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Unit 6: Capital Investments
Performance Indicators:
6.1 Explain the time value of money (CS)
6.2 Calculate the time value of money (SP)
6.3 Use the time value of money to make business decisions (e.g., projects, investments, etc.) (SP)
Unit Assessment:
Unit Assessment:
FI:062 Explain the time value of money
Curriculum Planning Level: CS
Objectives:
a. Define the terms time value of money, inflation, interest rate, present value, and compound interest.
b. Describe how time impacts the value of money.
c. Explain information that is needed when considering the time value of money (i.e., date at which the dollar amount is measured and the interest rate applied).
d. Explain the impact of inflation on the value of money.
e. Discuss situations in which the present value is needed.
Activity:
Use you knowledge of the time value of money concept to write a letter providing financial advice to yourself when you were in 6th grade.
In that letter, you should explain how time impacts the value of money, identify information that is needed when considering the time value of money, and describe the impact of inflation on the value of money.
When finished, be prepared to share with a partner.
6.1 Explain the time value of money (CS)
The Time Value of Money—Discussion Guide
Performance Indicator: Explain the time value of money
THINK ABOUT IT
Suppose you won an award at school with a $100 prize.
Congratulations! Now, you have a decision to make.
You can accept this money now.
Or, you can claim the prize money in one year after you graduate.
What do you do?
One hundred dollars now is the same as $100 later, right?
Not necessarily—and that’s because of the time value of money.
KEY CONCEPTS
Slide #1 What Is the Time Value of Money?
Simply put, the time value of money is the concept that money you have now is always worth more than the exact same amount in the future.
This is because money you have now is able to earn interest over time—say, in a savings account or other investment opportunity.
Interest is the reward or cost of lending or borrowing money, usually figured as a percentage of the initial amount.
If you wait to accept money, then you miss out on the chance for that money to earn interest, which ultimately gives you more money.
When you consider the time value of money, you need to know the date on which the dollar amount is measured and the interest rate applied.
Let’s go back to our scenario above.
Suppose you chose to accept the $100 prize now.
Then, you invested that money in a savings account with a 10% interest rate (the percentage figure used in calculating interest charges).
After one year, the original $100 earned $10 from interest.
You earned an additional ten dollars simply because you chose to receive your money and invest it now, not later.
Slide #2 Compound Interest
An additional $10 might not seem like much on the surface—but consider that people often invest money in amounts much larger than $100 over many years.
That means they earn interest not just on the principal amount they invested, but, as the years go by, they earn interest on the previous years’ interest, too.
This “interest on interest” (called compound interest) can lead to greater financial gains than simple interest alone.
Let’s continue the scenario from above.
You earned $10 in interest after one year.
You decide to keep your money in the savings account—which means that, this second year, the 10% interest rate is calculated not just on your original $100 prize money, but also on the $10 interest it earned.
This compound interest continues year after year, exponentially increasing your earnings.
Imagine how much money you can earn after 10 years simply by accepting and investing your prize money now!
Slide #3 Impact of Inflation on Time Value of Money
The ability to earn interest on invested funds is not the only reason that money now is worth more than the same amount of money in the future.
Inflation also has a large impact on the time value of money.
Inflation is the steady increase in the general price levels of consumer goods and services over a period of time.
For example, a gallon of milk now costs about $2-3.
One hundred years ago, milk often cost just 1/10th of that price.
Did the milk become more difficult or more costly to produce?
No—it simply experienced a steady increase in price over time to adjust to the rising costs of everything else.
Inflation affects everything from milk and gas to salaries and wages.
When inflation increases the price of goods and services, it means that your money won’t be able to buy as much over time.
One hundred years ago, $3 was enough to buy many gallons of milk!
But now, due to inflation, that same $3 is only able to purchase one gallon.
Consider your prize money: One hundred dollars today might be able to purchase a lot more than it’s able to in 10, 20, even 50 years.
Inflation is just another reason that money now is worth more than money later.
Slide #4 Present Value
Present value is the current value of an amount of money.
This is often contrasted with future value, which is the value of an amount of money after it has been invested for a period of time.
Present value is usually less than future value because of the income-earning potential of money—that is, because invested money can earn interest over time, its value increases as time progresses.
Present value is an important figure, as knowing this amount can help you make informed decisions and reach financial goals.
Present value represents the amount of money that must be invested now in order to achieve a future financial goal.
For example, let’s say you set a goal of having $5,000 ready for college tuition by the time you graduate high school.
Present value represents the sum of money you must invest now in order to successfully achieve your tuition goal in the future.
Similarly, investors use present value to make informed decisions in areas like financial modeling, stock valuation, and bond pricing.
By using present values to compare values over time, investors can gauge future financial benefits of both assets and liabilities.
Curriculum Planning Level: SP
Objectives:
a. Define the term future value.
b. Explain why having an amount of money now is worth more than having that same amount later.
c. Discuss information needed to calculate the present value of money.
d. Identify information needed to calculate the future value of money.
e. Calculate the present value of money (i.e., Present Value = Future Value/(1 + Discount Rate).
f. Calculate the future value of money (i.e., Future Value = Present Value X (1 + Discount Rate).
g. Calculate the time value of money for a period longer than one year using a compound interest formula (e.g., Future Value = Present Value X (1 + Discount Rate)5 where the period is five years).
Activity:
Get in Groups of two. develop a scenario in which the main character needs to calculate one of the following:
the present value of money (Present Value = Future Value/(1 + Discount Rate)
the future value of money (Future Value = Present Value X (1 + Discount Rate)
the time value of money for a period longer than a year (Future Value = Present Value X (1 + Discount Rate)5 where the period is five years)
Provide all information necessary to calculate the value of money.
Trade your scenarios with another pair. Work in pairs to solve and complete the given scenarios.
Teacher NOTES
Once finished, have the pairs come together in a small group to double check calculations and ensure accuracy.
6.2 Calculate the time value of money (SP)
Discussion Guide
Performance Indicator: Calculate the time value of money
THINK ABOUT IT
The time value of money is the concept that money you have now is always worth more than the exact same amount in the future.
But why? And, perhaps more importantly, how can we determine the value of money both now and in the future to make sure we are managing our finances most efficiently?
Read on to learn more about calculating the time value of money.
KEY CONCEPTS
Slide #1 What Is the Time Value of Money?
The time value of money concept states having an amount of money now is worth more than having that same amount later.
This is because money you have now can earn interest over time—say, in a savings account or other investment opportunity.
(It’s because inflation gradually decreases money’s buying power over time, too.)
If you wait to accept money, then you miss out on the chance for that money to earn interest, which increases that money’s future value.
Future value is the value of an amount of money after it has been invested for a period of time.
The future value of money is often more than its present value because of the income-earning potential of money.
Slide #2 Calculating the Future Value of Money
Calculating the future value of money allows you to see what money currently claimed will be worth at a later date.
The formula for calculating the future value of money is expressed as follows:
Future Value = Present Value X (1 + Discount Rate)
So, to calculate the future value of an amount of money, we need to know the present (or current) value of that money and the discount (or interest) rate.
(If the money is invested for a period of time longer than one year, the formula will change slightly.)
Let’s apply the formula to an example.
Stacey currently has $100 and wants to know how much that money will be worth in one year’s time after she invests it.
In this example, the present value is $100.
If she invests that money in an account with a 10% interest rate, her discount rate is .10.
By plugging in these values and solving the equation, here is our answer:
Future Value = $100 X (1 + .10) 🡪 FV = $100 X (1.10) 🡪 FV = $110
Thus, the future value of Stacey’s original $100 is $110.
That is, by investing her money now in an account with a 10% interest rate for one year, Stacey’s money has a future value that is $10 more than its present value.
Slide #3 Calculating the Present Value of Money
Sometimes, investors want to calculate the present value of money.
On the surface, this might seem silly—isn’t the present value of money just the current value?
Yes. But, sometimes investors need to know how much money to invest now in order to achieve a future financial goal.
Think of it this way: if you wanted to have $1,000 ready for a new laptop by next school year, how much money would you need to “put away” or invest now in order to achieve that financial goal?
That’s where calculating the present value of money becomes important.
The formula for calculating the present value of money is expressed below.
You’ll see that to determine present value, you need to know the future value (or amount of money) you are aiming to obtain and the discount (or interest) rate.
Formula: Present Value = Future Value / (1 + Discount Rate)
Let’s apply this formula to the example above.
Abraham needs to have $1,000 exactly one year from now to purchase a new laptop for the next school year, so he needs to know how much money to invest now in an account with a 10% interest rate.
In this example, the future value is $1,000 and his discount rate is .10.
By plugging in these values and solving the equation, here is our answer:
Present Value = $1,000 / (1 + .10) 🡪 PV = $1,000 / (1.10) 🡪 PV = $909
Thus, Abraham needs to invest $909 now in order to have $1,000 in one year.
Slide #4 Calculating Compound Interest
Until now, both our equations looked just one year in the future.
If we need to calculate the time value of money for a period longer than one year, we use a compound interest formula.
(Compounding refers to earning interest on interest.)
Below are the compound interest formulas for future value and present value.
You’ll note that each equation seems the same as the simple interest version, except for the variables “n,” which refers to the number of compounding periods per year, and “t,” which refers to the number of years.
Future Value = Present Value X [1 + (Discount Rate / n)](n X t)
Present Value = Future Value / [1 + (Discount Rate / n)](n X t)
Slide #5 Calculating Compound Interest
Let’s calculate compound interest using Stacey’s and Abraham’s scenarios.
To start, we will assume that each investment earns an interest payment once per year.
(In other words, they earn interest annually.)
So, if Stacey wants to know how much her $100 will be worth in five years, here is what her calculation would look like:
Future Value = $100 X [1 + (.10 / 1)](1 X 5) 🡪 FV = $100 X (1.10)5 🡪 FV = $161
If Abraham wants to know how much to invest now so he can buy a $1,000 laptop in three years (assuming he, like Stacey, earns interest annually), here is his equation:
Present Value = $1,000 / [1 + (.10 / 1)](1 X 3) 🡪 PV = $1,000 / (1.10)3 🡪 PV = $751
Slide #6 Calculating Compound Interest
Now, you’ll note that so far, the variable “n” (number of compounding periods per year) hasn’t made much of an impact in the above equations.
That’s because we’ve been calculating compound interest that is earned annually (once per year), and anything multiplied or divided by “1” is the original number.
But not all investments earn interest once per year.
Some earn interest daily, monthly, quarterly, etc.
Let’s say both Stacey and Abraham invest their money in an account that earns interest quarterly, which means there are now four compounding periods per year.
If everything else stays the same, here are their new equations:
Stacey’s FV = $100 X [1 + (.10 / 4)](4 X 5) 🡪 FV = $100 X (1.025)20 🡪 FV = $164
A’s PV = $1,000 / [1 + (.10 / 4)](4 X 3) 🡪 PV = $1,000 / (1.025)12 🡪 PV = $744
Therefore, Stacey will have $164 after investing $100 into an account with a 10% quarterly interest for five years, and Abraham needs to invest $744 now in an account that earns 10% interest quarterly in order to have $1,000 in three years.
FI:646 Use the time value of money to make business decisions (e.g., projects, investments, etc.)
Curriculum Planning Level: SP
Objectives:
a. Define the following terms: hurdle rate, discount rate, weighted average cost of capital, present value, net present value, and payback period.
b. Identify reasons for considering time value of money when evaluating business decisions.
c. Distinguish between discount rate and weighted average cost of capital.
d. Distinguish between discount rate and hurdle rate.
e. Describe decision evaluation methods that use time value of money (e.g., discounted payback method, net present value, internal rate of return).
f. Explain the role of decision evaluation methods in capital budget screening and preference decision-making.
g. Evaluate business decisions using time-value of money techniques.
Activity: 6.3 Worksheet
Teacher Notes
6.3 Use the time value of money to make business decisions (e.g., projects, investments, etc.) (SP)
Discussion Guide
Performance Indicator: Use the time value of money to make business decisions (e.g., projects, investments, etc.)
THINK ABOUT IT
Business leaders must make important decisions every day.
To make informed, efficient, and strategic choices, leadership relies on many tools, such as the time value of money (TVM).
This tool helps companies make decisions regarding the viability of different business projects and ventures.
KEY CONCEPTS
Slide #1 Why Is the Time Value of Money Important?
The TVM is used in discounted cash flow (DCF) analysis, which estimates an investment’s value based on anticipated future cash flows.
While investors can’t predict the future with absolute certainty, the TVM provides information about how the value of funds will change over time to help investors make informed business decisions.
Investors use the TVM to calculate both present value and future value, two factors that have far-reaching implications in a variety of financial scenarios.
Future value is the value of an amount of money after it has been invested for a period of time.
By calculating the future value of money, investors can determine how much a given amount will be worth in the future, helping them decide if a business opportunity is worthwhile.
Present value is the current value of an amount of money.
By calculating the present value of money, investors can determine how much money to invest now so that they can reach financial goals in the future.
Slide #2 What Is a Discount Rate?
A discount rate is the interest rate used to calculate either present or future value in a DCF analysis.
Using the discount rate helps determine whether a financial investment will be worthwhile or viable, because it represents an anticipated amount of financial return.
Discount rate is closely linked to two other types of return: weighted average cost of capital (WACC) and hurdle rate.
The cost of capital refers to the amount of return a company needs to receive in order to justify a capital project, such as developing a new facility.
There are multiple ways a company can raise capital (such as through debt or equity).
The weighted average cost of capital, then, refers to the required return a company must receive for a project, calculated by giving proportional weight to each category of capital.
Like discount rate, WACC represents a type of return—in fact, many companies use WACC as the discount rate when making calculations for a new venture.
However, while the cost of capital is the minimum rate needed to warrant a new project’s cost, the discount rate is the figure that must meet or exceed that cost of capital.
A hurdle rate, similar to both WACC and discount rate, is the minimum amount of return required to approve an investment.
Because the WACC and hurdle rate are so similar, many companies use the WACC as a hurdle rate.
However, a hurdle rate in particular considers associated risks with a given investment, which helps companies determine whether a project should be pursued.
In general, riskier projects have a higher hurdle rate, while lower hurdle rates indicate less risk.
Slide #3 Decision Evaluation Methods
Capital budgeting is a process in which a firm’s financial managers determine the projects it should invest in (e.g., acquiring land or purchasing machinery).
For measurability and accountability, businesses often use decision evaluation methods that use the TVM to help with screening decisions (which determine if a project meets certain requirements) and later with preference decisions (which help narrow down potential investments).
Here are some evaluation methods:
Discounted payback period (DPB) method.
A payback period is the amount of time it takes a business to recover its initial investment, or break even, into a certain decision or project.
The DPB method uses TVM to calculate how long it takes for the investment to be recovered.
A shorter payback period is preferable, because it means the company recovers its initial investment within a smaller time frame.
Net present value (NPV) method.
Net present value (NPV) is the value of all future cash flows (both positive and negative) over an investment’s life.
Businesses use NPV to calculate today’s value of a potential investment opportunity—a positive NPV generally indicates a profitable investment, while a negative NPV indicates an investment to avoid.
(This premise is also known as the Net Present Value Rule.)
Internal rate of return (IRR) method.
A rate of return is the expected return on a project.
The internal rate of return is the discount rate that would result in an NPV of zero.
This provides a standard, or benchmark, to help companies compare and evaluate investment opportunities.
If the rate is higher than the cost of capital, it is likely a profitable investment.
For more information about capital budgeting and decision evaluation methods, click here: https://www.investopedia.com/articles/financial-theory/11/corporate-project-valuation-methods.asp.
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