How to Calculate Bonds

Currently, investment has become an activity carried out by many people, even young people now have broad insights into this matter. One of the commonly known investment instruments is bonds.

Well, in this article, we will discuss bonds, especially about how to calculate bonds. This is inseparable to help new investors who want to estimate how the benefits can be obtained when saving their money in the form of debt securities aka bonds. Please here is an explanation of how to calculate bonds.

When referring to the Module of the Ministry of Education and Culture of Economics prepared by Tuni Rahayu, SE., M. Pd., Bonds are debt securities issued by parties who owe debts to those who owe debts. Meanwhile, the definition in the book 'Indonesian Bond Market' written by Tarmiden Sitorus, Ph.D,bonds are securities that have a medium and long term that contain debt recognition from the issuer and can be traded.

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The KBBI lists two contexts for bonds, firstly interest-bearing loans from the government that can be traded. Both bonds with a period of more than one year and have a certain interest issued by the company with the intention of collecting funds from the public to cover their financing.

In short, we can conclude that, bonds are debt securities that can be traded in which the person who buys will get a profit in the form of interest later. These timed securities can be issued by the government or companies to help finance.

Usually, the maturity date for debt payments along with the interest in the bond is listed. Especially for bonds, the term for Interest is coupon. Where this coupon must be given to the bondholder by the issuer to be the benefit of the bondholder. Therefore, bonds are also often used as investment instruments.

The term or maturity of bonds in Indonesia is from 1 to 10 years. Therefore, bonds are defined as medium-long-term debt securities. Like other instruments, such as stocks and others, bonds are also listed on the stock exchange.

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However, it should be noted that bonds and stocks are different, although the purpose is almost the same, namely the means used by companies to attract capital from the public. The fundamental difference between the two is that an investor who owns a share gets the right to the company's profits and voting rights according to the amount of shares he owns. While the bond owner only has the status of a creditor.

When a company issues shares, it means that they sell part of their ownership of the company to another party. As for companies that issue bonds, they issue debt securities that can be purchased.

Shareholders, which means that they also own part of the company's ownership rights, will get a profit derived from the company's profits called dividends. While bonds are debt securities that are issued as a form of borrowing money, so the owner will benefit from interest called a coupon that will be paid along with the return of the cost of debt. Therefore, the way to calculate bonds is different from stocks.

Characteristics of Bonds

So that you understand more about what bonds are, you must know how the characteristics of this one securities are. The following are the characteristics of bonds seen from several aspects:

Bond Term

The term of bonds in Indonesia generally starts from 1 to 10 years. But the majority of the maturity of a bond is 5 years. Investors usually prefer short-term bonds because they are considered to have a smaller level of risk.

Bond Value

The bond issuer needs to inform information regarding the amount of money they need or the term is the amount of bond issuance. The amount of bond issuance issued must be determined in accordance with the company's performance, cash flow and the amount of business needs.

Payment Schedule

The bond issuer must make coupon payments periodically in accordance with the established agreement. The payment period may vary depending on the agreement, it can be quarterly, per semester or once every quarter.

Principal and Coupon Rate

Another characteristic of bonds is that they have a Principal rate, which is the value of money that must be paid by bond issuers to bondholders when they step on maturity. The value is influenced by aspects such as redemption value, par value, maturity value or face value.

In addition to the Principal rate, there is also a coupon rate, which is an interest rate that must be issued by bond issuers to be paid to bondholders every agreed period.

How to Calculate Bonds

Now as an investor, of course, you need to know how to calculate bonds. This ability is important to make you more optimal in calculating the profit that can be obtained. Here are the ways:

How to calculate bonds sold at a discounted price

The price or discount rate is the difference between the face value and the selling price of the bond. Under certain conditions, bonds sold at discounted prices can provide more benefits for investors.

Usually, investors will use the discount rate to calculate bonds when the Market interest rate is higher than the coupon rate. The reason is, this condition will have an impact on the discount price, where the selling price of the bond will be lower than the face value.

If you want these benefits, you need to master how to calculate bonds sold at a discounted price. There are 5 steps that you can do in how to calculate bonds sold at a discounted price, namely:

1. Find discounted value

As the definition suggests, discount is the difference between the face value and the selling price of a bond. Then you can calculate the discount value with the formula:

Discount = Face Value – The selling price of the bond

The face value is the value of the bonds issued by the company, while the selling price you must first take into account because it is influenced by the interest rate that applies when the sale occurs. In order to better understand it, we will explain how to use the above formula in the example of a bond question and its answer.

Example problem:

For example, PT Ingin Jaya Abadi issues bonds with a maturity period of 5 years of RP 6,000,000 and 10% interest is paid every mid-year (6 months). If the market interest when a sale occurs is 12%, what is the discounted price?

Answer:

From the example questions above, you can draw several conclusions, namely:

Interest is paid every mid-year so that the nominal interest rate in each period is 6% (in the form of 12% divided by 2).

The number of periods is 10 periods (2 periods x 5 years).

The interest payment per period is IDR 300,000 (IDR 6,000,000 x 5%).

As is known that the selling price of bonds is the difference between the present face value and the present value of the interest payment (coupon payment). Then the way to calculate the discount value of bonds is by the formula:

The selling price of the bond = the present value of the principal of the bond + the present value of interest.

First we will look for face value now. The present face value is the result of the multiplication between the face value of the bond and the present value interest factor (PVIF). Since we don't know how much pvif value is, then we have to find it first with the formula:

PVIF = 1 : (1+r)^t

r = market interest rate at each period

t = number of periods

PVIF=1 : (1+0.06)^10 = 0.5586

Now we already know that the PVIF value is 0.05586, then the nominal value now is Rp6,000,000 x 0.5586 = Rp3,351,600.

Second, we have to look for the present value of the interest payment. You can calculate it by multiplying the amount of interest payment by the current value factor of ordinary annuity (present value of ordinary annuity aka PVOA).

Since we don't know the PVOA value yet, then we first look for it with the formula:

PVOA + (1 – (1 : (1+r)^t)) : r

PVOA = (1 – (1 : (1+0.06)^10)) : 0.06 = 7.3567

Now you have got a PVOA score, which is 7,360. To get the present value of interest, you just need to multiply the amount of interest payment with PVOA. Then the calculation becomes:

IDR 300,000 x 7.3567 = IDR 2,207,010

The selling price of the bond = the present value of the principal of the bond + the present value of interest.

IDR 3,351,600 + IDR 2,207,010 = IDR 5,558,610

Now that you have obtained the selling price of the bond, just look for the discount value. Please use the formula at the beginning just now:

Discount = Face Value – The selling price of the bond

Discount = IDR 6,000,000 – IDR 5,558,610 = IDR 441,390

2. Calculating interest payments in each period

Interest payments in each period are the amount of profit received by investors in each period, of course as an investor you need to master how to calculate it. You can search

the amount of interest payments in each period by multiplying the amount of interest payments by the face value of the bond.

Interest payment for each period = Interest payment x face value of the bond

We'll reuse the example of the problem above. In the example of the question above, it has been shown how to find the value of interest payments, namely:

5% (10% : 2 payments per year = 5%)

While the nominal value of the bond is IDR 6,000,000.

IDR 6,000,000 x 0.05 = IDR 300,000

3. Calculate the total effective interest expense in each period

Bonds sold at a discounted price make the market interest rate on the bond issuance date the effective interest rate for the bond. How to calculate this effective interest expense, you can use the following formula:

Total interest expense = present value of the bond x effective interest rate of each period

Returning to the example above, you can apply this formula as follows:

The current value of the bond at the time of issuance is IDR 5,558,610. Well as the formula above, to find the total interest expense you just need to multiply the current value of the bond by the effective interest rate per period, then the value is

IDR 5,558,610 x 0.06 = IDR 333,516

4. Record the amount of interest paid as well as the amortization of the discount

In the example above, bonds issued at a discounted price make you pay an effective interest of IDR 333,516. However, the amount of interest to be paid to you and the amortization of the discount must be recorded separately on the investor's monthly financial statements.

Recording can be done by means of, writing a total effective interest expense of IDR 333,516 is carried out in the debit column and the amount of interest payments to investors, which is IDR 300,000 in the credit cash section. Meanwhile, the discounted amortization expense in this period, which is IDR 333,516 – IDR 300,000 = IDR 33,516 is written in the credit column.

5. Verify the final present value of the bond

Finally, you have to recalculate the current value of the bond. The way to calculate it is to add the initial present value with amortization.

Later, the final present value of the bond from this period will be used for the initial present value of the bond in the next period when you calculate the total interest expense back.

An example of calculating the final present value of a bond is, as follows:

The current value of the initial bond for this period is IDR 5,558,610

Meanwhile, the discounted Amortization value in this period is IDR 33,516

Then the calculation of the final present value of the bond for this period is

IDR 5,558,610 + IDR 33,516 = IDR 5,592,126.

When you are going to calculate the next effective interest expense, you must use IDR 5,592,126 as the initial current value.

How to calculate bonds sold at a premium price

There are 5 stages also for how to calculate bonds sold at a premium price. This method can be applied to various types of bonds. We will start reviewing one by one of the five stages through examples of bond questions as follows.

1. Determine the premium price of the bond

When the market interest value is lower than the nominal interest, the bonds sold will apply a premium price. That is, the bond passes the face value or par value. This premium price is a method that is often used by investors to compensate for the difference between nominal interest and market interest.

So that you can understand more clearly, let's look at the following formulas and examples.

Example Problem:

PT Ingin Jaya Abadi issues bonds with a maturity period of 5 years of IDR 6,000,000 and 10% interest paid per half year (every 6 months). Because the market interest rate when issued is 8% then bonds are issued at a premium price. How to calculate this bond?

Answer:

From the example of the above question, it is known that the selling price of the bond is the present value of the principal value of the bond plus the present value of the interest payment. While the premium is the difference between the selling price of the bond and its face value. How to calculate a bond at a premium price is as follows:

Interest is paid quarterly so that the market interest rate in each period is 4% (derived from 8% divided by 2).

The number of interest payment periods is 10 (2 periods a year x 5 years).

The amount of interest payment per period is IDR 300,000 (IDR 6,000,000 x 5%).

The calculation of the present value of the principal value of the bond can be done by multiplying the nominal value of the bond by PVIF.

Since we don't know the PVIF yet, we have to look for it first. The formula is the same as the formula on how to calculate bonds sold at the discounted price previously described, namely:

PVIF = 1/(1+r)^t

r = market interest rate per period

t = number of periods

PVIF=1/(1+0.04)^10 = 0.6757

After knowing pvif, just multiply it by the nominal value of the bond to get the principal value of the bond, so the calculation is as follows:

The current value of the principal value of the bond = IDR 6,000,000 x 0.6757 = IDR 4,054,200

After obtaining the present value of the principal value of the bond, then next we have to calculate the present value of the interest payment. The calculation can be done by multiplying the amount of nominal interest payment by the present value of ordinary annuity or abbreviated (PVOA).

Since we do not yet know the value of PVOA, then we have to search with the same formula of looking for PVOA by calculating bonds sold at the previous discounted price. that is:

PVOA = (1 – (1 / (1 + r)^t)) / r

(1 – (1 / (1 + 0.04)^10)) / 0.06 = 0.2643

IDR 300,000 x 5,405 = IDR 1,621,500

Now it's just a matter of looking for the selling price of the bond that you can calculate by adding the current value of the principal of the bond and the current value of interest. Then the count becomes

IDR 4,054,200 + IDR 1,621,500 = IDR 5,675,700

Bond premium is IDR 6,000,000 – IDR 5,675,700 = IDR 324,300

2. calculate the interest payment in each period

The interest payment in each period is the amount of profit that the investor will receive in each period. The way to calculate it is to multiply the amount of interest payments by the face value of the bond.

In the example above, the interest payment in each period is 5%, which can be from 10% divided by two payments per year. Meanwhile, the nominal value of the bond is IDR 6,000,000.

Rp6.000.000 x 0.05 = Rp300.000,-

So, the profit as an investor from the interest paid each period is IDR 300,000

3. How to calculate the total effective interest expense in each period

When bonds are sold at a premium price, the effective interest rate used is the market interest rate at the time of issuance. The way to calculate it is by the formula:

Total interest expense = present value of the bond x effective interest rate

This load is always calculated for each period. If referring to the example above, The current value of the bond when the securities were issued was IDR 4,054,200, then the effective interest expense will be:

Total interest expense = present value of the bond x effective interest rate per period

IDR 5,675,700 x 0.04 = IDR 227,028

4. Record the amount of interest paid as well as premium amortization

When the bond is issued at a premium price, you must pay an effective interest of IDR 227,028. However, you need to record the amount of interest paid to investors and amortize the premium separately in your monthly financial statements.

You can do the following recording:

The effective interest expense amount is IDR 227,028 written in the debit column.

The amount of interest payments to investors, which is IDR 300,000, is written in the credit cash column.

Premium amortization expense in this period is IDR 300,000 – IDR 227,028 = IDR 72,972 written in the debit column.

5. Verify the current value of the end bond

The last stage is to verify the final present value of the bond. You can do this by looking at the difference between the initial present value of the bond in this period and the amortization recorded for this period.

When returning to calculate the total interest expense, the current value of the end of the bond from this period you must use for the current value of the beginning of the bond in the next period.

In the example above, the calculation can be done as follows:

The current value of the initial bond for this period is IDR 5,675,700. While the premium amortization in this period is IDR 72,972. Then the final current value of the bond for this period is IDR 5,675,700 – IDR 72,972 = IDR 5,602,725.

Furthermore, you must use IDR 5,602,725 as the initial current value when calculating the effective interest expense in the next period.

How to calculate a bond sold at nominal price

How to calculate bonds sold at a nominal price is much simpler than the previous two ways. You can complete it in just three steps as follows:

1. Know the face value of bonds and the nominal interest rate

Bonds issued at a nominal price mean that the selling price of the bond is equal to the principal value of the bond. In addition, the yield on bonds aka yield is equal to the interest rate. Therefore, the first thing that needs to be done is to find out the nominal price of the bond and the nominal interest rate.

Example Problem:

PT Ingin Jaya Abadi issued a 5-year bond with a principal value of IDR 6,000,000 million, 10% interest paid per half year (6 months). The market interest rate at that time was 10% so these bonds were issued at nominal prices.

Answer:

Because interest payments are made every half year so that the nominal interest rate becomes 10% divided by 2, which is 5% and the market interest rate is also equal to 10%/2, which is 5%.

Since there are 2 periods each year, the number of periods is 10

2. Calculate interest payments in each period

How to calculate the payment of interest in each period for bonds issued at this nominal price is very easy. You can calculate it by multiplying the face value by the nominal interest rate of each period.

From the example above, we already know that the nominal value of bonds is IDR 6,000,000, while the nominal interest rate is 5%.

IDR 6,000,000 x 0.05 = IDR 300,000.

Therefore, the interest paid to investors in each period is IDR 300,000.

3. Record the total interest expense

Bonds that are sold at nominal prices also make journal recording quite simple.

You don't have to write premium amortization or discounts on your monthly report. All that needs to be done is:

Recorded interest expense, which is IDR 300,000 in the debit column

Cash of IDR 300,000 in the credit column.

How to calculate bonds and their interest

In addition to the above three methods, there are 5 other ways of calculating bonds. You can also apply these five to calculate Islamic bonds or sukuk.

1. Nominal Yield

Nominal yield is a profit in the form of annual coupon interest for bondholders. The formula used to calculate the nominal yield is as follows:

Coupon Rate = Interest Income : Face Value.

2. Current Yield

Current yield is the annual coupon interest gain (nominal yield) divided by the market price of the bond. The formula for calculating the value of the current yield is:

Current Yield = Annual Interest Income (Coupon rate): Bond Market Price.

3. Yield to Maturity (YTM)

Yield to maturity (YTM) is a compound rate of return that will be returned to the investor if he holds the bond until it matures.

YTM is the most commonly used measure of yield, because it can represent returns with the compounded rate of return expected by investors. For how to calculate YTM, you can do it in the following way:

YTM = (INT + ((M-PV) / n)) : (M + PV) / 2

Information:

INT = Coupon Value

M = Maturity value (par value)

PV = Current bond price

N = maturity period

4. Yield to Call (YTC)

Yield to call is a variable yield obtained from bonds that can be repurchased. Such bonds usually allow issuers to pay off or buy bonds before maturity.

The formula used to calculate YTC is:

YTC = (AI + (CP – MP) / NYC)) / ((CP + MP) / 2)

Information:

MP = Bond Price now

NYC (Number of years to call) = number of years up to the nearest yield to call

AI (Annual interest) = coupon income annually

CP (Call Price) = bond call price

5. Realized Yield

Realized yield is the level of return on bonds that investors expect. This realized yield can also be used to estimate the level of return that investors can get using an investment trading strategy.

Types of Bonds

Bonds are divided into several types based on several aspects, namely in terms of issuers, nominal, interest payments, and yields. The following is an explanation of the types of bonds.

By Who The Publisher Is

When viewed from who the issuer is, there are 3 types of bonds, namely:

• Corporate Bonds issued by private companies or State-Owned Enterprises (BUMN).
• Government Bonds issued by the government. In Indonesia itself, this type of bond is usually issued once a year, the term is Retail Government Bond (ORI).
• Regional Bonds issued by local governments. These bonds are issued with the aim of helping local governments to carry out various developments.

Based on Nominal Value

If you look at the nominal, bonds can be divided into two types, namely:

• Conventional Bonds, this type of bond is a very large nominal bond, which is around Rp. 1 billion per slot.
• Retail Bonds, this type is sold with a small nominal, such as 1 million rupiah.

Based on How to Pay Interest

If you look at how to pay interest, there are 4 types of bonds, namely:

• Coupon Bonds which are debt securities whose interest payments are made periodically. Coupon is a certain amount of interest that has been agreed upon by both parties in advance.
• Zero Coupon Bond is a bond without interest, and does not need to be paid periodically. Investors' profits will be obtained through the difference between the discounted selling price and the bond price when it was first issued. This type of bond generally has a maturity period from 1 to 10 years.
• Fixed Coupon Bonds are bonds offered at a fixed interest rate until maturity.
• Floating Coupon Bonds are bonds offered with interest that changes in value based on the money market index. In this bond, there is a minimum coupon limit that is valid until the maturity time.

By Yield

Meanwhile, for yields, bonds can be divided into 2 types, namely:

• Conventional Bonds are bonds issued with the aim of collecting borrowed funds that will be used as additional capital by providing interest returns on the part of bond buyers (investors) within a certain period of time.
• Sharia bonds are bonds issued to provide yields in the form of rent that are claimed using Islamic sharia calculations so that they do not contain elements of usury. The yield on Islamic bonds will be received by investors periodically within a predetermined period.

Bond Advantages

Although the profit is not as big as stocks, these bonds are considered safer. Among the several advantages that can be obtained by bond owners are the following:

• The advantage is in the form of coupons or periodic ratios of securities that have the nature of the purchased debt. Getting capital gains
• The yield level is taken into account in advance at the beginning of the invest
• Available in many options in the secondary market
• More guaranteed security, especially for types of government bonds.
• Bonds can be used as collateral or collateral to make loans to banks or buy shares on the stock exchange.

Bond Risk

Of course, not only profits, bonds also contain some risks. Among the risks of investing in bonds are the following:

Liquidity Risk

Both private and government bonds contain liquidity risks. Although this type of government bond is safer, it is not impossible for these bonds to always be easy to resell in the secondary market. The reason is, it is quite rare for investors to be interested.

Risk Maturity

This risk is more common in corporate bonds, that is, risks arising from the maturity of bonds. The longer the maturity period the higher the risk. You can overcome this risk by asking for a premium maturity, so that the maturity period is shorter.

Default Risk

Default risk aka default risk only occurs in company bonds, because this type is not guaranteed by the government.

That's our full review of bonds alanis bonds, here's how to calculate bonds accompanied by examples of questions and answers. Hope it helps, yes!

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