Time Value of Money
Complete Guide to Time Value of Money for Australians
One of the most important corner stones of all investments and financial planning pertains to the phenomenon known as the time value of money or TVM for short.
Simply put, “A dollar today is worth more than a dollar in the future.”
When this is explained to people, they’re usually quite baffled as this is an obvious statement to make and hardly some groundbreaking paradigm shift in understanding how money works as it’s almost a universal truth if given the choice the between taking $100 today or $100 a week from now everyone, all things being equal, would take $100 today.
Given this… what makes the concept of time value of money so important?
It’s because this principle underpins many financial decisions and allows us to become more scientific regarding the questions we need to ask before taking a course of action…. chiefly the natural follow up logical extrapolation of this thing goes something along these lines:
“Okay if I don’t get the $100 today and instead get paid in the future... I need to be paid more OR I’ll just take the $100 right away. Either give me $100 right now or let’s negotiate what the amount will be because I’m not taking the same amount of money a week from now. If I’m waiting a full week it needs to be more money or I’ll just take the $100 right now”.
Now that we’ve established this line of thinking we can then ask the following questions:
How much more would need to be offered a week from now to be happy with the deal? i.e $200? $300? And how happy would the person be? Can we calculate an exact amount? (pro tip you can).
How much would need to be offered a week from now to be indifferent with the deal? i.e. $101, $105? Etc? i.e. you couldn’t care less if you got the $100 today or the nominated amount a week from now as the difference is immaterial. Please note the rate of this “indifference” is often referred to as the “risk-free rate” and we’ll circle back to that later.
How much would need to be offered a week from now to be unhappy with the deal? i.e. $100?, $101$, $110? Etc. Obviously if the amount offered a week from now is less then $100 it wouldn’t make any sense to proceed but what if it was only slightly more? Would you be better off taking $100 now or the proposed amount a week later?
Having the capacity to answer these types of questions will require us to have additional information regarding investment goals and alternative investment options but what makes the TVM concept so powerful is it allows us to answer the following types of questions:
If I want to send my kids to semi-private school in 8 years’ time and the total tuition cost is $15K per annum over a 6 year period and the bank is offering me 5% on my savings account and inflation is 2.5% (annualised) how much do I need to save per month?
If I have a $610,000 mortgage at an interest rate of 6.9% over a 30 year term paid monthly how much does each repayment reduce the actual debt by? What’s the impact if I increase the frequency or payment amounts?
If my lifestyle cots $5,000 a month and I plan to retire in 30 years’ time how much do I need in investments given inflation is at 3.5%? how much would I need to save per week given a fixed rate or return OR what rate of return would I need given a fixed amount of weekly investments?
These are just very high level examples of the types of problems that we’ll teach you how to solve! You’ll never have to guess and say “ohh I don’t know I guess around x per week sounds right” ever again….you’ll be armed with the knowledge licensed professionals have to answer these questions correctly!
Let's get started.
"Wait?! There's Maths?! That was not on the brochure!"
The first thing to call out is please don’t be alarmed or have panic attacks based on the examples listed above……having lots of numbers all doing different things simultaneously and it can be very overwhelming.
The point of this article isn’t to increase your numerical skills but to provide you with an appreciation of the tools available to solve these types of questions.
If you can understand what each number is effectively “doing” within the problem you’re trying to solve you can then use any of the amazing online calculators to try and solve the problem for you…..or just give us a call! Let’s see what we can do to help 😊
With all that being said….what are the main bits of information we’ll need to solve these types of questions? Let’s look at them below:
Okay what information is needed?
Depending on the exact question you’re trying to solve you’ll most likely have most, but not all, the information required to solve the problem already which are shown below in their finance jargon and we’ve then explained as a concept:
Please note in order to get more information on the underlying concepts please click on the related articles which go into much more detail and provide clearly worked examples.
This article is designed to explain the high level concepts only as shown below:
Present Value
Future Value
Rate of Return / Risk Free Rate
Number of Periods
Present Value
The technical definition of Present Value (or PV for short) is “the amount of money today that is equivalent to a specified amount in the future after accounting for the time value of money”…yikes……. what does that mean?!
It’s trying to say given a future amount and interest rates how much would you have today? For example if you were promised $1,000 a year from now and you could earn 5% per annum how much would it be worth today?
Would it be $800? $1200? Somewhere in between? Please click on the link below to find out more information regarding this concept including how to use it and how to calculate it correctly.
Future Value
The technical definition of Future Value is “the value of a current sum of money at a specified date in the future given a certain rate of return over time”. This concept is effectively saying how much will I end up with for my investment and is a concept most people are familiar with.
For example, If I invest $1,000 for a year at an interest rate of 5% per annum how much would my investment be worth in a year?
This is an easy example but it can get more complicated when additional curve balls are thrown in i.e. you invest $1,000 for a year at 5% but the 5% income is paid every month or daily…how would that change the overall calculations? Would you be better or worse off?
Please click on the link below to get a full breakdown on how future value works.
Why Does Time Value of Money Matter?
The core idea of TVM is that money available today can be invested to earn interest or returns, making it more valuable than the same amount received later. This is due to several factors:
Earning Potential: Money today can be invested in interest-bearing accounts, stocks, or other assets that grow over time.
Inflation: Over time, inflation erodes the purchasing power of money, meaning a dollar in the future will buy less than it does today.
Risk and Uncertainty: Future payments carry risks, such as default or economic changes, which reduce their present value.
Opportunity Cost: Holding money now provides opportunities to use it, whereas waiting limits those options.
For example, if you have $1,000 today and can invest it at a 5% annual interest rate, it will grow to $1,050 in one year. Conversely, receiving $1,000 a year from now is less valuable because you miss out on that $50 in earnings. TVM helps quantify this difference, guiding decisions about saving, investing, and spending.
Key Components of Time Value of Money
To apply TVM, you need to understand its key components:
Present Value (PV): The current worth of a future sum of money, discounted at a specific rate.
Future Value (FV): The value of a current sum of money at a future date, assuming a certain rate of return.
Interest Rate (r): The rate of return or cost of borrowing, often expressed as an annual percentage.
Time (t): The duration over which money is invested or borrowed, typically measured in years.
Compounding Frequency (n): How often interest is calculated and added to the principal (e.g., annually, semi-annually, monthly).
These components are used in TVM formulas to calculate how money grows or diminishes over time.
Core TVM Formulas
TVM calculations rely on two primary concepts: future value and present value. Below are the basic formulas:
Future Value (FV)
The future value formula calculates how much a sum of money today will be worth after earning interest over time.
FV = PV × (1 + r)^t
FV: Future value
PV: Present value
r: Interest rate per period
t: Number of time periods
For example, if you invest $10,000 at a 6% annual interest rate for 5 years, the future value is:
FV = 10,000 × (1 + 0.06)^5 = 10,000 × 1.338 = $13,380
Present Value (PV)
The present value formula determines how much a future sum is worth today, discounted at a given rate.
PV = FV / (1 + r)^t
Using the previous example, if you expect $13,380 in 5 years and the discount rate is 6%, the present value is:
PV = 13,380 / (1 + 0.06)^5 = 13,380 / 1.338 = $10,000
Compounding and Discounting
When interest is compounded more frequently than once a year, the formula adjusts to:
FV = PV × (1 + r/n)^(n×t)
n: Number of compounding periods per year
For example, $10,000 invested at 6% compounded monthly (n=12) for 5 years:
FV = 10,000 × (1 + 0.06/12)^(12×5) = 10,000 × (1.005)^60 = $13,488.50
This shows that more frequent compounding increases the future value.
Applications of Time Value of Money in Australian Financial Planning
TVM is a versatile tool used in various aspects of financial planning. Here are some common applications:
1. Retirement Planning
TVM helps determine how much you need to save today to achieve your retirement goals. For instance, if you want $1 million in 30 years and expect an 8% annual return, you can calculate the present value to find out how much to invest now:
PV = 1,000,000 / (1 + 0.08)^30 = 1,000,000 / 10.062 = $99,377
This means investing $99,377 today could grow to $1 million in 30 years at 8% interest.
2. Loan and Mortgage Analysis
When borrowing, TVM helps calculate the present value of future loan payments to determine affordability. For a $200,000 mortgage with a 4% interest rate over 30 years, TVM formulas can compute monthly payments and the total interest paid.
3. Investment Evaluation
TVM is critical for comparing investment options. For example, if one investment promises $10,000 in 5 years and another offers $12,000 in 7 years, TVM can help you determine which has a higher present value based on your required rate of return.
4. Budgeting and Savings Goals
TVM aids in setting realistic savings goals. If you want to buy a $50,000 car in 10 years, TVM can tell you how much to save monthly, factoring in expected returns.
Factors Influencing TVM Calculations
Several factors can affect TVM outcomes:
Interest Rates: Higher rates increase future values and decrease present values.
Time Horizon: Longer periods amplify the effects of compounding or discounting.
Inflation: Adjusting for inflation ensures realistic calculations.
Risk: Riskier investments may require a higher discount rate to account for uncertainty.
Practical Tips for Applying TVM in Australian Investing
To make the most of TVM in your financial planning:
Start Early: The earlier you invest, the more time your money has to grow through compounding.
Choose the Right Tools: Use financial calculators or software for complex TVM calculations, especially with frequent compounding.
Consider Inflation: Always factor in inflation to ensure your future money retains its purchasing power.
Review Regularly: Reassess your TVM calculations as interest rates, goals, or time horizons change.
Seek Professional Advice: A financial planner can help tailor TVM-based strategies to your unique circumstances.
Common Misconceptions About TVM
Despite its importance, TVM is often misunderstood. Here are some myths:
Money’s Value is Static: Many assume $1,000 today equals $1,000 tomorrow, ignoring growth potential or inflation.
Only Applies to Investments: TVM is relevant for loans, savings, and even everyday budgeting.
Complex and Inaccessible: While the math can seem daunting, user-friendly tools simplify TVM calculations.
Conclusion
The time value of money is a cornerstone of financial planning, offering a framework to evaluate the worth of money across time. By mastering TVM, you can make smarter decisions about saving, investing, and borrowing, ensuring your financial goals are within reach. Whether planning for retirement, buying a home, or growing your wealth, TVM provides the clarity needed to navigate the financial landscape. Start applying TVM today to unlock the full potential of your money and secure a brighter financial future.
