Sinking Fund

Chapter
c 16
 SINKING FUND
Learning Target
A long-term debt with a large amount suggests that the debtor
periodically deposit a sum of money in a sinking fund in order to retire
the principal on the maturity date. The periodic deposit may or may not
be of equal amounts nor be at equal intervals. However, in this chapter
only illustrations of periodic deposits made at equal intervals and in
equal amounts are considered. Since the deposits may be made either at
the end of or the beginning of each period, the deposits thus form an
annuity problem.
Sinking Fund Payment Using the
Table
Learning Target
In a sinking fund, the future value is known;
therefore, the future value of an annuity table
or Table 3 is used to compute the amount of
the payment.
Future Value of the Sinking Fund
Sinking Fund Payment =
Future Value Table Factor
Illustration:
What sinking fund payment is required at the end of
each 6-month period. at 6% interest compounded
semiannually, to amount to P120,000 in 4 years?

This sinking fund is for 8 periods (4 years x 2 periods per year) at 3% per period
(6% ÷ 2 periods per year). From Table 3, The future value table factor is
8.892336
Future Value of the Singking Fund
Sinking Fund Payment =
Future Value Table Factor
120,000
Sinking Fund Payment =
8.892336

Sinking Fund Payment = P13,494.77

 Sinking Fund Payment Using the
Formula
Learning Target
Sinking fund payments may be computed using the formula:
where:
FV = Amount needed in the future
i = Interest rate per period (nominal rate ÷ periods per year
n= Number of period (years x period per year)

i
Sinking Fund Payment = FV x
(1 + i )^n -1
Illustration:
Calantha Corporation needs P1,000,000 in 5 years to pay
off a bond issue. What sinking fund payment is required
at the end of each month, at 12% interest compounded
monthly, to meet this financial obligation?

i
Sinking Fund Payment = FV x
(1 + i )^n -1
.01
Sinking Fund Payment = 1,000,000
(1 + .01)^60 - 1

Sinking Fund Payment = 1,000,000 x .0122444

Sinking Fund Payment = 12,244,40

Sinking Fund Schedule

Since the sinking fund is established for paying the principal

of the debt at maturity, the periodic interest on the debt
should not be paid out of the fund. The interest rate of the
debt is an interest expense, while the interest from the
sinking fund is called sinking fund interest income.
Importantly, the dates for paying debt interest and making
sinking fund deposits are usually the same-- the debtor
makes two separate payment on each date.
 Sinking Fund Schedule

Illustration 1: A P40, 000 debt is to be repaid at the end of 1 ½ years.

Interest charged is 15% payable at the end of every 3 months. The debtor
established a sinking fund that earns 12% interest compounded quarterly.
Find the interest payment on the debt for each 3-month period. Construct
a sinking fund schedule.
Interest payment: No. of period: 1 ½ years x 4 periods/year = 6 periods
I = PRT Rate : 12%/4 periods = 3%
I = P40, 000 x 15% x ¼ Sinking fund payment =
Future value of the sinking fund
Future value table factor
I = P1, 500 P40, 000
Sinking fund payment = 6. 468410
(¼ = 3 months/12 months)
Sinking fund payment = P6, 183. 90
Sinking Fund Schedule

Future Value Annuity Table Factor

Formula for FV:

Sinking Fund Schedule
 Sinking Fund Schedule

Illustration 2: Using the information from Illustration 1. Find the (a) amount
in the sinking fund at the end of the fourth period, (b) the sinking fund
interest income for the fifth period, and ( c) the book value of the debt at the
end of the fourth period, without constructing a schedule.

( a ) Future value = 6, 183. 90 x 4.183627

Future value = P 25, 871. 13

( b ) Interest income at the end of the 5th period:

Interest income= Future value x rate
Interest income = P25, 871. 13 x 3%
Interest income = P776. 13

( c ) Book value = Original amount of the debt - Accumulated amount in the fund at that period
Book value = P40, 000 - 25, 871 13
Book value = P14, 128. 87
 ADJUSTED PERIODIC DEPOSITS
SCHEDULE

(1) (2) (3) (4) (5) (6)

Schedule Actual Interest Adjusted Deposit Periodic Increase in
At End of period
Interest Income Interest Income Discrepancy Schedule Fund
(3months) SEC. III.1 See Below (2) - (3) P 6,183.90 + (4) (3) + (5)

1 ... .... ... 6,183.90 6,183.90

2 185.52 185.52 ... 6,183.90 6,369.42
3 376.6 439.37 -62.77 6,121.13 6,560.50
4 573.41 668.98 -95.57 6,088.33 6,757.31
5 776.13 646.78 129.35 6,313.25 6,960.03
6 984.93 820.78 164.15 6,348.06 7,168.84
TOTAL 2,896.59 2,761.43 135.16 37,238.57 40,000.00
The interest in column (3) is based on the following expression (see column (5) of illustration 1):

Actual interest income = Sinking fund accumulated x Interest rate

Thus, the interest for each period is computed as follows:

First Period = 0 x 3%
Second Period = 6,183.90 x 3% = 185.52
Third Period = 12,553.32 x 3 1/2% = 439.37
Fourth Period = 19,113.82 x 3 1/2% = 668.98
Fifth Period = 25,871.13 x 2 1/2% = 646.78
Sixth Period = 32,831.16 x 2 1/2% = 820.78

Notice that the values in column (6), periodic increase in fund, of the above schedule are
the same as the values in column (4) of the sinking fund schedule of illustration 1. The
sum of the periodic increases in the fund equals the sum of the actual interest income
plus the sum of the adjusted (actual) deposits: 2, 761.43 + 37 ,238.57=P40,000.
AMORTIZATION
Amortization method refers the process of paying for a loan or
discharging a debt by making a series of fixed payments each
month until your balance reaches zero . In order to discharge a
debt, each payment must be greater than the periodic interest ,
so that a part of the payment applies to the principal until the
principal becomes zero.
Amortization payment using the table

Amortization payment = Original amount of obligation

Present value annuity table
factor

Present value annuity table factor

Amortization payment using the table

Amortization payment = Original amount of obligation

Present value annuity table
factor
 Example 1:

Lisa plans to buy a new equipment worth P100, 000, but she does not have
enough budget yet, so she decided to buy it in installment for 2 years with
12% interest. What is the amortization payment required each month?
Amortization payment = Original amount of obligation
Present value table factor

12% = 1% P100, 000

Amortization payment =
12 21. 2434
2 x 12= 24 months Amortization payment = P4, 707.34
Example 2:

Anna purchased a brand new car worth P850, 000 and made a
downpayment of P200, 000. She agreed to pay the balance by making
equal payments at the end of each month for 2 ½ years. If the interest
charge is 12% compounded monthly. What is the amortization payment?
Balance = P850, 000 - P200, 000 Amortization payment = Original amount of obligation
Balance = P650, 000 Present value table factor
No. of period = 2.5 x 12 P650, 000
No. of period= 30 months Amortization payment =
Present value : 25. 8077
12%/12 = 1%
Present value = 25. 8077
Amortization payment = P25, 186. 28
Amortization payment using the formula

i
Amortization = PV x
-n
1 - (1+ i)
PV = amount of the loan or obligation
i= interest rate per period (nominal rate/ periods per year)
n = number of periods (years x periods per year)
Example 1:

What amortization payment is required each month if Lee

decided to borrow a loan worth P50, 000 at 18% interest, payable
in 3 years?
i
Amortization = PV x
-n i = 18%/ 12 years
1 - (1+ i)
i = 0. 15

Amortization = P50, 000 x

0. 15 n = 3x12
-36
1 - (1+ 0. 15) n= 36
19
$18 800 = $3572
100
Amortization payment = P7, 549. 29
 Outstanding Principal

•Unpaid amount of the original loan after some payments.

Oftentimes both the creditor and the borrower must know the amount of the
outstanding principal or the unpaid balance on a certain date. The
information may be needed for various reasons:
•It may be necessary for accounting purposes;
•The creditor may want to sell the unpaid balance;
•The borrower may wish to know his or her equity from an investment;
•Or the creditor and the borrower may agree to settle the balance on an earlier
date.
 Outstanding Principal

The outstanding principal may be determined under two types

of arrangements:

(a) All periodic payments are equal

or
(b) All periodic payments, except the final payment, are equal
 All Periodic Payments are Equal

Step 1: Find monthly payment

Amortization payment = Original amount of obligation

Present value annuity table factor
Step 2: Find remaining time left for payment
Step 3: Find table factor for remaining payments
Step 4: Outstanding Principal =
Monthly Payment x Table Factor
 All Periodic Payments are Equal

Illustration: Bensent Palambing purchased P1,000,000 worth of

gym equipment and made a P250,000 down payment. He
agreed to pay the balance by making equal payments at the
end of each month for 15 years. If the interest charged is 12%
compounded monthly, Find the Outstanding Principal after
Calvin made the monthly payment for 13 years.
 All Except Final Payments are Equal

Step 1: Monthly Payment

PV= P750,000 (1,000,000 - 250,000) Monthly Payment = 750,000
i= 1% (12% ÷ 12 months) 83.321664
n= 180 (15 years x 12 months) MonthlyPayment = P9,001.26
Table Factor is 83.321664
Step 2: Remaining Time for Payment
(15 years - 13 paid years) = 2 years / 24 months
 All Periodic Payments are Equal

Step 3: Table Factor of Remaining Time for Payment

Table Factor is 21.2434

Step 4: Outstanding Principal

9,001.26 x 21.2434
=P191,217.37
Amortization Schedule
Amortization Schedule
 All Except Final Payments are Equal

Illustration: Bensent Palambing purchased P1,000,000 worth of gym

equipment and made a P250,000 down payment. He agreed to pay
the balance by making equal payments at the end of each month for
15 years. If the interest charged is 12% compounded monthly,
(a)Find the Outstanding Principal after Calvin made the monthly
payment for 14 1/2 years. (b) How much will Bensent pay for the final
payment to settle his balance?
 All Except Final Payments are Equal

Step 1: Monthly Payment

PV= P750,000 (1,000,000 - 250,000) Monthly Payment = 750,000
i= 1% (12% ÷ 12 months) 83.321664
n= 180 (15 years x 12 months) MonthlyPayment = P9,001.26
Table Factor is 83.321664
Step 2: Remaining Time for Payment
(15 years - 14 1/2 paid years) = 1/2 years / 6 months
 All Except Final Payments are Equal

Step 3: Table Factor of Remaining Time for Payment

Table Factor is 5.7955

Step 4: Outstanding Principal

9,001.26 x 5.7955
=P52,166.80
 All Except Final Payments are Equal

Bensent Palambing has extra cash to fully cover his

Outstanding Balance so he decided to clear his debt paid in full.

a) Outstanding Principal is P52,166.80

b) Instead of paying P9,001.26 monthly, Bensent Palambing

fully pays the remaining balance as his final payment in the
amount of P52,166.80
 STOCKS, BONDS,
and MUTUAL FUNDS

chapter 17
 Learning Target
Learning Target

1 Understand the nature of Stock and Stock Quotation

2 Compute dividends on preference and ordinary shares.

 STOCKS

Corporations are built and expanded through money called

capital, and one way they raise capital is by issuing and selling
shares of stock. Stocks represent ownership shares in a
corporation. When you own shares, you’re called a stockholder.
You don't just own a portion of the company — you also have the
right to receive income in the form of dividends. Each
ownership portion is represented by a stock certificate.
 STOCK QUOTATION

Stock quotation tables, commonly found in

newspapers and business websites, provide a daily
summary of stock market activities. They present key
information such as price movements, trading volume,
and other market indicators, offering investors a quick
overview of the market’s performance for the day.
Each stock quotation includes important information, such as:

a & b. 52-Week High and Low - The highest and lowest prices in
the past year.
c. Name - The company’s name.
d. EPS or Earnings Per Share - How much a company earns for
each share.
e. Previous Close - The closing price from the day before.
f. Open - The price when trading opened.
g & h. High and Low - The highest and lowest prices for that
specific day.
Each stock quotation includes important information, such as:

i. Close - The price when trading ended for the day.

j. Volume - Number of shares traded.
k. Value - Total peso value of the shares traded.
l. % Change or Percent Change - How much the price changed
compared to the previous day. Calculated as ( i - e)/d
m. PE Ratio or Price Earnings Ratio - The Price-Earnings ratio,
showing how much investors are willing to pay for one peso of
earnings. Calculated as i/d
Example of Stock Quotation:
Illustration:

From the stock quotation table, explain the information listed for Bank of
the Philippines (BPI) and Universal Robina.
BPI is listed second under the Banks classification. On that specific
days, the corporation’s stock opened at ₱76.20. The high for the day was
₱76.20 while the low, ₱75.80. The stock closed at ₱76.10. 690,780 shares
of stock were traded during the day. On the same day, Universal Robina
stock’s (third from the bottom under Food, Beverage, and Tobacco
classification) open price was ₱59.90. The day’s high was ₱60.75 and lo
₱58.85. It finally closed at ₱60.60. 1,173,483 shares were traded
throughout the day.
 SCRIPLESS TRADING

Since March 1995, the Philippine Stock Exchange

moved to a scripless trading system. This means stock
ownership is now recorded electronically — no more
physical certificates! Investors who buy stocks today don’t
automatically receive a paper certificate unless they
specifically request one. This system makes stock trading
faster, safer, and more efficient.
 DIVIDENDS on PREFERENCE
and ORDINARY SHARES

Dividends on preference and ordinary

shares represent a portion of a company's
profits distributed to its shareholders.
 DIVIDENDS on PREFERENCE
and ORDINARY SHARES

Companies offer two types of shares:

Ordinary shares and

Preference shares
 DIVIDENDS on PREFERENCE
and ORDINARY SHARES

Preference shareholders typically receive fixed dividends and are

prioritized in payments, even if the company faces financial difficulties.
Meanwhile, Ordinary shareholders receive dividends only after preference
dividends are paid and may also benefit from additional earnings if the
company performs well.

Preference shares can be issued with or without a par value.

For example, if a P100 par value preference share pays an 8% dividend, each
share earns P8.00 per year.
DIVIDENDS on PREFERENCE
and ORDINARY SHARES

Cumulative - If dividends aren’t paid one year, they accumulate

and must be paid later.
Non-participating - Only the fixed dividend is given — nothing
extra.
Participating - If the company does really well, stockholders
might get extra dividends.
Convertible - These preference shares can be exchanged for
ordinary shares in the future.
 STEPS in DISTRIBUTING DIVIDENDS on
PREFERENCE and ORDINARY SHARES

1. If the preference share is cumulative, any dividends that are in

arrears are paid first; then the preference dividend is paid for the
current period. When the dividend per share is stated as a percent
(par stock), multiply the par value by the dividend rate.

Dividend per share (preference) = Par value x Dividend rate

 STEPS in DISTRIBUTING DIVIDENDS on
PREFERENCE and ORDINARY SHARES

2. Calculate the total amount of the preference share dividend by

multiplying the number of preference shares by the dividend per
share. When the dividend per share is stated in pesos (no-par
stock).
Total preference dividend = Number of shares x Dividend per share
 STEPS in DISTRIBUTING DIVIDENDS on
PREFERENCE and ORDINARY SHARES

3. Calculate the total ordinary share dividend by subtracting the

total preference share dividend from the total dividend declared.

Total ordinary dividend = Total dividend - Total preference dividend

 STEPS in DISTRIBUTING DIVIDENDS on
PREFERENCE and ORDINARY SHARES

4. Calculate the dividends per share for ordinary share by

dividing the total ordinary share dividend by the number of
shares of ordinary share.

Dividend per share = Total ordinary dividend

(ordinary) Number of shares (ordinary)
Illustration:

Kish Corporation has 2,500,000 shares of

ordinary share outstanding. If a dividend of
₱4,000,000 was declared by the company
directors last year, what are the dividends
per share of ordinary share?
Illustration:

Since Kish has no preference share, the

ordinary shareholders will receive the entire
dividend. Proceed to Step 4.

Dividend per share = Total ordinary dividend

(ordinary) Number of shares (ordinary)
Illustration:

Dividend per share = Total ordinary dividend

(ordinary) Number of shares (ordinary)

Dividend per share = 4,000,000

(ordinary) 2,500,000

= ₱ 1.60 per share

Illustration:

The board of directors of Sabell Developers, Inc.,

declared a dividend of ₱300,000. The company has
60,000 shares of preference share that pay ₱0.50
per share and 100,000 shares of ordinary share.
Calculate the amount of dividends due the
preference shareholders and the dividend per
share of ordinary share.
Illustration:

1. Since the preference dividend is stated

in pesos (₱0.50 per share), proceed to
Step 2 to 4.
Illustration:

2. Total preference dividend = Number of shares x Dividend per share

Total preference dividend = 60,000 x .50 = ₱30,000
3. Total ordinary dividend = Total dividend - Total preference dividend
Total ordinary dividend = 300,000 - 30,000 = ₱270,000

4. Dividend per share (ordinary) = Total ordinary dividend

Number of shares (ordinary)

Dividend per share (ordinary) = 270,000

100,000
= ₱2.70 per share
Illustration:

Mog Company has 100,000 shares of ₱100

par value, 6%, cumulative preference share and
2,500,000 shares of ordinary share. Although no
dividend was declared last year, a ₱5,000,000
dividend has been declared this year. Calculate
the amount of dividends for the current period.
Illustration:

1. Dividend per share (preference) = Par value x Dividend rate

Dividend per share (preference) = 100 x .06 = ₱6.00 per share

2. Total preference dividend = Number of shares x Dividend per share

Total preference dividend = 100,000 x 6.00 = ₱600,000
Total preference dividend = 600,000 (arrears) + 600,000 (current year)
= ₱1,200,000

3. Total ordinary dividend = Total dividend - Total preference dividend

Total ordinary dividend = 5,000,000 - 1,200,000 = ₱3,800,000
Illustration:

4. Dividend per share (ordinary) = Total ordinary dividend

Number of shares (ordinary)

Dividend per share (ordinary) = 3,800,000

2,500,000

= ₱1.52 per share

CURRENT YIELD FOR A STOCK

The Current Yield - is a way of evaluating the Current Value of a stock.

- tells how much the dividend is as a percentage
of the current price of the stock.
CURRENT YIELD FOR A STOCK

Annual dividend per share

Current Yield=
Current price of the stock
Illustration:

Calculate the current yield for Prettier Than

Pink Corporation stock, which pays a
dividend of P1.70 per year and is currently
selling at P34.50 per share.
 CURRENT YIELD FOR A STOCK

1.70
Current Yield= = .0492753 = 4.93%
34.50
PRICE-EARNINGS RATIO OF A STOCK

The Price-earnings ratio per share (P/E ratio) is a

financial metric that measures the valuation of a
company's stock. It is defined as the current market
price of a single share of the company's stock divided by
the earnings per share (EPS) of the company.
PRICE-EARNINGS RATIO OF A STOCK

The formula is:

Current price per share

Price-earnings ratio=
Earnings per share

Round answer to the nearest whole number

(may be written as a ratio, X:1)
Illustration:

Alix stock is currently selling at P104.75.

If the company had earnings per share of
P3.60 last year, calculate the price-earnings
ratio of the stock.
PRICE-EARNINGS RATIO OF A STOCK

Current price per share

Price-earnings ratio=
Earnings per share

104.75
Price-earnings ratio=
3.60

= 29. 09722 = 29 or 29:1

 COST, PROCEEDS AND GAIN OR
LOSS ON A STOCK TRANSACTION

Investment Strategies:
Buy stocks for dividends.
Buy low and sell high for profit.
Cost of Purchasing Stock:
Purchase price + Brokerage commission (1.50% to 2%).
Proceeds from Selling Stock:
Selling price - Brokerage commission.
Gain or Loss:
Proceeds from sale - Total cost of purchasing stock.
 COST, PROCEEDS AND GAIN OR
LOSS ON A STOCK TRANSACTION

Cost: The total expense incurred by an investor to

purchase a stock.
Proceeds: The total amount received by an investor
from selling a stock.
Gain (or Loss): The financial outcome of a stock
transaction, determined by subtracting the total cost of
purchasing the stock from the proceeds received from
selling it.
Illustration:

Buying Transaction:

Ben Aman decides to buy a stock whose market price

is P10.00 and with a par value of P1.00. Based on the
Board Lot Table, the minimum number of shares he
can buy at a regular transaction is 1,000 shares. In
this case, the amount that he needs is about
P10,000.00 plus charges. His required cash outflow
will be as follows:
Illustration:

Market Price Per Share P 10.00

Multiply by Minimum No. of Shares 1,000
P10,000.00
Add: Broker’s Commission (1.5%) 150.00
Total Cash Outlay P10,150.00
Illustration:

Selling Transaction:

After a year, Ben opts to sell all the shares he

previously bought. Current market price is P13.00 per
share. In this case, the proceeds of the sale is about
P13,000 less charges. His cash inflow will be as
follows:
Illustration:

Buying Transaction:

Market Price Per Share P 13.00

Multiply by Minimum No. of Shares 1,000
P13,000.00
Less: Broker’s Commission (1.5%) 195.00
Net Cash Receivable P12,805.00
RETURN ON INVESTMENT

The Return on Investment (ROI) measures the total

monetary gain on a stock for an investor. It is found by
adding the amount that a stock has gone up in value
during one year (net gain), assuming it was sold at the
end of one year, to the total dividends paid the investor,
minus, of course, any commissions and other fees.
RETURN ON INVESTMENT

The formula is:

Net Gain + Total Dividends

ROI=
Total cost of stock purchase
Illustration:

Using the data in the previous

illustration and assuming that a total of
P1,300 in dividends was received for
the year, Ben's ROI is calculated as
follows:
RETURN ON INVESTMENT

Net Gain + Total Dividends

ROI= Total cost of stock purchase

(12,805 - 10,150) + 1,300

ROI=
10,150

ROI = 0.3897 or 38.97%

Ben’s ROI at 38.97% is a very good return.

BONDS
A bond is a formal unconditional promise to pay a specified
sum of money (face value) at a determinable future date
(maturity date) plus interest over a set of period. It’s a debt
contract where one party, the issuer, borrows fund from
another party called the investor. The agreemnt is documented
in a bond indenture.
 Bonds vs. Stocks
With Stocks, the investor becomes a part
owner of the corporation; while with bonds,
the investor becomes creditor. Bonds are
known as fixed-income securities because the
issuer promises to pay a specified amount of
interest regularly.
Bond Issuance
Bonds issued by corporations can be bought by investors at face
value and held until maturity, or bought and sold through brokers
and banks. They’re often issued in small denominations such as
P100, P1000,P10000, to attract more investors.

A quoted market price for bonds represents a percentage of their

face value. For example, P3,000,000 worth of bonds quoted at 90
would have market value of P 2,700,000 ( P3,000,000 X 90%).
Coupon Rate & Bond Price Fluctuation

Bonds pay a fixed interest rate known as the coupon rate on a

regular basis usually semi annually.

However, their market price fluctuates inversely with prevailing

interest rates between the issue date and maturity date. If interest
rates fall, the bond’s fixed rate becomes more attractive, increasing
its price above face value. When this occurs, the bonds are said to
be selling at a premium.

If interest rates rise, the bond’s rate is less appealing, decreasing its
price below face value. If bonds sell below face, it is known as
selling at a discount. At maturity date, the bond returns to its face
value.
Types of Bonds
Secured Bonds- are backed by a lien on a plant, equipment, or other
corporate asset.

Unsecured Bonds- also known a debentures, are backed only by the

general credit of the issuing corporation.

Convertible Bonds- Can be converted into, or exchanged for, a

specified number of shares of ordinary shares.
Types of Bonds
Callable Bonds- gives the issuer the right to call or redeem bonds
before the maturity date.

Serial Bonds- are those which have a series of maturity dates or

those bonds which are payable in installments.

Term Bonds- are bonds with a single maurity date.

Cost, Proceeds, and Gain (or Loss) on a Bond Transaction

Cost Components:

Purchase Price(current market price plus accrued interest),

Brokers Commission, Taxes and other charges incurred in their
acquisition.

Accrued Interest : I= PRT

where;
P= face value of the bond
R= coupon rate
T= the number of days since the last payment date divided by 360.
When it’s in months, the denominator is 12
Cost, Proceeds, and Gain (or Loss) on a Bond Transaction

Proceed from Sale = Sales Price - Less Commissions, Taxes,

and Other Fees

Gain/Loss = Proceeds - Cost

Cost, Proceeds, and Gain (or Loss) on a Bond Transaction

Example:

A company purchased a bond with a face value of P10,000 for

P9,800 on July 15th. The purchase also included a broker’s
commission of P100 and documentary stamp tax of P50. The bond
pays interest semi-annually on January 1 and July 1 at a 7% annual
st st

rate. The bond was sold for P10,200 on August 15 . The broker’s
th

commission on the sale was P100.

Cost, Proceeds, and Gain (or Loss) on a Bond Transaction

Solution:

Cost of the Bond ( excluding accrued interest):

P9,800 + P100 + P50 = P9,950
Accrued Interest:
The bond pays 7% annually, or 3.5% semi-annually (7%/2)
The interest payment for the period is : P10,000 x 0.035= P350
Number of days from July 1st to August 15th : 45 days
Accrued Interest : P10,000 x 0.035 x (45/180) = P87.50
Cost, Proceeds, and Gain (or Loss) on a Bond Transaction

Solution:

Total cost of the Bond:

P9,950 + P87.50 = P10,037.50

Proceeds from the sale:

P10,200-P100= P10,100

Gain(or Loss) :
P10,100- P10,037.50= P62.50 GAIN
Current Yield for a Bond

Just as with stocks, the current yield of a bond is a simple

measure of the return on investment based on the current
market price. When bonds are purchased at face, the current
yield is equal to the coupon rate.
 Current Yield for a Bond

Formula:

Current Yield= Annual Interest/ Current Market Price

Where:

Annual Interest = Face Value x Coupon Rate

Current Market Price= Face value x Price Percent
Current Yield for a Bond

Example 1:

A bond with a face value of P1,000 and a coupon rate of 7%

pays P70 annually (P1,000 * 0.07). If the bond’s current market
price is P1,072.50, the current yield is:
Current Yield for a Bond

Solution:

Current Yield = P70 / P1,072.50 = 0.0653 = 6.53%

Current Yield for a Bond

Example 2:

Consider a bond with a face value of PHP 20,000 and a coupon

rate of 8% per year, payable semi-annually on March 1 and
September 1. On July 15, 2025, an investor purchased this
bond at a market price of 105. What is the current yield of the
bond at the time of purchase?
Current Yield for a Bond

Solution:

Calculate the Annual Interest:

Annual Interest = Face Value * Coupon Rate

Annual Interest = P 20,000 x 0.08
Annual Interest= P 1,600
Current Yield for a Bond

Solution:

Calculate the Current Market Price:

The bond was purchased at a market price of 105, which means

105% of its face value.
Current market price = (Quoted price / 100) * Face value
Current market price = (105 / 100) * P 20,000
Current market price = PHP 21,000
Current Yield for a Bond

Solution:

Calculate the Current Yield:

Current Yield = P1,600 / P21,000 = 0.0762 = 7. 62%

MUTUAL
FUNDS

CHAPTER17
 WHAT IS MUTUAL FUND?

A mutual fund is a fund managed by an

investment company. Depending on the type of
fund, the investment company buys stocks, bonds,
and other investments on behalf of the fund. The
money in the fund may come from individuals and
institutions
Fund Management:
The investment company acts as an advisor, making
decisions about buying and selling securities.
There are open-end funds (issue/redeem shares
anytime) and closed-end funds (stop issuing after
reaching a size limit)
Types of Mutual Funds:

High-growth funds: Higher potential

returns but higher risk.
Low-risk funds: Lower returns but more
stability.
Fees and Charges

Load Fees: Charged when buying or selling shares (0.25% to 3%).

No-Load Funds: No entry or exit fees.
Early Redemption Fee: 1% penalty for withdrawing before the
minimum holding period.
Management & Advisory Fees: 0.75% to 2% annually based on
Net Asset Value (NAV).
Net Asset Value (NAV):
NAV = (Fund's Total Assets - Liabilities) / Number of
Shares Outstanding
Calculated daily using the closing price of securities.
NAV determines the cash value when redeeming
shares.
Interpreting a Mutual Fund
Quotation

Illustration: Equity Fund

FUND NAV NET CHG YTD %RET

Fixed Income Fund 179.47 0.08 11.05

Equity Fund 255.82 0.03 30.31

Balanced Fund 135.67 0.01 21.34

FUND- “Equity Fund” in the name of the fund The Fund aims
to achieve long-term capital growth.
NAV. - Today, P255.82 is the net asset value per share
NET CHG (net change)- It is the difference between the price
paid for the last share today and the price paid for the last
share the previous trading day. The Equity Fund closed
PO.03 higher than yesterday's closing price
YTD% RET (year-to-date percentage return)- The Fund has
a 30.31% return since January 1.
RETURN ON
INVESTMENT
(ROI)
RETURN ON INVESTMENT

End-of-year NAV + Dividend Distribution - Beg.-of-Year NAV

ROI=
Beg.-of-Year NAV
RETURN ON INVESTMENT

Example:
Growth Fund's net asset value on January I was
P100. During the year, the fund distributed P25 per
share to investors. At the end of the year, the net
asset value was P104. Calculate the return on
investment.
RETURN ON INVESTMENT

End-of-year NAV + Dividend Distribution - Beg.-of-Year NAV

ROI=
Beg.-of-Year NAV
104 + 25 - 100
ROI=
100

29
ROI=
100
The Return on Investment
ROI= 0.29 X 100 = 29%
is 29%
RETURN ON INVESTMENT

Example:
James bought shares of a company at the beginning
of the year worth P5,000.
By the end of the year, the shares were worth
P5,800, and he also received P200 in dividends
during the year.
RETURN ON INVESTMENT

End-of-year NAV + Dividend Distribution - Beg.-of-Year NAV

ROI=
Beg.-of-Year NAV
5,800 + 200 - 5,000
ROI=
5,000

1,000
ROI=
5,000
The Return on Investment
ROI= 0.20 X 100 = 20%
is 20%