Name
Grade Level & Section:
Quarter2-Week5-Day2. Illustrate stocks and bonds. Distinguishes
between stocks and bonds. Describes the different markets for stocks
and bonds. analyzes the different market indices for stocks and
bonds.
I.
II.
III.
Specific Objectives for the day
1. Illustrate and distinguish stocks and bonds
2. Describes the markets for bonds.
References
General Mathematics Module 8
Development of the Lesson
Hi! It is me again, Mark
I hope you have considered stocks as a good investment
during our last meeting. but I must remind you that investing in
stocks is risky since the market always fluctuates and may
crash especially in times like the pandemic.
I have a new offer for you that you may consider. It is called BONDS. If
you want assurance of a return in your investment, bonds can do it.
Suppose you are to buy bonds with a face value of ₱50,000.00, if the
company pays 10 %, payable semi-annually for its coupons for 5 years, it
means you’ll receive a fixed payment semi-annually, how much will you be
receiving in total after 5 years?
STOCKS
A form of equity financing or raising
money by allowing investors to be
part owner s of the company
Stock prices vary every day. These
prices are reported in various
media (newspaper, TV, internet,
etc.)
Investing in stocks involves some
uncertainty. Investors can earn if
the stock prices increase,, but they
can lose money if the stock prices
decrease or worse, if the company
goes bankrupt.
BONDS
A form of debt financing or raising
money by borrowing from investors.
Investors are guaranteed interest
payments and a return of their money
at the maturity date
Uncertainty comes from the ability of
the bond issuer to pay the
bondholders. Bonds issued by the
government pose less risk than those
by
companies
because
the
government has guaranteed funding
(taxes) from which it can pay its loans.
Higher risk but with possibility of Lower risk but lower yield.
higher returns.
Can be appropriate if the Can be appropriate for retirees
investment is for the long term(10 (because of the guaranteed fixed
years or more). This can allow income) or for those who need the
investors to wait for stock prices to money soon(because they cannot
increase if ever they go low.
afford to take a chance at the stock
market)
Investors purchased bonds issued by companies to fund their expenses
in expansion, projects, etc.. Investors who purchased bonds are essentially
‘lenders’ to the issuer. However, the investors should be compensated for
the lending their money. Aside from being paid the loan at the end of a
fixed amount of time, the investor also receives payments, usually every six
months.
 Bond – interest bearing security which promises to pay a stated amount
of money on the maturity date, and regular interest payments.
 Coupon – periodic interest payment that the bondholder receives during
the time between purchase date and maturity date: usually semiannually.
 Coupon Rate – the rate per coupon payment period; denoted by r.
 Price of a Bond – the price of the bond at purchase time, denoted by P.
 Par Value or Face Value – the amount payable on the maturity date;
denoted by F.
If P = F, the bond is purchased at par
If P < F, the bond is purchased at a discount
If P > F, the bond is purchased at premium.
 Term (Tenor) of a Bond – fixed period of time (in years) at which the
bond is redeemable as stated in the bond certificate, number of years
from time of purchase to maturity date.
 Fair Price of a Bond – present value of all cash inflows to the
bondholder.
The main platform for bonds or fixed income securities in the
Philippines is the Philippine Dealing and Exchange Corporation (or PDEx).
Unlike stock indices which are associated with virtually every stock market
in the world, bond market indices are far less common. In fact, other than
certain regional bond indices which have sub-indices covering the
Philippines, our bond market does not typically compute a bond market
index. Instead, the market rates produced from the bond market are
interest rates which may be used as benchmarks for other financial
instruments.
Score: _______
So now, calculating for the coupons that you may receive semi-annually,
Given: Face Value = ₱50,000.00
Coupon Rate = 10%
Find: Amount of the Semi-annual Coupon
Annual Coupon amount: 50,000(0.10) = 5,000
Semi-annual Coupon Amount = 5,000(1/2) = 2,500
Thus, the amount of the semi- annual coupon is 2,500. You’ll be receiving 2,500
semi-annually for five years plus the Face value of the bond which is
₱50,000.00
Examples.
1. Determine the amount of semi-annual coupon paid for a 4% bond with a face
value of ₱ 200,000 which matures after 10 years. How much and how many
coupons are paid?
Given: Face Value, F = ₱ 200,000
Coupon Rate, r = 4%
Find: Number and Amount of each Coupon
𝑟
0.04
Semi-annual Coupon Amount = (F)( ) = 200,000 ( ) = 4, 000
2
2
In 10 years, there are 10 x 2= 20 payments
Thus, each semi-annual coupon is ₱4,000, paid 20 times every 6 months.
2. A certain bond pays coupons of ₱ 6,000 every six months for 6 years,
Given:
Semi-annual coupons = 6,000
Face Value = 150,000
Time to maturity = 6 years
Number of periods = 2(6) = 12
Market rate = 4%
Find:
Fair Price of the bond
Present Value of the ₱ 150,000:
𝑭
𝟏𝟓𝟎,𝟎𝟎𝟎
P=
𝒏 =
𝟔 = 118, 547.18
(𝟏+𝒋)
(𝟏+𝟎.𝟎𝟒)
Present Value of 12 semi-annual payments of ₱6,000 each with 4% interest per
period:
Convert 4% to equivalent semi-annual rate:
(1+0.04)1 = (𝟏 +
𝒊(𝟐)
𝟐
Thus,
P= R
=
= 0.019804
𝟏− (𝟏+𝒋)−𝒏
𝒋
𝒊(𝟐) 𝟐
)
𝟐
= 6,000
𝟏− (𝟏+𝟎.𝟎𝟏𝟗𝟖𝟎𝟒)−𝟏𝟐
𝟎.𝟎𝟏𝟗𝟖𝟎𝟒
= 63,528.49
Fair Price = 118, 547.18+ 63,528.49 = ₱182,075.67
Thus, a price of ₱182,075.67 is equivalent to all future payments, assuming an
annual market rate of 4%.
IV. Exercises
1. Determine the amount of semi-annual coupon paid for a 2.75%
bond with a face value of ₱75,000.00 which matures after 10 years.
2. Suppose that a bond has a face value of ₱100,000.00 and its
maturity date is 10 years from now. The coupon rate is 5% payable
semi-annually. Find the amount of the semi-annual coupon.
3. Find the amount of the semi-annual coupon for a ₱ 500,000 bond
which pays 3.5% convertible semi-annually for its coupons.
4. A ₱300,000.00 bond is redeemable at ₱425,000.00 after 6 years.
Coupons are given at 4% convertible semi-annually. Find the
amount of the semi-annual coupon.
5. A bond promises to pay the bondholder equal payments of ₱ 4,000
in six-month intervals for 15 years. If the face amount is ₱225,000,
what is the fair price of the bond? Assume that the market rate is
2.5% compounded semi-annually.
Answer Key
1. ₱ 1,031.25
2. ₱ 2,500.00
3. ₱ 8,750.00
4. ₱ 6,000.00
5. ₱ 238,721.12
V.
Evaluation
General Instructions: Solved for what is asked in each item: Show your
solutions neatly on the space provided. (3 points each)
3 points
 Complete
solutions
 Correct final
answer
Rubrics for Scoring
2 points
1 point
 Incomplete
 No solutions
solutions
 Correct final
 Correct final
answer
answer
1. Determine the amount of the semi-annual coupon for a bond with a face
value of ₱ 200,000.00 that pays 8%, payable semi-annually for its
coupons.
2.
Suppose that a bond has a face value of ₱ 250,000 and its maturity
date is 15 years from now. The coupon rate is 6% payable semiannually. Find the fair price of this bond, assuming that the annual
market rate is 6%.
3.
Determine the amount of the semi-annual coupon for a bond with a
face value of ₱ 650,000 that pays 8.5%, payable semi-annually for
its coupons.
4.
Suppose that a bond has a face value of ₱ 50,000 and its maturity
date is 7 years from now. The coupon rate is 10% payable semiannually. Find the fair price of this bond, assuming that the annual
market rate is 8%.
For items 5-10: Tell whether the following is a characteristic of a stocks or
bonds.
5. It can be appropriate for retirees because of guaranteed fixed income
Answer:
6. Investors are guaranteed interest payments and a return of their money at
the maturity date.
Answer:
7. Investors can earn if the security prices increase, but they can lose money
if the security prices decrease or worse, if the company goes bankrupt.
Answer:
8. A form of debt financing, or raising money by borrowing from investors.
Answer:
9. A form of equity financing or raising money by allowing investors to be part
owners of the company.
Answer:
10. Higher risk but with possibility of higher returns.
Answer: