn 8% annual interest rate from your bank, then how
much should you deposit today?
• Computation: You deposit $X today, then
$X x (1+0.08)2 = $116.64
$X = $116.64/ (1+0.08)2 = $116.64/ 1.1664 = $100

15. Present Value Formula
You may use the following formula to find the present value of
cash flow:
Present Value Formula: PV = FV ⁄ (1+i)n
• FV (Future value): A future amount in $.
• PV (Present value): A present amount in $.
• i: Annual interest rate (in decimals)
• n: Number of years
• Example: At 8% interest rate, $125.97 three years later is equivalent to
PV = $100 / (1+0.08)3 = $100 today

16. Some Popular Investments
Wide variety available to investors.
Three features:
• Must pay to acquire
• Chance to receive future payment
• Some risk in future payments

17. Stocks
• Stocks represents ownership in a company.
 Stocks are not IOU. Company’s assets and profits belong to stockholders.
 A value of assets is derived from its assets and current and future profits.
 Most CEOs are not owners of companies but hired to manage the companies by
stockholders.
• Stocks involve risk.
 If a company going bankrupt, then company’s assets will be liquidated to pay for its
liabilities, and no more assets may be left for stockholders.
 Limited liability rule: Stockholders will not owe more than company’s
assets.
• Investors receives financial gains from stocks in form of
 Capital gains: Price of stock increases over time (sales price in future is greater than a
purchase price)
 Dividends: Company may distribute a share of its profits each quarter to
stockholders (owners of company).

18. Bonds
• Bonds: Debt contracts (IOU) issued by government and corporations
 U.S. Treasury bonds, NC Educational bonds, Bonds issued by Verizon
 Bond issuer promises to pay back its face value at a maturity date and
makes periodic interest payments until maturity.
 Bond investors may receive financial gains from capital gain (purchase
price is less than the face value) and interest payments
• Bonds are subject to default: Issuer of bonds may not be able to apy
regular interest payments or face value at maturity.

19. Mutual Funds
• Mutual fund: stocks of company that maintains a portfolio of
either stocks or bonds
 Holders of mutual fund are owners of the mutual fund company, so
they own all stocks or bonds held by the mutual fund indirectly.
 It is easy way to build a portfolio of stocks by purchasing mutual
funds than purchasing individual stocks and bonds.
• Variety of mutual funds
 Index funds: Portfolio only includes those stocks or bonds on a market
index
 Actively managed funds: Mutual funds manager actively invest in
various stocks and bonds

20. Stock Market Index
Stock market index is a weighted average price of a basket of stocks.
It is used to gauge an overall performance of stock markets.
There are many stock market indices.
• Dow Jones Industrial Average (DJIA): a weighted average of prices of
stocks of largest and widely-held public companies in the U.S., selected by
Dow Jones.
 It includes Apple, Microsoft, Visa, Coca-Cola, Wal-Mart, McDonald’s,
Walt Disney, Verizon, and other well-know corporations.
• Standard & Poor’s 500: a weighted average of prices of stocks of 500 large
public companies representing each industry in the U.S.

21. The 10 Largest Mutual Funds, October 2021
Fund Name
Assets under
Management, Billions
Vanguard 500 Index Admiral Shares $411.0
SPDR S&P 500 ETF 386.4
Fidelity 500 Index Fund 350.3
Vanguard Total Stock Index Admiral Shares 315.5
iShares Core S&P 500 287.0
Vanguard Total Stock Index Institutional Plus 269.7
Vanguard Total Stock Market Index ETF 263.0
Vanguard 500 Index ETF 247.0
Vanguard Total Stock Market Index Institutional 230.8
Fidelity Government Cash Reserves 210.0

22. Rate of Return
• If an investor sells a security at a price higher than
purchase price, he will gain from his investment.
 Michelle purchased Apple stock at $200 and sells at $250, then
she gains $50 from her investment.
• If an investor sells a security at a price lower than
purchase price, he will incur loss from his investment.
 Michael purchased Meta stock at $150 and sells at $120, then he
incurs loss of $30 from his investment.
• Rate of return measures a gain or loss from investment as
percentage rate.

23. Formula of Rate of Return
R: Rate of Return
P1: Price of bond in year 1 (Purchase price)
P2: Price of bond in year 2 (Sales price)
C: Any payments from security between year 1 and year 2
• For example, Michelle purchased Microsoft stock at $80 (P1) and sells at
$110 (P2). While holding the stock, she received $20 dividends (C).
R =
C + P2 – P1
P1
x 100
R =
20 + 110 – 80
80
x 100 = 62.5%

24. Price and Rate of Return
• Rate of return inversely related to purchase price.
 When a purchase price (P1) is $80, a rate of return is 62.5%.
 If a purchase price (P1) is $100, then a rate of return will be
R =
C + P2 – P1
P1
x 100
R =
20 + 110 – 100
100
x 100 = 30.0%
• Bonds promise to pay back a set price (P2) and interests (C).
Bond price and interest rate are inversely related.

25. Risk
Risk: Uncertainty
Diversification: Investing in a collection (portfolio) of assets whose
returns do not always move together.
• Don’t put all your eggs in one basket!
 If you have $10,000 cash, you may purchase a variety of stocks – Meta,
Apple, Amazon, FedEx, Toyota, BP, Bank of America, etc.
 When a price of one stock (Bank of America) suddenly falls, a price of
another stock (Amazon) may rise and offset a loss, so that your portfolio
maintains more predictable overall return.
 Of course, if the stock market crashes, you may lose a lot, so you may
diversify your portfolio to a variety of assets such gold, real estate, collector
cards, bonds, etc.
• Mutual funds provide instant diversification.

26. Risk and Return
Risk and return trade-off: Higher the risk, higher the return
(Positively related)
• In general, a saver does not like risk (risk-averse).
• In order to make investors more willing to purchase risky
securities, securities with high risk must pay an extra-return (risk
premium) to compensate such risk.
• There is no free-lunch. Any investment opportunities, which claim
any financial gains, involve more or less risk.

27. Last Word: Index Funds versus Actively Managed Funds
• Choice of actively or passively managed mutual funds.
• After costs, index funds outperform actively managed
funds by 1% per year.
 Management costs are significant.
• Index funds are boring—no chance to exceed average
rates of return.
• To gain more than average, you must invest individual
stocks by yourself.

28. Disclaimer
Please do not copy, modify, or distribute this presentation
without author’s consent.
This presentation was created and owned by
Dr. Ryoichi Sakano
North Carolina A&T State University
It includes copy-righted materials from
©2021 McGraw Hill Education. All rights reserved. No reproduction or further distribution without the prior written consent of McGraw Hill Education.