Fixed Income
The Time Value of Money
Present Value: How much you got now.
Future Value: How much what you got now grows to when compounded at a given rate
I give you Rs. 100. You take it to the bank. They will give you 10% interest per year for 2 year.
· The Present Value = Rs. 100
· Future Value = Rs.121.
FV= PV (1 + i )N
· FV = Future Value
· PV = Present Value
· i = the interest rate per period
· n= the number of compounding periods
Determine Future Value Compounded Monthly
What is the future value of Rs.34 in 5 years if the interest rate is 5%? (i equals .05 divided by 12, because there are 12 months per year. So 0.05/12=.004166, so i=.004166)
· FV= PV ( 1 + i ) N
· FV= Rs. 34 ( 1+ .004166 ) 60
· FV= Rs. 34 (1.283307)
· FV= Rs.43.63.
Annuity
An Annuity is a bunch of structured payments or equal payments made regularly, like every month or every week.
You win the lottery. The lottery guy comes to your house and says you have to choose between getting Rs. 1,000,000 now in one lump sum, or getting structured payments of Rs. 50,000 a year for the next 22 years. Which do you take?? Or, similarly, let's say you were injured on the job or whatever and were awarded an annuity of structured payments of Rs.50,000 a year for the next 22 years. Perhaps you want to sell your annuity (the payments) to someone and get a lump sum of cash today. Is it worth Rs.1,000,000?
First you have to choose an interest rate. Money is generally worth less in the future, right? So that Rs.50,000 payment you get in 22 years is not going to be worth as much as it is today? You know, stuff will be more expensive then, right? So guess an interest rate, in this case, the rate of inflation for the next 22 years. Lets say 4%. Now, you have to figure out what is the present value of the Rs.50,000 times 22 years discounted by 4%:
FV= PV ( 1 + i ) N
0 = PV (1+ 4)**22
I need to know here what is the formula to ???
Perpetuities:
are equal payments made regularly, like every month or every year, that go on forever (ie. For infinite times).
You are rich. (Yes, but are you really happy?) You want to start the YOUR NAME HERE Scholarship at your university. Every year, some student will receive a Rs.1000 scholarship. You're paying for it. Even after you, your kids and your grandkids are dead, you are still paying for it. Forever.
The question is....How much money will it cost you. In today's dollars. What is the present value of this perpetuity. (Hint: starting now and going on forever and ever, you assume the interest rate at your bank is going to be 3%).
PV (of a perpetuity) = payment / interest rate
Every year the interest you earn is used to pay for the scholarship. The principal in your bank account doesn't really change year to year.
Payment = 1000
Interest = 3/100 = 0.03
PV = 1000/ 0.03
= 33,333
So, you put Rs. 33,333 into the bank. Each year the money earns Rs.1000 interest. That interest becomes the scholarship.
Cash Flow:
Cash Flow is money you get a little at a time.
Lets say, for example that for the next 4 years you will get the following cash flow.
Cash Flow
in 1 year Rs. 320
in 2 years Rs. 400
in 3 years Rs. 650
in 4 years Rs. 300
If you assume that the interest rate is 6.5% (which means that after you get the money, it will be invested and you will get 6.5% interest from it), compounded monthly, how much money will you have in 4 years? In other words, what will the future value of this cash flow be?
Compounding Formula: FV=PV ( 1 + i / m)mn
· FV = Future Value
· PV = Present Value
· i = Interest rate (annual)
· m = number of compounding periods per year
· n = number of years
So you have to figure out the future value of each payment and then add them together.
First Payment
· FV = PV ( 1 + i / m)mn
· FV = Rs.320 (1 + .065 / 12 )12 X 3 (three years)
· FV = Rs.320 (1.0054167)36
· FV = Rs.320 (1.2146716)
· FV = Rs.388.69
Second Payment
· FV = PV ( 1 + i / m)mn
· FV = Rs.400 (1 + .065 / 12 )12 X 2 (two years)
· FV = Rs.400 (1.0054167)24
· FV = Rs.400 (1.1384289)
· FV = Rs.455.37
Third Payment
· FV = PV ( 1 + i / m)mn
· FV = Rs.650 (1 + .065 / 12 )12 X 1 (one year)
· FV = Rs.650 (1.0054167)12
· FV = Rs.650 (1.0669719)
· FV = Rs.693.53
Fourth Payment - ( The payment is not compounded. There no time to earn interest)
· FV = PV ( 1 + i / m)mn
· FV = Rs.300 (1 + .065 / 12 )12 X 0(0 years.)
· FV = Rs.300 (1.0054167)0
· FV = Rs.300 (1) (remember anything to the power of zero is 1)
· FV = Rs.300
Finally, add up all the numbers
Rs. 388.69
Rs. 455.37
Rs. 693.53
Rs. 300.00
----------
Rs.1,837.59
So after 4 years, you will have Rs.1,837.59. That is the future value of your uneven cash flow.
Few Termology
Bond: When a company (or government) borrows money from the public or banks (bondholders) and agrees to pay it back later
Par Value :The amount of money that the company borrows. Usually it is Rs.1,000. It is also called as Principle or face value.
Coupon Payments: This is like interest. The company makes regular payments to the bondholders, like every 6 months or every year.
Indenture : The legal stuff. A written agreement between the company and the bond holder. They talk about how much the coupon payments will be, and when the money (par value) will be paid back to the bondholder.
Maturity Date : Date when the company pays the par value back to the bondholder.
Market Interest Rate: This changes everyday.
BOND
A bond is basically a loan. The owner of a bond has given the issuer-whether it be a corporation, a government or another agency-a sum of money that can be used at any point. In exchange, the issuer will pay interest to the bondholder over a period of time and will eventually return the initial amount loaned, called the principal. Unlike a stock, the bondholder does not own a part of the company. Because a bond is basically a loan, they are often called "debt securities" because they represent a debt obligation from the issuer to the bondholder. Bonds are also known as fixed income securities. The reason for this name is that at the time of the purchase of a basic bond, the amount of income and the timing of the payments are known to the purchaser. Bonds are called debentures and debt instruments as well.
There are really two markets for bonds: the primary market and the secondary market. The primary market is when the bond is first issued. In the primary market the bond is purchased directly from the issuer (the details of buying and selling bonds will be covered later). The secondary market occurs later, when bonds are sold from one bondholder to another. The prices on bonds in the secondary market are set by supply and demand and are impacted by what is expected of interest rates and inflation, how many coupon payments are left to maturity, and how long it will be until the bond matures. View the section Bonds and Your Portfolio below to see more about the relationship between interest rates and bonds.
Some advanced topics in BOND:
Callability
When a bond is issued, it will be either callable or non-callable. A callable bond is one in which the company can require the bondholder to sell the bond back to the company. Buying back outstanding bonds is called "redeeming" or "calling". When issued, the bond will explain when it can be redeemed and what the price will be. In most cases, the price will be slightly above the par value for the bond and will increase the earlier the bond is called. A company will often call a bond if it is paying a higher coupon than the current market interest rates. Basically, the company can reissue the same bonds at a lower interest rate, saving them some amount on all the coupon payments; this process is called "refunding." Unfortunately, these are also the same circumstances in which the bonds have the highest price - interest rates have decreased since the bonds were issued, increasing the price. In many cases, the company will have the right to call the bonds at a lower price than the market price. If your bond is called, you will be notified by mail and have no choice in the matter. The bond will stop paying interest shortly after the bond is called, so there is no reason to hold on to it. Companies also typically advertise in major financial publications to notify bondholders. Generally, callable bonds will carry something called call protection. This means that there is some period of time during which the bond cannot be called.
Zero Coupon Bonds
Some bonds, called zero coupon bonds, don't pay out any interest prior to maturity. These bonds are sold at a deep discount because all of the value from the bond occurs at maturity when the principal is returned to the bondholder along with interest. These bonds are also known as "zeros." One type of zero-coupon bond is a "strip." The interest payments are separated from a bond's principal and multiple zero coupon securities are created, one representing the principal amount and one representing each coupon payment. A problem with zero-coupon bonds is that, even though you do not receive any interest payments during the time you hold the bond, you are still responsible for paying taxes on the suggested interest you are earning. The taxes are based on the appreciation of the bond's market value, which will increase consistently as it approaches maturity. Zeros are also more volatile than bonds that have regular interest payments. The main benefit of zero coupon bonds is if you are saving for a specific event that will occur at a specific time, such as paying for college. You can purchase the zero coupon bonds to mature just before you will be needing the money.
Secured vs. Unsecured Bonds
Bonds can either be secured by some sort of collateral or unsecured. Unsecured bonds, called debentures, are considered to be riskier than secured bonds because they are simply backed by the issuer's word that it will repay the bonds.
Secured bonds are backed by some goods that can be sold by the issuer to raise money to pay off the debt in the event of default. Bonds issued by the federal government are unsecured.
The most common form of secured bonds are mortgage bonds. These bonds are backed by real estate or physical equipment that can be liquidated. These are thought to be high-grade, safe investments. Other bonds are secured by the revenues created by projects.
So if a company file for Bankrupcy: Then amount will paid first to Secure Bond holder, Then Unsecure bond holder. And lastly to Stock holders (share holders) if any money is left.
There are two general forms of bankruptcy: Chapter 7 and Chapter 11. With Chapter 7, the company is liquidated and bondholders should file a claim to receive a portion of the value of their bonds. In Chapter 11 proceedings, however, the process is quite different.
Chapter 11 allows the corporation to reorganize. Its bonds might continue to trade, but holders will not receive principal and interest payments. As a result, a default could occur, and the value of the bonds might decline significantly. Or the court may approve an exchange of the old bonds for new ones, which could have a lower value.
Bond Valuation
The thing about bonds is that the interest rate (coupon payments) is fixed. It doesn't change. And bonds last a long time. Like 10 years or whatever. So in the meantime, the market interest rate (the interest rates in general) go up and down. OK, well, if the coupon payments are for 10% and then the market interest rates fall from 10% to 8%, then that bond at 10% is valuable, right. It is paying 10% while the overall interest rate is only 8%. Exactly how much is it worth? You mean 'what is the present value of a bond?'
The Present Value of a Bond = The Present Value of the Coupon Payments (an annuity) +
The Present Value of the Par Value (time value of money)
Example
· Par Value = Rs. 1,000 (say you invested in Bond)
· Maturity Date is in 5 years (for 5 years)
· Annual Coupon Payments of Rs.100, which is 10% (even market has 8% interest Bond wala company will pay you @10%)
· Market Interest rate of 8% (the current market interest rate is 8 %when market is not well)
The Present Value of the Coupon Payments (an annuity) = Rs.399.27
The Present Value of the Par Value (time value of money) =Rs.680.58
The Present Value of a Bond = Rs. 399.27 + Rs. 680.58 = Rs.1,079.86
Stock Valuation
Preferred Stock: Preferred stock is somewhat like a bond. They pay the same equal dividends forever. (this is nothing else but perpetuity)
Common Stock: Common stock represents ownership in the company. Sometimes there are dividends, sometimes not. (what is this ?? )
Beta - Beta is the overall risk in investing in a large market, like the New York Stock Exchange. Beta, by definition equals 1.0000. 1 exactly. Each company also has a beta. You can find a company's beta at the Yahoo!! Stock quote page. A company's beta is that company's risk compared to the risk of the overall market. If the company has a beta of 3.0, then it is said to be 3 times more risky than the overall market.
Ks = Krf + B ( Km - Krf)
· Ks = The Required Rate of Return, (or just the rate of return).
· Krf = The Risk Free Rate (the rate of return on a "risk free investment", like U.S. Government Treasury Bonds - Read our Disclaimer)
· B = Beta (see above)
· Km = The expected return on the overall stock market. (You have to guess what rate of return you think the overall stock market will produce.)
What is the value of Common Stock?
This is not easy. This is a mess. Think about it. What is the value of a share of stock in a specific company? In one sense it is the price the stock trades at. Both the buyer and seller agree to exchange the stock at that price.
We assume that they are both rational people and both know something about the company and its future plans and profit potential. So, yes, that is one method: check the price of the stock in the paper or on the internet. But that's pretty darn easy. It's not really finance. It's more like reading. And I don't know if you realize this or not, but they don't give Nobel Prizes for reading. So there are other ways of doing stock valuation too.
The Gordon Growth Formula, also known as The Constant Growth Formula assumes that a company grows at a constant rate forever. This, by the way, is impossible. I mean, it can't grow forever. You know, if a company doubles in size every 5 years, pretty soon every single person in the world is their customer and then they can't grow at that rate anymore. (because the world population isn't doubling ever 5 years).
BUT, if we go ahead and assume that a company has a constant growth rate, we can use the following formula to get its value.
Constant Growth Formula Po = D 1 / ( Ks - G )
· Po = Price
· D1 = The next dividend. D1 = D0 (1 + G)
· Ks = Rate of Return
· G = Growth Rate
What is all this D1 and D0 stuff ?
· D1 is the next dividend
· D0 is the last dividend
Well we are assuming that the company has constant growth, right. So we take the last divided, multiply it by the growth rate and we can get the next dividend.
Example
· Last years dividend = $ 1.00
· Growth Rate = 5%
· Rate of Return = 10%
First figure out D1.
· D1 = D0 (1 + G)
· D1 = $1.00 ( 1 + .05)
· D1 = $1.00 (1.05)
· D1 = $1.05
Next us the formula.
· Po = D 1 / ( Ks - G )
· Po = $1.05 / (10% - 5%)
· Po = $1.05 / 5%
· Po = $21.00
So, if we want to get a 10% rate of return on our money, and we assume that the company will grow forever at 5% per year, then we would be willing to pay $21.00 for this stock. That is the theory anyways. And again, here is our disclaimer.
How to calculate the Ks = Rate of Return ????
Present Value: How much you got now.
Future Value: How much what you got now grows to when compounded at a given rate
I give you Rs. 100. You take it to the bank. They will give you 10% interest per year for 2 year.
· The Present Value = Rs. 100
· Future Value = Rs.121.
FV= PV (1 + i )N
· FV = Future Value
· PV = Present Value
· i = the interest rate per period
· n= the number of compounding periods
Determine Future Value Compounded Monthly
What is the future value of Rs.34 in 5 years if the interest rate is 5%? (i equals .05 divided by 12, because there are 12 months per year. So 0.05/12=.004166, so i=.004166)
· FV= PV ( 1 + i ) N
· FV= Rs. 34 ( 1+ .004166 ) 60
· FV= Rs. 34 (1.283307)
· FV= Rs.43.63.
Annuity
An Annuity is a bunch of structured payments or equal payments made regularly, like every month or every week.
You win the lottery. The lottery guy comes to your house and says you have to choose between getting Rs. 1,000,000 now in one lump sum, or getting structured payments of Rs. 50,000 a year for the next 22 years. Which do you take?? Or, similarly, let's say you were injured on the job or whatever and were awarded an annuity of structured payments of Rs.50,000 a year for the next 22 years. Perhaps you want to sell your annuity (the payments) to someone and get a lump sum of cash today. Is it worth Rs.1,000,000?
First you have to choose an interest rate. Money is generally worth less in the future, right? So that Rs.50,000 payment you get in 22 years is not going to be worth as much as it is today? You know, stuff will be more expensive then, right? So guess an interest rate, in this case, the rate of inflation for the next 22 years. Lets say 4%. Now, you have to figure out what is the present value of the Rs.50,000 times 22 years discounted by 4%:
FV= PV ( 1 + i ) N
0 = PV (1+ 4)**22
I need to know here what is the formula to ???
Perpetuities:
are equal payments made regularly, like every month or every year, that go on forever (ie. For infinite times).
You are rich. (Yes, but are you really happy?) You want to start the YOUR NAME HERE Scholarship at your university. Every year, some student will receive a Rs.1000 scholarship. You're paying for it. Even after you, your kids and your grandkids are dead, you are still paying for it. Forever.
The question is....How much money will it cost you. In today's dollars. What is the present value of this perpetuity. (Hint: starting now and going on forever and ever, you assume the interest rate at your bank is going to be 3%).
PV (of a perpetuity) = payment / interest rate
Every year the interest you earn is used to pay for the scholarship. The principal in your bank account doesn't really change year to year.
Payment = 1000
Interest = 3/100 = 0.03
PV = 1000/ 0.03
= 33,333
So, you put Rs. 33,333 into the bank. Each year the money earns Rs.1000 interest. That interest becomes the scholarship.
Cash Flow:
Cash Flow is money you get a little at a time.
Lets say, for example that for the next 4 years you will get the following cash flow.
Cash Flow
in 1 year Rs. 320
in 2 years Rs. 400
in 3 years Rs. 650
in 4 years Rs. 300
If you assume that the interest rate is 6.5% (which means that after you get the money, it will be invested and you will get 6.5% interest from it), compounded monthly, how much money will you have in 4 years? In other words, what will the future value of this cash flow be?
Compounding Formula: FV=PV ( 1 + i / m)mn
· FV = Future Value
· PV = Present Value
· i = Interest rate (annual)
· m = number of compounding periods per year
· n = number of years
So you have to figure out the future value of each payment and then add them together.
First Payment
· FV = PV ( 1 + i / m)mn
· FV = Rs.320 (1 + .065 / 12 )12 X 3 (three years)
· FV = Rs.320 (1.0054167)36
· FV = Rs.320 (1.2146716)
· FV = Rs.388.69
Second Payment
· FV = PV ( 1 + i / m)mn
· FV = Rs.400 (1 + .065 / 12 )12 X 2 (two years)
· FV = Rs.400 (1.0054167)24
· FV = Rs.400 (1.1384289)
· FV = Rs.455.37
Third Payment
· FV = PV ( 1 + i / m)mn
· FV = Rs.650 (1 + .065 / 12 )12 X 1 (one year)
· FV = Rs.650 (1.0054167)12
· FV = Rs.650 (1.0669719)
· FV = Rs.693.53
Fourth Payment - ( The payment is not compounded. There no time to earn interest)
· FV = PV ( 1 + i / m)mn
· FV = Rs.300 (1 + .065 / 12 )12 X 0(0 years.)
· FV = Rs.300 (1.0054167)0
· FV = Rs.300 (1) (remember anything to the power of zero is 1)
· FV = Rs.300
Finally, add up all the numbers
Rs. 388.69
Rs. 455.37
Rs. 693.53
Rs. 300.00
----------
Rs.1,837.59
So after 4 years, you will have Rs.1,837.59. That is the future value of your uneven cash flow.
Few Termology
Bond: When a company (or government) borrows money from the public or banks (bondholders) and agrees to pay it back later
Par Value :The amount of money that the company borrows. Usually it is Rs.1,000. It is also called as Principle or face value.
Coupon Payments: This is like interest. The company makes regular payments to the bondholders, like every 6 months or every year.
Indenture : The legal stuff. A written agreement between the company and the bond holder. They talk about how much the coupon payments will be, and when the money (par value) will be paid back to the bondholder.
Maturity Date : Date when the company pays the par value back to the bondholder.
Market Interest Rate: This changes everyday.
BOND
A bond is basically a loan. The owner of a bond has given the issuer-whether it be a corporation, a government or another agency-a sum of money that can be used at any point. In exchange, the issuer will pay interest to the bondholder over a period of time and will eventually return the initial amount loaned, called the principal. Unlike a stock, the bondholder does not own a part of the company. Because a bond is basically a loan, they are often called "debt securities" because they represent a debt obligation from the issuer to the bondholder. Bonds are also known as fixed income securities. The reason for this name is that at the time of the purchase of a basic bond, the amount of income and the timing of the payments are known to the purchaser. Bonds are called debentures and debt instruments as well.
There are really two markets for bonds: the primary market and the secondary market. The primary market is when the bond is first issued. In the primary market the bond is purchased directly from the issuer (the details of buying and selling bonds will be covered later). The secondary market occurs later, when bonds are sold from one bondholder to another. The prices on bonds in the secondary market are set by supply and demand and are impacted by what is expected of interest rates and inflation, how many coupon payments are left to maturity, and how long it will be until the bond matures. View the section Bonds and Your Portfolio below to see more about the relationship between interest rates and bonds.
Some advanced topics in BOND:
Callability
When a bond is issued, it will be either callable or non-callable. A callable bond is one in which the company can require the bondholder to sell the bond back to the company. Buying back outstanding bonds is called "redeeming" or "calling". When issued, the bond will explain when it can be redeemed and what the price will be. In most cases, the price will be slightly above the par value for the bond and will increase the earlier the bond is called. A company will often call a bond if it is paying a higher coupon than the current market interest rates. Basically, the company can reissue the same bonds at a lower interest rate, saving them some amount on all the coupon payments; this process is called "refunding." Unfortunately, these are also the same circumstances in which the bonds have the highest price - interest rates have decreased since the bonds were issued, increasing the price. In many cases, the company will have the right to call the bonds at a lower price than the market price. If your bond is called, you will be notified by mail and have no choice in the matter. The bond will stop paying interest shortly after the bond is called, so there is no reason to hold on to it. Companies also typically advertise in major financial publications to notify bondholders. Generally, callable bonds will carry something called call protection. This means that there is some period of time during which the bond cannot be called.
Zero Coupon Bonds
Some bonds, called zero coupon bonds, don't pay out any interest prior to maturity. These bonds are sold at a deep discount because all of the value from the bond occurs at maturity when the principal is returned to the bondholder along with interest. These bonds are also known as "zeros." One type of zero-coupon bond is a "strip." The interest payments are separated from a bond's principal and multiple zero coupon securities are created, one representing the principal amount and one representing each coupon payment. A problem with zero-coupon bonds is that, even though you do not receive any interest payments during the time you hold the bond, you are still responsible for paying taxes on the suggested interest you are earning. The taxes are based on the appreciation of the bond's market value, which will increase consistently as it approaches maturity. Zeros are also more volatile than bonds that have regular interest payments. The main benefit of zero coupon bonds is if you are saving for a specific event that will occur at a specific time, such as paying for college. You can purchase the zero coupon bonds to mature just before you will be needing the money.
Secured vs. Unsecured Bonds
Bonds can either be secured by some sort of collateral or unsecured. Unsecured bonds, called debentures, are considered to be riskier than secured bonds because they are simply backed by the issuer's word that it will repay the bonds.
Secured bonds are backed by some goods that can be sold by the issuer to raise money to pay off the debt in the event of default. Bonds issued by the federal government are unsecured.
The most common form of secured bonds are mortgage bonds. These bonds are backed by real estate or physical equipment that can be liquidated. These are thought to be high-grade, safe investments. Other bonds are secured by the revenues created by projects.
So if a company file for Bankrupcy: Then amount will paid first to Secure Bond holder, Then Unsecure bond holder. And lastly to Stock holders (share holders) if any money is left.
There are two general forms of bankruptcy: Chapter 7 and Chapter 11. With Chapter 7, the company is liquidated and bondholders should file a claim to receive a portion of the value of their bonds. In Chapter 11 proceedings, however, the process is quite different.
Chapter 11 allows the corporation to reorganize. Its bonds might continue to trade, but holders will not receive principal and interest payments. As a result, a default could occur, and the value of the bonds might decline significantly. Or the court may approve an exchange of the old bonds for new ones, which could have a lower value.
Bond Valuation
The thing about bonds is that the interest rate (coupon payments) is fixed. It doesn't change. And bonds last a long time. Like 10 years or whatever. So in the meantime, the market interest rate (the interest rates in general) go up and down. OK, well, if the coupon payments are for 10% and then the market interest rates fall from 10% to 8%, then that bond at 10% is valuable, right. It is paying 10% while the overall interest rate is only 8%. Exactly how much is it worth? You mean 'what is the present value of a bond?'
The Present Value of a Bond = The Present Value of the Coupon Payments (an annuity) +
The Present Value of the Par Value (time value of money)
Example
· Par Value = Rs. 1,000 (say you invested in Bond)
· Maturity Date is in 5 years (for 5 years)
· Annual Coupon Payments of Rs.100, which is 10% (even market has 8% interest Bond wala company will pay you @10%)
· Market Interest rate of 8% (the current market interest rate is 8 %when market is not well)
The Present Value of the Coupon Payments (an annuity) = Rs.399.27
The Present Value of the Par Value (time value of money) =Rs.680.58
The Present Value of a Bond = Rs. 399.27 + Rs. 680.58 = Rs.1,079.86
Stock Valuation
Preferred Stock: Preferred stock is somewhat like a bond. They pay the same equal dividends forever. (this is nothing else but perpetuity)
Common Stock: Common stock represents ownership in the company. Sometimes there are dividends, sometimes not. (what is this ?? )
Beta - Beta is the overall risk in investing in a large market, like the New York Stock Exchange. Beta, by definition equals 1.0000. 1 exactly. Each company also has a beta. You can find a company's beta at the Yahoo!! Stock quote page. A company's beta is that company's risk compared to the risk of the overall market. If the company has a beta of 3.0, then it is said to be 3 times more risky than the overall market.
Ks = Krf + B ( Km - Krf)
· Ks = The Required Rate of Return, (or just the rate of return).
· Krf = The Risk Free Rate (the rate of return on a "risk free investment", like U.S. Government Treasury Bonds - Read our Disclaimer)
· B = Beta (see above)
· Km = The expected return on the overall stock market. (You have to guess what rate of return you think the overall stock market will produce.)
What is the value of Common Stock?
This is not easy. This is a mess. Think about it. What is the value of a share of stock in a specific company? In one sense it is the price the stock trades at. Both the buyer and seller agree to exchange the stock at that price.
We assume that they are both rational people and both know something about the company and its future plans and profit potential. So, yes, that is one method: check the price of the stock in the paper or on the internet. But that's pretty darn easy. It's not really finance. It's more like reading. And I don't know if you realize this or not, but they don't give Nobel Prizes for reading. So there are other ways of doing stock valuation too.
The Gordon Growth Formula, also known as The Constant Growth Formula assumes that a company grows at a constant rate forever. This, by the way, is impossible. I mean, it can't grow forever. You know, if a company doubles in size every 5 years, pretty soon every single person in the world is their customer and then they can't grow at that rate anymore. (because the world population isn't doubling ever 5 years).
BUT, if we go ahead and assume that a company has a constant growth rate, we can use the following formula to get its value.
Constant Growth Formula Po = D 1 / ( Ks - G )
· Po = Price
· D1 = The next dividend. D1 = D0 (1 + G)
· Ks = Rate of Return
· G = Growth Rate
What is all this D1 and D0 stuff ?
· D1 is the next dividend
· D0 is the last dividend
Well we are assuming that the company has constant growth, right. So we take the last divided, multiply it by the growth rate and we can get the next dividend.
Example
· Last years dividend = $ 1.00
· Growth Rate = 5%
· Rate of Return = 10%
First figure out D1.
· D1 = D0 (1 + G)
· D1 = $1.00 ( 1 + .05)
· D1 = $1.00 (1.05)
· D1 = $1.05
Next us the formula.
· Po = D 1 / ( Ks - G )
· Po = $1.05 / (10% - 5%)
· Po = $1.05 / 5%
· Po = $21.00
So, if we want to get a 10% rate of return on our money, and we assume that the company will grow forever at 5% per year, then we would be willing to pay $21.00 for this stock. That is the theory anyways. And again, here is our disclaimer.
How to calculate the Ks = Rate of Return ????
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