*If you’re just stopping by for the first time, this is a class in a series of classes over the next few months which will culminate in the development of a complete financial plan. Stop by HERE for a complete list of classes currently available and HERE for more information about the website.*

**Class Objectives: **To learn the essential fundamentals of time value of money including calculating present and future value.

**Prerequisites: **PF101: Intro to Personal Finance & Goals

**Handout: **Time Value of Money Scenario Examples

**Assignment**: TVM Calculations in Excel | Google Docs (previews in lecture material)

**CLASS LECTURE**

What would you say if I asked you to borrow $1,000, but that I *promise* that I will return that $1,000 in a year? We’re friends right? I’m a very trustworthy person, really I am! No thanks?

My 8-year old daughter recently came to me and asked to borrow some money to be able to buy an extra book at the book fair that day. She already had money to buy several others but was a few dollars short of being able to buy an additional book that she *really* wanted. I told her that she would have to keep saving up her allowance if she wanted that other book and we could find somewhere else to buy it later. “But mom!” she immediately told me, “I’ll pay you some *extra* money too.”

And there you have it – time value of money is so simple in theory that even a kid can understand the concept. My daughter even understood that no one wants to loan someone money without a return. She’s going to be an accountant like her mom someday. Or a politician.

Going back to loaning me that $1,000, one of the reasons that you likely would not consider that transaction is that you would have an opportunity cost of not being able to use that money for a year, namely not being able to earn a return during that time (such as interest or growth on stock investments). Another factor that comes into play is inflation: a dollar today will buy you more than it will in several years when prices increase. The last reason you may not be interested in loaning me the money is the risk that I won’t repay it later and then you’ll be out the money.

**Time value of money is simply the concept that money is worth more today than in the future.**

It includes the following basic ideas:

- We would rather have money now than later.
- We expect that providing someone else the use of our money should result in an additional amount of money to compensate us for that time and risk of not receiving our money back.
- We would rather pay money later than right now.
- We can anticipate that someone providing us with a loan will expect to receive additional money in some form of interest that we will be required to pay.

**OPPORTUNITY COST**

I mentioned opportunity cost above and it’s another essential component of learning about time value of money.

**Opportunity cost is the measured value, expressed as a percentage, of giving up a dollar today for a dollar in the future.**

Interest rates are the perfect example of opportunity cost. There are two things that factor into the interest rate percentage used for time value of money:

*Risk-free rate*– This rate is a minimum opportunity cost assuming that you are 100% positive that you will be able to get a full return of your investment. The percentage used is generally the rate on a 3-month treasury bill. From our previous class SA301: Bank Accounts, we see that the current rate is about .32%.*Risk premium*– The additional interest includes the components of inflation, the default risk, the risk of the market value of investments declining and several other risks that we won’t go to in detail. This component is why someone with a credit score of 600 will not receive the same interest rate on a loan of someone with a credit score of 800.

Often, the rate used for time value of money calculations for financial goals is about 7%, which is the projected after-inflation adjusted return expected for the stock market in the future.

Now that we have the basics of time value of money, it will be helpful to look at specific different TVM calculations and examples to be able to further understand the concepts. There are many additional examples given in the handout for this class (linked above and previewed at the end of this class).

**FUTURE VALUE OF A SUM**

Let’s start with the absolute most simple scenario: **you receive a sum of money today and want to know how much it will be worth in the future if you invest it**. This is calculating the future value of a single sum. The power of compounding interest will be working for us, which means that interest is not only being earned on the principal sum invested, but also on the interest that was previously earned. In order to calculate the future value of a sum you need the following inputs:

- Current amount to be invested
- Length of time (years for our calculations) that you’ll have to invest your sum of money
- Interest rate

*Assume this example: Your child has just received an inheritance from a grandparent in the amount of $50,000 and you want to invest the entire sum in a 529 college savings plan, where it will grow tax-free. Any earnings will earn additional earnings on them as well as the $50,000 you deposited. You want to know how much you will have in 10 years when your child is ready to start college. You assume that your investments will earn a rate of 7% annually.*

Based on these assumptions, you will have $98,358 saved in your child’s 529 college savings plan. Your money is expected to nearly double!

**FUTURE VALUE OF A STREAM OF CASH FLOWS**

A more complicated and more common situation is to have a **stream of cash flows over time that you want to find the value of at a future date in time**. For this calculation you will need the following inputs:

- Whether you will be investing at the beginning or end of the year
- Initial investment amount and cash inflows for each year
- Length of time (years) that you’ll be investing the money
- Interest rate

*Assume this example: You are suddenly concerned about your retirement plan (or lack thereof) and decide to max out contributions to a Traditional IRA. Current maximum contributions per IRS rules are $5,500 annually with an additional $1,000 contribution allowed for those 50 and older. You want to know how much you will have when you plan to retire at age 60, which is 20 years away. You assume that your investments will earn a rate of 7% annually. *

Based on these assumptions, you will have $256,042 if you begin your traditional IRA savings immediately (beginning of year calulation) and $239,292 if you begin to save at the end of the year. This is a good chunk of money that can help supplement your other retirement plans and social security, which we’ll be talking about in-depth in the future.

**PAYMENTS USING FUTURE VALUE **

A basic future value situation assumes that you have a **specific amount in the future that you want to achieve through regular, consistent investments**. This will probably be one of your most used time value of money calculations. Basically, this will be used when you have a long-term financial goal and want to know how much you need to contribute each year (or month) to meet that end goal. For this calculation you will need the following inputs:

- Future value amount that you want to achieve (your goal)
- Present value amount (the amount that you already currently have toward this goal)
- Whether you will be investing at the beginning or end of the year
- Length of time (years) that you’ll be investing the money
- Interest rate

*Assume this example: You have a long-term goal of accumulating $100,000 in your HSA account to cover a portion of your post-retirement health care costs. You will be retiring in 20 years and currently do not have anything invested, but plan to start this year. You assume that your investments will earn 7% per year. You want to know how much you need to invest over the next 20 years to be able to have that total amount of $100,000 saved.*

Based on these assumptions, you will need a monthly contribution of $191 or $2,280 annually if you start contributing immediately (beginning of the year). If you start your contributions at the end of the month or year, you will need $192 per month or $2,439 per year to meet the $100,000 goal. Just think of how happy you are going to be to have that money (wink, wink!). Also, are you starting to see the benefit of investing immediately?

**PRESENT VALUE OF A SUM**

On the opposite side of the time value of money calculation are the present value calculations. The most simple form of this is** calculating the present (current) value of one sum of money to be received in the future**. For this calculation, you need the following inputs:

- Future sum amount
- Length of time before you receive the money
- Interest rate

*Assume this example: You are expecting that your roof will need to be replaced in 5 years and want to set aside the money today. It will cost $15,000 and you expect to earn an annual return of 5% since you will be investing in less risky investments due to the relatively short time period. How much would you need to set aside today to meet that goal?*

Based on these assumptions, you will need to set aside $11,753 today in investments earning 5% to have the $15,000 in cash that you need to replace your roof. That sounds like a significance difference from the $15,000, but that’s the benefit of investing.

**PRESENT VALUE OF A STREAM OF CASH FLOWS (Net Present Value)**

The most complicated present value calculation to understand, but one that is especially useful and vital for investing is the **present value of a stream of cash flows**. This is usually referred to as “**net present value**” or NPV. This time value of money calculation shows how much the cash inflows and outflows would be worth today at a certain rate of return. For this calculation, you need the following inputs:

- Whether you will be investing at the beginning or end of the year (generally this calculation is based on end of year)
- Initial investment and cash inflows and outflows for each year
- Length of time that you’ll be investing the money (years in this situation)
- Interest rate

*Assume this example: You are interested in investing in a rental property and want to know how much of a monetary return you will receive in the next 15 years from the investment in today’s dollars. You assume a 7% required rate of return and an annual net cash flow of $2,500 for the first 5 years, -$5,000 for the 6 ^{th} year due to expected improvements and then $3,000 for the remaining 9 years. The initial investment will be $20,000.*

Based on these assumptions the net present value of the investment is -$57. Because this number is negative, it means that this investment will have less value than a 7% rate of return. If the investment was positive, it would mean that it returned more than 7% on the investment. Note that the actual cash inflows will be $14,500, but when they are computed to present value they are not worth nearly as much due to the time factor.

A related concept to the NPV (net present value) is the IRR or internal rate of return on the investment. The **internal rate of return** is calculated at the bottom as the actual return that the investment is getting over the period of time. In this case, it is 6.96% which is consistent with the previous explanation that the net present value is slightly negative. This signifies that the real estate investment was earning slightly less than 7% return.

**PAYMENTS USING PRESENT VALUE (A LOAN)**

If you take out a loan, your payment will be calculated using present value calculations. This calculation is used for loans and is used to calculate the **annual or monthly payment required based on giving up an amount now for future payments with interest**. The current value will be the amount you’re financing and the future value at the end of the loan term will be zero, which signifies that you have completely paid off the loan. For this calculation, you need the following inputs:

- Current lump sum being financed
- Length of time (years) for the financing
- Interest rate

*Assume this example: You purchase a car for $22,000 and finance $20,000 of it through a 60-month vehicle loan with a 3.8% interest rate. You want to know what your monthly payment will be for the vehicle.*

Based on these assumptions you would have a monthly payment of $367. Most loan payments that you will use will be on a monthly payment basis, so you should generally ignore the annual payment option for your personal loan calculations.

As another note about loan calculation, a detailed schedule that shows the breakdown of principal and interest is called a loan amortization table. We discussed it in the class DM102: Debt Reduction This schedule will allow you to see the impact of making additional principal payments in addition to your required monthly payments to see how much more quickly you can pay off your loan.

**SUMMARY**

Time value of money is an essential concept to master before learning more about investing. The main takeaways are that:

- Money invested grows in an exponential, not a linear fashion.
- The rate of return makes a huge difference in the amount you will have in the future
- Time is an enormous factor in building wealth
- Analyzing investments requires a consideration of inflation and opportunity cost even if actual cash inflows exceed outflows

**EXAMPLE: THE SMITH FAMILY**

The Smith family identifies a few financial goals that they would like to analyze using time value of money calculations.

**GOAL #1: Buy a new car for Jim by 12/31/2017 **

First, they’ve determined the cost to be $14,179 already and want to know how much they would need to set aside on a monthly basis to meet this goal. They first need to subtract the cost of their trade-in vehicle, which they estimate will reduce their total amount needed by approximately $4,000. They summarize the following inputs needed for their calculation:

- Type of TVM problem: Payments Based on Future Value
- Future Value: $10,179 ($14,179-4,000)
- Interest Rate: 1.25% (they will save for this short-term investment using an online savings account)
- Time Period: 24 months

As shown, they would need to save $419 every month to be able to pay cash for the vehicle.

**GOAL #1 Update: What would the monthly payment be if they financed the car instead with $1,000 down?**

In addition, they want to analyze the monthly payment that would be required if they prioritized other goals ahead of the auto payment (especially with regards to paying down their high-interest-rate debt). The payment calculation would include the following inputs:

- Type of TVM problem: Payments Based on Present Value
- Present Value: $9,179 (assuming they pay $1,000 down and all taxes, fees, etc. in cash)
- Interest Rate: 3.75%
- Time Period: 60 months

If they financed their vehicle based on the previously shown terms, they would have a monthly loan payment of $168.

**GOAL #2: Retire by age 55 with $1 million.**

- Type of TVM problem: Payments Based on Future Value
- Future Value: $1,000,000
- Present Value: $24,632 (current amount saved in 401k)
- Interest Rate: 7%
- Time Period: 23 years

If they want to retire by age 55 with a million dollars, they would need approximately $1,286 per month including all contributions from both Jim and his employer. This is a lofty goal and they would definitely need to find a way to increase their income significantly to be able to come anywhere close to meeting this goal.

**GOAL #2 Update: Retire by age 65 instead of 55 with $1 million.**

If they instead changed the goal to retiring 10 years later at a more traditional age of 65, the monthly requirement would go down to $488 per month.

**GOAL #3: Fund college savings accounts for kids in the amount of $100,000.**

This goal will be split up between two separate calculations, one for each child. To simplify, we’ll assume that each child will receive $50,000 for college funding and that sum should be available at the beginning of the first year that they begin college. The following inputs are needed:

- Type of TVM Calculation: Payments Based on Future Value
- Future Value: $50,000/$50,000
- Present Value: $0
- Interest Rate: 7%
- Time Period: 13 years/16 years

The payments for both children are shown above. Child #1 (Emma) would need $197 per month to meet the goal and Child #2 (Jacob) would need $142 per month to be able to meet the goal. Again, this is a significant payment that would require the Smith family to significantly increase their income. In addition, they need to put their retirement goal ahead of this goal, as they can get help funding college, but will not be able to take out a loan to fund their retirement.

After breaking down these goals to monthly requirements, they now know exactly what it will take to achieve them and can find ways to adjust their lifestyle to work toward them and/or adjust them as needed.

**HOMEWORK ASSIGNMENT**

Your homework assignment is to analyze your financial goals using time value of money calculations.

**IMPROVING**– Pick your most important financial goal (may I suggest retirement?) and use the future value payment calculation spreadsheet to calculate how much you need to save on a monthly basis to reach that goal.**INVESTED**– Choose several of your financial goals to analyze as above.**UNSTOPPABLE**– Spend the time to analyze each possible financial goal that you have that uses time value of money calculations such as retirement, education planning, future home and auto purchases, vacation planning, etc. Revise your financial goals to reflect the information you receive from these calculations.

File your financial goal analysis in your Financial Plan binder under the tab “Financial Goals” and/or under the specific tabs relating to that goal. For example, retirement calculations should be filed under “Retirement” and college saving calculations should be filed under “Special Topics-College.”

**HANDOUT: Time Value of Money Scenarios**

I came up with some additional examples for each time value of money calculation type. This should help you when you are looking through your financial goals and need to know which spreadsheet to use to get the information you need. Click on the preview below to download.

*Have you used present and future value calculations before to make a plan to reach your financial goals?*

*Have you used present and future value calculations before to make a plan to reach your financial goals?*

[…] Time value of money calculations come into play here, especially including the expected market rate that you hope to earn in your investments and inflation. In addition, I’ve factored in taxes in both scenarios (if you’ve been around here long enough you know that I focus a lot on taxes!). […]