Tag Archives: Managerial Economics

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 = 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?

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 = 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:

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 = 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?

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. 

JPEG

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

Future Value

Present Value

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 = 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?

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 = 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:

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 = 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?

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. 

JPEG

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

Future Value

Present Value

Calculating the Value of a Company

25 Apr

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

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:

  • 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

EXAMPLE

Year 1, Company A makes $180,000. Year 2, Company A makes $150,000. Year 3, Company A makes $100,000. The Risk-Adjusted Discount Rate is 13%. 1年,公司180000美元。2年,公司150000美元。3年,公司100000美元。风险调整贴现率为13%

The Equation for 1 Year is:

The Equation for 3 Years is:

Filling in our known information, the equation for the Value of Our Firm is:

Value of the Firm = $346,069

 

Economics ~ Introduction to Managerial Economics

24 Mar

Hello-our internet sucks, so I’m posting this for some of my students 🙂 You’re welcome to enjoy it too!

What is Managerial Economics?

  • Economics (经济学)= The study of how resources (资源) are created (创造), gathered (搜集,聚集), traded (营业), and divided (分离,划分).
    • Resources = Anything you use to help the company work. Examples: time, money, land, tools, labor, raw materials.
      • Natural Resources (自然资源) = Resources created by nature. Examples: wood, water, air, rocks/stones, flowers, natural chemicals
      • Man-Made Resources (人造资源) = Resources created by humans by either combining (mixing together) or changing natural resources into something new. Examples: jewelry, paint, fabric, steel, hammers.
      • Limited Resources (限制性资源) = Resources either no longer being created or only created in small amounts. Meaning the supply is not enough.Examples: Gold, Diamonds, Water in a desert.
      • Unlimited Resources (无限制性资源) = Where there is a large amount of the resource or it is created fast enough to replace any that is lost. Supply is enough.Examples: Water, Air.
      • Raw Materials (原材料) = The resources that are put into the product. Example: If we make a computer, raw materials would include wires, plastic, metal, paint, springs, etc.
      • Market-Supplied Resources (市场提供的资源) = Resources owned by someone outside of the company. Examples = Taxes, Utilities, Rent, Raw Materials, Wages
      • Owner-Supplied Resources (业主提供的资源) = Resources owned by the company’s owners.
  • Manager (经纪, 经理) = A person who is obligated to ensure the company (or department) is effectively organized and controlled.
  • Managerial Economics (管理经济学) = The study of the best method for managers to create, gather, trade, and divide the company’s resources.

Goal of Effective Managers 

  • Wealth or Profit (收益) Maximization Rule = #1 Goal of Effective Managers is to make the owner’s the most profit (as long as they do so ethically and legally)

How to Maximize Profits (收益)?

  • Profit = Revenue – Cost
  • Two ways to Maximize Profit:
    • Make the Highest Revenue
    • Pay the Lowest Costs

What are Revenue, Cost, and Profits?

  • Revenue (收入) = Total Income or Money the Company makes from its work.
  • Cost (成本)  = The losses or sacrifices the company makes in exchange for getting and using resources in its work. 
    • Opportunity Costs (机会成本) = The company’s costs created because it lost some opportunity. 
      • Opportunity Cost of using Market-Supplied Resources = $$ Spent paying for those resources (you lose the opportunity to spend the money on something else)
      • Opportunity Cost of using Owner-Supplied Resources = $$, time, effort lost that the owner would have had if they spent their resources on something else.
    • 2 Types of Opportunity Costs
      • Explicit Costs (明确的成本) = Any money the company pays owners of Market-Supplied Resources
      • Implicit Costs (隐性成本) = Anything the Owner loses by giving the company Owner-Supplied Resources
    • Total Economic Cost = Explicit Costs + Implicit Costs 
  • Profit (收益)  = Everything the company gets to keep from the Revenue after it pays its costs!
    • Present Profit v. Future Profit
      • Present Profit = What we are keeping right now. (Most Important)
      • Expected Future Profit = What we think we’ll get in the future (Companies with higher expected future profits have more value. While companies with a possibility of low future profits will have a lower value)
    • Profit is Counted in Two Ways
      • Example: Joshua has a company (Company A) that just made $150,000 in Revenue. The company spends $9,000 on Taxes and Utilities, $3,000 on Wages, and $5,000 on Raw Materials. Joshua gave the company the building but would have made $2,000 if he used it as a school instead. He also lost $5,000 on his original investment. 
      • Economic Profit (经济利润) = Revenue – Total Economic Cost
        • What is Company A’s Economic Profit?
      • Accounting Profit (会计利润) = Revenue – Explicit Costs.
        • What is Company A’s Accounting Profit?
      • In Managerial Economics, we usually mean Accounting Profit when we say “Profit”

More to come later 🙂

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