## Understanding Compound Interest

14 Jun

As always, this lesson is not intended to be professional advice. This is simply lesson material for ESL students in a Managerial Economics and Corporate Finance class. Posted here for their use or for helping other students.

## Corporate Value (值)

Financial officers and Managers are extremely responsible for the monetary (货币) goings-on in their companies. As we said before, the Wealth Maximization Rule means that Financial and Corporate Managers are required to maximize (最大化) the profits (收益) for their investors (投资者).

However, maximizing profits requires in-depth (深入)planning and micro-managing (微观) your funds today while considering (考虑) future profits as well.

There are two types of Value (值) that you should be aware of in Finance and Economics.

The first is called Present Value (现值) and is the value today of something that will increase in value in the future. ExampleWhen we loan someone $1,000 at 10% interest, we know that our$1,000 loan will increase in value in the future. Present Value = PV.

The second is called Future Value (未来价值) and is the value that the item will have in the future. Future Value = FV.

## Interest (利)

I’ll make another post later discussing the many ways to use Present and Future value in your company, but today I just wanted to talk about using them to calculate (计算) “Compound Interest” (复利).

Usually, when we loan money to someone or invest (投资) our money in something, we do so on the condition that we receive back more money than we put in.  Our corporation is not a charity (慈善机构), we don’t loan you things for free!  The original money we invest is called the Principal (本息).  The extra money we get on top is called the Interest (利).

Example ~ Company A (a large global corporation) invests $100,000 in a small new business called Company B. Company B has 10 years to pay it back. But Company A doesn’t do this for free ~ they want to maximize their profits too. That means they have to make some money on this contract (合同). So they ask Company B to pay an additional 7% per year.$100,000 = Principal
7% = Interest

## COMPOUND INTEREST (复利)

Problem! ~ 7% of what?
Answer! ~ It depends   It depends on how Company A decides to count it.

There are two separate mathematical formulas (数学公式) you can use to figure out the Interest.

The first one is called Simple Interest (单利) and I’ve already looked at it before.

The second method is called Compound Interest (复利). Compound Interest says that each payment period, Company B is going to pay an additional 7% of the currently owed principal! Lenders and Investors really like compound interest a lot better than simple interest.

For example: I borrow $1000 due in two years. My interest rate is 10%. If I use Simple Interest: Year 1, I owe$1000 + 10% interest = $1100. Year 2, I owe$1100 + (10% of $1000) =$1200. 🙂

If I use Compound Interest: Year 1, I owe $1000 + 10% interest =$1100.  Year 2, I owe $1100 + (10% of$1100) = $1210 The formula for Compound Interest is: $I = P(1+r) ^{nt} - P$ I = Interest P = Present Value R = Interest Rate T = Number of Years Involved N = Number of Times a Year ### Example Company A (a large global corporation) invests$100,000 in a small new business called Company B.  Company B has 10 years to pay it back. The interest rate is 7% compounded  bi-annually.   What is the Total Interest (利) you will pay over 10 Years?

$I = P(1+r) ^{nt} - P$

$I = 100,000 (1 + .07) ^{(2)(10)} - 100,000$

$I = 386,968.446 - 100,000 = 286,968.45$

## Calculating FUTURE VALUE and PRESENT VALUE using COMPOUND INTEREST

The total interest is of course important to both Company A and Company B, there are two other important numbers that the financial managers of Company A want to know–the Present Value of their money and the Future Value of their money.

### Future Value

$FV = P(1+r)^{nt}$

FV = Future Value (how much money you will make in total)
PV = Present Value

R = Interest Rate
T = Number of years involved
N = Times per Year

Using our example above with Company A & B, the Future Value is calculated like this:

$FV = 100,000 (1+.07)^{(2)(10)}$

$FV = 386,968.46$

That means Company A will make a total of $286,968.46 if they invest their$100,000 in Company B now. Over 10 years, their $100,000 will change into$386,968.46. We like this plan!

### Present Value

Sometimes, for example with bonds (债券), we know the Future Value (how much money will be paid to us in the end). But we don’t know how much money has to be invested (Present Value) to get that future result.  So Present Value is calculated by the formula:

$PV = \frac{FV}{(1 + r)^{nt}}$

PV = Present Value
FV = Future Value

R = Interest Rate
T = Number of years involved
N = Number of Times per Year

Example: Mary Jane knows that in 4 years, she needs to have a total of $150,000 to pay her college tuition. She has an interest-generating account that gives her a 4% compound interest rate bi-annually on everything she puts in. How much money should she invest today (Present Value) in order to have$150,000 in 4 years?

$PV = \frac{150,000}{(1 + .04)^{(2)(5)}}$

$PV = \frac{150,000}{1.48024428} = 101,336.67$

That means that Mary Jane needs to put $101,336.67 in her bank account now in order to get$150,000 in the future.

## KEY TERMS TO REMEMBER

1. Value (值)
2. Present Value (现值)
3. Future Value (未来价值)
4. Interest (利)
5. Simple Interest (单利)
6. Compound Interest (复利)
7. Principal (本息)
8. Monthly (每月一次)
9. Weekly (每周)
10. Annually (每年)
11. Bi-Annually (一年两次)
12. Quarterly (季刊)

## FORMULAS TO REMEMBER

### Compound Interest

$I = P(1+r) ^{nt} - P$

### Future Value

$FV = P(1+r)^{nt}$

### Present Value

$PV = \frac{FV}{(1 + r)^{nt}}$

## Understanding Simple Interest

6 Jun

As always, this lesson is not intended to be professional advice. This is simply lesson material for ESL students in a Managerial Economics and Corporate Finance class. Posted here for their use or for helping other students.

## Corporate Value (值)

Financial officers and Managers are extremely responsible for the monetary (货币) goings-on in their companies. As we said before, the Wealth Maximization Rule means that Financial and Corporate Managers are required to maximize (最大化) the profits (收益) for their investors (投资者).

However, maximizing profits requires in-depth (深入)planning and micro-managing (微观) your funds today while considering (考虑) future profits as well.

There are two types of Value (值) that you should be aware of in Finance and Economics.

The first is called Present Value (现值) and is the value today of something that will increase in value in the future. ExampleWhen we loan someone $1,000 at 10% interest, we know that our$1,000 loan will increase in value in the future.  Present Value = PV.

The second is called Future Value (未来价值) and is the value that the item will have in the future. Future Value = FV.

## Interest (利)

I’ll make another post later discussing the many ways to use Present and Future value in your company, but today I just wanted to talk about using them to calculate (计算) “Simple Interest” (单利).

Usually, when we loan money to someone or invest (投资) our money in something, we do so on the condition that we receive back more money than we put in.  Our corporation is not a charity (慈善机构), we don’t loan you things for free!  The original money we invest is called the Principal (本息).  The extra money we get on top is called the Interest (利).

Example ~ Company A (a large global corporation) invests $100,000 in a small new business called Company B. Company B has 10 years to pay it back. But Company A doesn’t do this for free ~ they want to maximize their profits too. That means they have to make some money on this contract (合同). So they ask Company B to pay an additional 7% per year.$100,000 = Principal
7% = Interest

## SIMPLE INTEREST (单利)

Problem! ~ 7% of what?
Answer! ~ It depends 🙂   It depends on how Company A decides to count it.

There are two separate mathematical formulas (数学公式) you can use to figure out the Interest.  The first one is called Simple Interest (单利). Simple Interest says that each payment period Company B is going to pay an additional 7% of the original principal ($100,000). The formula for Simple Interest is: $I = PRT$ I = Interest P = Present Value R = Interest Rate T = Number of Years Involved ### Example Company A (a large global corporation) invests$100,000 in a small new business called Company B.  Company B has 10 years to pay it back. The interest rate is 7% per year.   What is the Total Interest (利) you will pay over 10 Years?

$I = PRT$

$I = (100,000)(.07)(10) = 70,000$

## Calculating FUTURE VALUE and PRESENT VALUE using SIMPLE INTEREST

The total interest is of course important to both Company A and Company B, there are two other important numbers that the financial managers of Company A want to know–the Present Value of their money and the Future Value of their money.

### Future Value

$FV = PV(1+RT)$

FV = Future Value (how much money you will make in total)
PV = Present Value

R = Interest Rate
T = Number of years involved

Using our example above with Company A & B, the Future Value is calculated like this:

$FV = (100,000)(1+(.07)(10))$

$FV = (100,000)(1.7) = 170,000$

That means Company A will make a total of $70,000 if they invest their$100,000 in Company B now. Over 10 years, their $100,000 will change into$170,000. 🙂 We like this plan!

### Present Value

Sometimes, for example with bonds (债券), we know the Future Value (how much money will be paid to us in the end). But we don’t know how much money has to be invested (Present Value) to get that future result.  So Present Value is calculated by the formula:

$PV = \frac{FV}{(1+RT)}$

PV = Present Value
PV = Future Value

R = Interest Rate
T = Number of years involved

Example: Mary Jane knows that in 4 years, she needs to have a total of $150,000 to pay her college tuition. She has an interest-generating account that gives her a 4% interest rate on everything she puts in. How much money should she invest today (Present Value) in order to have$150,000 in 4 years?

$PV = \frac{150,000}{(1+(.04)(4))}$

$PV = \frac{150,000}{(1.16)} = 129,310.35$

That means that Mary Jane needs to put $129,310.35 in her bank account now in order to get$150,000 in the future.

## KEY TERMS TO REMEMBER

1. Value (值)
2. Present Value (现值)
3. Future Value (未来价值)
4. Interest (利)
5. Simple Interest (单利)
6. Principal (本息)

## FORMULAS TO REMEMBER

### Simple Interest

$I = PRT$

### Future Value

$FV = PV(1+RT)$

### Present Value

$PV = \frac{FV}{(1+RT)}$

## Calculating the Value of a Company

25 Apr

### Finding the Value of the Firm

We measure the success of a financial manager (how well they maximize profits) by finding the overall Value of the Firm (公司的价值).

Value of the Firm = Value of the Company = Present Value (现值)= How much money (/￥/₩) the company would be worth if you tried to sell it today (多少钱该公司将是值得的，如果你想出售它). The Value of the Firm should include

1. How much money the company is worth today and
2. Expected profits in the future.

### Mathematical Equation for Calculating the Value of the Firm

1. Value of the Firm = Current Profit + Expected Future Profit.

Each Year’s Profit is calculated with the following formula:

$Y_{T}=\frac{X}{(1+R)^{T}}$

• X = Current or Expected Accounting Profit (预期会计利润) = Revenue – Explicit Costs
• R = Risk-Adjusted Discount Rate (风险调整贴现率) (although we hope we will make the expected accounting profit this year or in future years, there is always the possibility that we will not. No one will pay us the full expected value of the company because of this risk. So to give the buyer some protection, just in case, we remove the Risk-Adjusted Discount Rate from the total.)（我们从方程中删除的金额，因为我们现在可能不会真正使所有预期的利润，我们想要的）
• T = Number of Years from Today

## Sample Corporate Balance Sheet

24 Mar

If you are looking for a Sample Balance Sheet, here is one I created for my Corporate Finance students.  It’s not perfect of course, and you can always add or subtract things. Just download it as a Word Doc (or if that is not available, copy and paste to a word doc) and modify to suit your needs!

## SAMPLE BALANCE SHEET

Here are some real-world examples you can use to compare:

An EXCEL ready-made template is available as well here: “Corporate Balance Sheet & Income Statement (Automatically Formulated Worksheet with Metrics”

## China fashion~ Starshoes

24 Feb

These are totally not an infringement ~ can’t you see? It’s Starshoes Coffee not Starbucks!

## Having an Ethical Valentines!

10 Feb

Recently, several of my legal friends have been discussing the problem with buying unethically produced chocolate for the holidays.  Unfortunately, around the world, many of the major chocolate producers use cocoa beans gathered through the use of child labor

Using children to do work for lower costs is wrong on so many levels and completely unnecessary. Now, I fully support kids learning how to become adults through simple, child-friendly jobs. For example: babysitting, mowing yards, having a newspaper route, helping around the family business, shoveling snow.

What I do not support is major industrial companies using the poverty of third-world countries to unethically and immorally encourage children to drop out of school and work in conditions that are completely illegal in the United States. As a teacher of Business Ethics and Corporate Governance, one of the great issues that globalization has caused is that it allows international companies to pick and choose where to manufacture and thus avoid the legal standards of work and health safety.

With so many people in the work field looking for jobs, the devastating impact these jobs have on the children, the unethical underhanded dealings of this type of business ~ the use of child labor needs to end.  However, the companies that participate in this type of behavior are only interested in profits. So they are unlikely to stop the practice until it no longer benefits them to do so.

How do we take away their profits? By not consuming their products!

So take a  moment and do your own research.  Find companies that do not use child labor in their chocolate production when you buy your holiday candy this year.  You might check out the article “Ethical Chocolate Companies.” While I have not verified the information in their list, others claim they are legitimate.  Note that the major producers – Mars, Hershey’s, Nestle, and Godiva – are not on this list!

Companies that ignore or subvert the law will listen when their buyers speak out. So take a stand against the despicable practice of child labor this Valentine’s Day and share the power of love for our world.

9 Feb

I recommend these sites to my students when they are working on research for our International Econ course

## New Terms Added to Corporate Governance Vocabulary

2 Feb

I’ve added new terms to the list of Business or Corporate Governance Vocabulary

Don’t forget, the Chinese translations come from the Chinese students rather than professional translators. While I believe they are accurate, you may want to consult professionals before using them for official documents. This is mainly intended to contribute to daily conversation between English speaking Companies and Chinese companies.

Abbreviations:
v. = Verb
n. = Noun