Chapter 3 – The Valuation Principle: The Foundation of Financial Decision Making

Introduction

The task of every financial manager is to make educated decisions on behalf of the investors and shareholders of each company. People in these positions are faced with questions regarding investments, production, etc each and every day of their lives. It is too often that within a company, someone will propose an idea that sounds good at the time but may not be of benefit. It is the job of the financial manager to break the idea down into detail to analyze the benefits and the costs, and then make a decision based on concrete numbers. In this section, we explore the Valuation Principle, the foundation of financial decision making.

Step 1 – Identifying Cost-Benefit

The first step in making a financial decision is to analyze the cost and benefit of the decision at hand. Suppose you are a wholesale food distributor. Your suppliers come from Canada, Mexico, and Japan. Today, a customer offers you $14 million for a 1000 lb shipment. Buying the particular shipment the customer wishes to purchase from Canada would cost you $9 million plus shipping costs of $125.00 per pound. Japan offers to sell you the same shipment for a flat rate of $ 9,090,000. From Mexico, you can buy the same shipment for $ 9,050,000 plus shipping of $95.00 per pound. The task of the financial manager in this case would be to figure out the best alternative in order to create the biggest profit for the wholesale food distributor. Canada: Benefit = $14,000,000 Cost = 9,000,000 + (125 x 1000) = 9,125,000 Benefit – Cost = 14,000,000 – 9,125,000 = Total Benefit $4,875,000 Japan: Benefit = $14,000,000 Cost = 9,090,000 Benefit – Cost = 14,000,000 – 9,090,000 = Total Benefit $4,910,000 Mexico: Benefit = $14,000,000 Cost = 9,050,000 + (95 x 1000) = 9,145,000 Benefit – Cost = 14,000,000 – 9,145,000 = Total Benefit $4,855,000
From the computations above, one can clearly see that the best method of doing business would be to buy from Japan. It yields the greatest benefit to the company. By putting the decision in numbers and breaking it down, you can analyze that Mexico and Canada suppliers would charge more than the supplier from Japan. Giving quantities to the decision process makes it much easier and justified.

The computations above illustrate exactly what the Valuation Principle is: an analysis between the value of the benefits and the value of it's costs. It provides a basis for making decisions within a company. In a competitive market (a market in which the good can be bought and sold at the same price) the value of a good is set by it's price, and any personal opinion or preference is irrelevant when determining value.

Valuation Principle- The value of a commodity or an asset to the firm or its investors is determined by its competitive market price. The benefits and costs of a decision shold be evaluated using those market prices. When the value of the benefits exceeds the calue of the costs, the decision will increase the market value of the firm.

The Time Value of Money and Interest Rates

Because in many cases costs and benefits occur at different times (such as incurring upfront costs for projects that will pay off in the long run), we must incorporate the Time Value of Money when making financial decisions. This is the difference in value between money today and money in the future. Also, it is the observation that two cash flows at different points in time have different values. Let's say your investment today of $100,000 will produce a benefit of $105,000 in one year. We cannot just simply take the difference between the two and say our net benefit is $5,000. This ignores timing of the costs and benefits, essentially saying that money today is worth the same as money a year from now. We know this is false once we include interest rates and other factors.

An interest rate is the rate at which money can be borrowed or lent over a given period of time. Let's say our interest rate is 5%. This means that if today we invested $1 in the bank, a year from now we would have $1.05. In this example, we can exchange $1 today for (1+rate) dollars in the future. This (1+r) is referred to as the interest rate factor - One plus the interest rate, it is the rate of exchange between dollars today and dollars in the future in units of $ in one year/$ today. The interest rate depends on supply and demand changes. Once we get an interest rate, it is easier to apply our Valuation Principle. Going back to our previous example:

Suppose you invest $100,000 today at an interest rate of 5%. Cost = 100,000 x (1+rate) Cost = 100,000 x 1.05 = $105,000 in one year

This can be looked as follows: Investing 100,000 today means I will have 105,000 one year from now. Also, if we look at this from a borrowing perspective, if we took out a loan for $100,000 today, we would owe $105,000 a year from now.

From here, we can analyze if an investment is a good idea or not. Let's say that if we invested our money in Venture A, our interest rate would be 6% instead of the 5% we would get at the bank. Doing our math, we would find that in a year, the bank would yield us 105,000 and the investment in Venture A would yield us 106,000. With this, our net benefit would be $1,000 if we go with investing in Venture A. It has a higher rate of return. You have just applied the valuation principle!
We can also go backwards with the calculations. Let's say we start with the same 100,000 today. We are looking to see if the following investment would be a smart decision, essentially if we should spend it or not. For example, if we have a benefit of 105,000 in one year, what is the equivalent amount in money today assuming our interest rate is 6%?

Benefit = 105,000 one year from now / 1.06 = $99,056.60
This benefit is only worth 99,056.30. We would then reject this investment opportunity because to the firm 100,000 today means more than the 105,000 benefit a year from now (which is really worth 99,056 today). With the above examples, we have computed present and future value.

Present Value -The value of a cost or benefit compunded in terms of cash today. Future Value -The value of a cash flow that is moved forward in time.

With present and future value calculations, we have the discount factor, which is the value today of a dollar received in the future. In our previous calculations, the value of the dollar was (1/1+r) = (1/1.06) = .94 assuming the interest rate was 6%. This interest rate is also referred to as the discount rate of an investment.

The NPV Decision Rule

Net Present Value (NPV) is defined as the difference between the present value of a project or investment's benefits and the present value of its costs. To analyze this, let's look at an example: Assume your firm is offered an investment opportunity where you can invest $100 today and receive $175 a year from now. The interest rate is 5% per year. Your calculations would look something like this: PV(Benefit) = (175 in a year) / (1.05 in a year/$ today) = $166.67 today Once you figure out the benefit, you can calculate your NPV simply by taking the benefit and subtracting the costs: NPV = 166.67 - 100 = $66.67 today. This would mean the investment opportunity is a good opportunity.

Projects and investment opportunities with a positive NPV are good for the firm and should be done. They increase the value of the firm and the wealth of the investors. On the opposite end, the investments and projects with a negative NPV would be the same as saying you would lose that amount of money today if the project was done. This concept is captured in the NPV Decision Rule - When choosing among investment alternatives, take the alternative with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today. Accept projects with a positive NPV and reject those with a negative NPV. If by chance your NPV is zero, this means you will neither gain nor lose by doing the project instead of rejecting it. You can use the NPV Decision Rule when you are faced with alternatives. Should you keep a business running or should you sell it? These are all solved easily when you analyze the Net Present Value. We may come to a situation where we prefer cash today and would like to sell the business. However, we must remember that personal preferences have no say in the value. Regardless of our preferences for cash today versus cash in the future, we should always maximize NPV first. We can then borrow or lend to shift cash flows through time and find our most preferred patter of cash flows.

The Law of One Price

The practice of buying and selling equivalent goods or portfolios to take advantage of a price difference is called arbitrage. We call such situations where it is possible to make a profit without taking any risk or making any investment an arbitrage opportunity. In competitive markets, however, the price of a good will be the same in differing locations at any point in time. Let's say apples are in a competitive market. In Milwaukee the price of apples is $5 per bushel. In Chicago, they are selling for $10. Although initially this may be a quick profit for the lucky investor who exploits it first and fast, by purchasing apples in Milwaukee, you will drive their price up because demand rises. Likewise, if you sell them in Chicago, the demand will go down and and prices will fall, eventually coming to a competitive market where both goods will be selling for the same price. This concept is the Law of One Price - In competitive markets, securities or portfolios with the same cash flows must have the same price. When we apply this law to financial securities, we see that the price of a security should be equal to the present value of the future cash flows obtained from owning that security. We also need to keep in mind that with such transactions, there is always the possibility of incurring transaction costs, or expenses such as broker commission and the bid-ask spread investors must pay in most markets in order to trade securities.

## Chapter 3 – The Valuation Principle: The Foundation of Financial Decision Making

## Introduction

The task of every financial manager is to make educated decisions on behalf of the investors and shareholders of each company. People in these positions are faced with questions regarding investments, production, etc each and every day of their lives. It is too often that within a company, someone will propose an idea that sounds good at the time but may not be of benefit. It is the job of the financial manager to break the idea down into detail to analyze the benefits and the costs, and then make a decision based on concrete numbers. In this section, we explore the Valuation Principle, the foundation of financial decision making.## Step 1 – Identifying Cost-Benefit

The first step in making a financial decision is to analyze the cost and benefit of the decision at hand. Suppose you are a wholesale food distributor. Your suppliers come from Canada, Mexico, and Japan. Today, a customer offers you $14 million for a 1000 lb shipment. Buying the particular shipment the customer wishes to purchase from Canada would cost you $9 million plus shipping costs of $125.00 per pound. Japan offers to sell you the same shipment for a flat rate of $ 9,090,000. From Mexico, you can buy the same shipment for $ 9,050,000 plus shipping of $95.00 per pound. The task of the financial manager in this case would be to figure out the best alternative in order to create the biggest profit for the wholesale food distributor.Canada: Benefit = $14,000,000

Cost = 9,000,000 + (125 x 1000) = 9,125,000

Benefit – Cost = 14,000,000 – 9,125,000 = Total Benefit $4,875,000

Japan: Benefit = $14,000,000

Cost = 9,090,000

Benefit – Cost = 14,000,000 – 9,090,000 = Total Benefit $4,910,000

Mexico: Benefit = $14,000,000

Cost = 9,050,000 + (95 x 1000) = 9,145,000

Benefit – Cost = 14,000,000 – 9,145,000 = Total Benefit $4,855,000

From the computations above, one can clearly see that the best method of doing business would be to buy from Japan. It yields the greatest benefit to the company. By putting the decision in numbers and breaking it down, you can analyze that Mexico and Canada suppliers would charge more than the supplier from Japan. Giving quantities to the decision process makes it much easier and justified.

The computations above illustrate exactly what the

Valuation Principleis: an analysis between the value of the benefits and the value of it's costs. It provides a basis for making decisions within a company. In acompetitive market(a market in which the good can be bought and sold at the same price) the value of a good is set by it's price, and any personal opinion or preference is irrelevant when determining value.Valuation Principle

- The value of a commodity or an asset to the firm or its investors is determined by its competitive market price. The benefits and costs of a decision shold be evaluated using those market prices. When the value of the benefits exceeds the calue of the costs, the decision will increase the market value of the firm.## The Time Value of Money and Interest Rates

Because in many cases costs and benefits occur at different times (such as incurring upfront costs for projects that will pay off in the long run), we must incorporate theTime Value of Moneywhen making financial decisions. This is the difference in value between money today and money in the future. Also, it is the observation that two cash flows at different points in time have different values. Let's say your investment today of $100,000 will produce a benefit of $105,000 in one year. We cannot just simply take the difference between the two and say our net benefit is $5,000. This ignores timing of the costs and benefits, essentially saying that money today is worth the same as money a year from now. We know this is false once we include interest rates and other factors.An

interest rateis the rate at which money can be borrowed or lent over a given period of time. Let's say our interest rate is 5%. This means that if today we invested $1 in the bank, a year from now we would have $1.05. In this example, we can exchange $1 today for (1+rate) dollars in the future. This (1+r) is referred to as theinterest rate factor- One plus the interest rate, it is the rate of exchange between dollars today and dollars in the future in units of $ in one year/$ today. The interest rate depends on supply and demand changes. Once we get an interest rate, it is easier to apply our Valuation Principle. Going back to our previous example:Suppose you invest $100,000 today at an interest rate of 5%.

Cost = 100,000 x (1+rate)

Cost = 100,000 x 1.05 = $105,000 in one year

This can be looked as follows: Investing 100,000 today means I will have 105,000 one year from now. Also, if we look at this from a borrowing perspective, if we took out a loan for $100,000 today, we would owe $105,000 a year from now.

From here, we can analyze if an investment is a good idea or not. Let's say that if we invested our money in Venture A, our interest rate would be 6% instead of the 5% we would get at the bank. Doing our math, we would find that in a year, the bank would yield us 105,000 and the investment in Venture A would yield us 106,000. With this, our net benefit would be $1,000 if we go with investing in Venture A. It has a higher rate of return. You have just applied the valuation principle!

We can also go backwards with the calculations. Let's say we start with the same 100,000 today. We are looking to see if the following investment would be a smart decision, essentially if we should spend it or not. For example, if we have a benefit of 105,000 in one year, what is the equivalent amount in money today assuming our interest rate is 6%?

Benefit = 105,000 one year from now / 1.06 =

$99,056.60This benefit is only worth 99,056.30. We would then reject this investment opportunity because to the firm 100,000 today means more than the 105,000 benefit a year from now (which is really worth 99,056 today). With the above examples, we have computed present and future value.

Present Value -The value of a cost or benefit compunded in terms of cash today.Future Value -The value of a cash flow that is moved forward in time.With present and future value calculations, we have the

discount factor, which is the value today of a dollar received in the future. In our previous calculations, the value of the dollar was (1/1+r) = (1/1.06) = .94 assuming the interest rate was 6%. This interest rate is also referred to as thediscount rateof an investment.## The NPV Decision Rule

Net Present Value (NPV)is defined as the difference between the present value of a project or investment's benefits and the present value of its costs. To analyze this, let's look at an example: Assume your firm is offered an investment opportunity where you can invest $100 today and receive $175 a year from now. The interest rate is 5% per year. Your calculations would look something like this:PV(Benefit) = (175 in a year) / (1.05 in a year/$ today) = $166.67 today

Once you figure out the benefit, you can calculate your NPV simply by taking the benefit and subtracting the costs:

NPV = 166.67 - 100 = $66.67 today. This would mean the investment opportunity is a good opportunity.

Projects and investment opportunities with a positive NPV are good for the firm and should be done. They increase the value of the firm and the wealth of the investors. On the opposite end, the investments and projects with a negative NPV would be the same as saying you would lose that amount of money today if the project was done. This concept is captured in the

NPV Decision Rule- When choosing among investment alternatives, take the alternative with the highest NPV. Choosing this alternative is equivalent to receiving its NPV in cash today. Accept projects with a positive NPV and reject those with a negative NPV. If by chance your NPV is zero, this means you will neither gain nor lose by doing the project instead of rejecting it. You can use the NPV Decision Rule when you are faced with alternatives. Should you keep a business running or should you sell it? These are all solved easily when you analyze the Net Present Value. We may come to a situation where we prefer cash today and would like to sell the business. However, we must remember that personal preferences have no say in the value. Regardless of our preferences for cash today versus cash in the future, we should always maximize NPV first. We can then borrow or lend to shift cash flows through time and find our most preferred patter of cash flows.##

## The Law of One Price

The practice of buying and selling equivalent goods or portfolios to take advantage of a price difference is calledarbitrage. We call such situations where it is possible to make a profit without taking any risk or making any investment anarbitrage opportunity. In competitive markets, however, the price of a good will be the same in differing locations at any point in time. Let's say apples are in a competitive market. In Milwaukee the price of apples is $5 per bushel. In Chicago, they are selling for $10. Although initially this may be a quick profit for the lucky investor who exploits it first and fast, by purchasing apples in Milwaukee, you will drive their price up because demand rises. Likewise, if you sell them in Chicago, the demand will go down and and prices will fall, eventually coming to a competitive market where both goods will be selling for the same price. This concept is theLaw of One Price- In competitive markets, securities or portfolios with the same cash flows must have the same price.When we apply this law to financial securities, we see that the price of a security should be equal to the present value of the future cash flows obtained from owning that security. We also need to keep in mind that with such transactions, there is always the possibility of incurring

transaction costs, or expenses such as broker commission and the bid-ask spread investors must pay in most markets in order to trade securities.