The valuation of financial instruments, including shares, bonds, investment funds and financial derivatives, is the central technique that needs to be understood by financial professionals. The quantitative foundation of this process is the concept named ‘time value of money’. According to Melicher & Norton (2017, p. 219), time value of money is “the mathematics of finance whereby a financial return (for example, interest) is earned over time by saving or investing money”. Higher risk-taking behaviour is required to achieve a higher return in the market. The capital could be invested at any time to earn at least a risk-free interest rate. Therefore, the time value of the money should include any alternative investing opportunity cost in the open market. This is the financial reason why today’s one dollar ($1) would be worth more than the same one dollar ($1) in the future.
Welcome to Topic 5: Time Value of Money. In this topic, you will learn about:
- Time value of money in finance
- The effect of interest on the future value
- The effect of discounts on the present value
- Annuity.
These relate to the Subject Learning Outcomes:
- Understand the role of the finance and accounting functions in an organisation.
- Apply mathematics of finance to determine risk, return, evaluation of investment, financing, working capital and distribution decisions.
- Develop analytical skills drawing from key finance theories, concepts, and techniques.
Welcome to your pre-seminar learning tasks for this week. Please ensure you complete these prior to attending your scheduled seminar with your lecturer.
Click on each of the following headings to read more about what is required for each of your pre-seminar learning tasks.
Read Chapter 9 of the prescribed text - Melicher, RW & Norton, EA 2017, Introduction to finance: Markets, investments, and financial management, 16th edn., John Wiley & Sons, Inc.
Read the following journal articles:
- Sharpe, WF 1964, 'Capital asset prices: A theory of market equilibrium under conditions of risk', The Journal of Finance, 19(3):425-442.
- Lewin, P & Cachanosky, N 2015, 'The time-value of money and the money-value of time: Duration, roundaboutness, productivity and time-preference in finance and economics', SSRN Electronic Journal.
Identify the key takeouts and add these to your reflective journal. You can access the reflective journal by clicking on ‘Journal’ in the navigation bar for this subject. If you are unsure of any concepts, reach out to your lecturer.
Read the following web articles:
- Fernando, J 2021, Time value of money (TVM), Investopedia
- Myers, D 2021, Time value of money: Determining your future worth, Investopedia
- Pritchard, J 2022, What is compound interest?, Investopedia
- Elkins, K 2020, This simple formula tells you how long it will take for your money to double—while you sit back and relax, CNBC
Identify the key takeouts and add these to your reflective journal. If you are unsure of any concepts, reach out to your lecturer.
Read the case study, Inflation or Purchasing Power Implications, on p. 225 of the prescribed text.
Then consider Discussion question 1 on p.225. Make a note of your answers in your reflective journal and be ready to share your reflections with the class discussion during the scheduled seminar.
This topic has a discussion forum activity, which will enhance your knowledge and give you the opportunity to interact with your peers. You can access the activity by clicking on the following link. You can also navigate to the forum by clicking on 'FIN100 Subject Forum' in the navigation bar for this subject.
Read and watch the following content.
Time value of money in finance
Any money available today could be invested in different ways in the market to generate returns. For this reason, one dollar today is always worth more than one dollar in the future. There is a cost for inaction and not investing, and this is the opportunity cost. From the perspective of opportunity cost, the financial decision-makers need to understand the importance of the time value of money concept.
Cash that comes in the future is worth less than the cash that firms spend upfront, managers need a set of tools to help them compare cash inflows and outflows that occur at different times.(Gitman & Zutter 2012 p. 161.)
Managers across all industries must comprehend the role of time value in finance. For example, a hotel manager could be presented with an opportunity to earn greater returns through an attractive project or in interest-bearing securities or deposits. They may ask themselves questions such as, “Is it worth renovating our hotel rooms if it is only going to increase our occupancy by 20 %?”, “Should we extend our restaurant, or should we invest the hotel's excess cash into market securities?”.
Time value of money is based on the belief that a dollar today is worth more to an individual or business than a dollar received in the future. How do you think this premise would affect a hotel manager and their operations?
Future value versus present value
Future value is the value of a future outcome of a current investment at a consistent compound interest rate. Whereas present value is today’s value of a future sum discounted back at a consistent compound interest rate. In simple terms, the future value is how much you can buy with AUD 100 in five (5) years, while present value is how much AUD 100 buys today.
Learning Task
Read the article Present Value vs Future Value by Thakur & Vaidya (n.d.) and pay particular attention to the Present Value vs Future Value – Infographics, which summarises the seven (7) key differences between present value and future value.
The effect of interest on future value
The future value is affected by the amount and type of interest applied:
- Simple interest
- Compound interest.
Future value with simple interest
Interest is the amount of money you pay as a borrowing fee. With simple interest, you only multiply the agreed interest rate with the principal amount owed or invested to calculate the interest for the period.
As an example, AUD 1 000 invested at 10 % per annum for three (3) years will give you AUD 100 interest at the end of every year:
- Year 1: AUD 1 000 × 10 % = AUD 100
- Year 2: AUD 1 000 × 10 % = AUD 100
- Year 3: AUD 1 000 × 10 % = AUD 100
Calculating the future value with simple interest requires the following formula:
$$\mathsf{Future \; value} = \mathsf{present \; value} \; [1 + (\mathsf{interest \; rate} × \mathsf{number \; of \; years})]$$
For example, if you invest $1 000 (present value) for the next five (5) years with an interest rate of 10 %, the future value would be:
$$ \begin{aligned}\mathsf{FV} &= 1\,000 \;[1 + (0.10 \times 5)] \\ &= 1\,000 \times 1.5 \\ &= $1\,500\end{aligned} $$
Future value with compound interest
Compounded interest adds the previous period’s portion of interest to the principal amount borrowed or invested prior to calculating the current period interest. As a result, the principal amount increases at the end of every period.
Suppose you invested AUD 1 000 at 10 % per annum for three (3) years, the interest earned will increase every year as follows:
- Year 1: AUD 1 000 × 10 % = AUD 100
- Year 2: AUD 1 100 × 10 % = AUD 110
- Year 3: AUD 1 210 × 10 % = AUD 121
“Future value with compounded interest needs to account for exponential growth (since interest collects on interest)” (McCamish 2020). The following formula is used to calculated future value with compound interest:
$$\mathsf{Future \; value} = \mathsf{present \; value} \; (1 + \mathsf{annual\;interest \; rate})^{ \mathsf{number \; of \; periods}}$$
Using the same parameters as the previous example, if you invest $1 000 today (present value) for five (5) years with an interest rate of 10 % and let the interest compound annually, the future value of the investment at the end of five years would be:
$$ \begin{aligned}\mathsf{FV} &= 1\,000\;(1 + 0.10)^{5} \\ &= 1\,000 \times 1.61051 \\ &=$1\,610.51\end{aligned} $$
As you can see in the following figure, the difference between the present and future value of money depends on the interest rates and the time period. However, if there is no interest (zero interest) involved, both present and future values remain constant.
The effect of discounts on present value
The present value is affected by the type of discount applied:
- Once-a-year discount
- Compounding discount.
Present value with once-a-year discounted rate
Like simple interest, when discounting a future value into a present value, the once-a-year discount rate applies to the same future value on a yearly basis.
The following formula is used to calculate the present value with a once-a-year discount:
$$ \mathsf{Present\;value} = \frac{\mathsf{future\;cash\;flow}}{(1 + \,\mathsf{discounted\;rate})^{\mathsf{number\,of\,years}}} $$
For example, if you are eligible to be paid $1 000, starting one (1) year from today, for the next four (4) years with a discount rate of 4 %, the sum of the present value of that money today would be:
$$\begin{aligned} \mathsf{PV}_1&= \frac{1\,000}{(1+0.04)^1} = $961.54 \\ &\\ \mathsf{PV}_2&= \frac{1\,000}{(1+0.04)^2} = $924.56 \\&\\ \mathsf{PV}_3&= \frac{1\,000}{(1+0.04)^3} = $889.00 \\&\\ \mathsf{PV}_4&= \frac{1\,000}{(1+0.04)^4} = $854.80 \\ &\\ \mathsf{PV} &= \mathsf{PV}_1+\mathsf{PV}_2+\mathsf{PV}_3+\mathsf{PV}_4\\ \\&=$3\,629.90 \end{aligned}$$
Present value with multiple compoundings for a year
When discounting a future value into a present value using a compounding discount, the discount rate will multiply according to the discounting frequency or the number of compounding periods.
The following formula is used to calculated present value with a compounding discount:
$$\mathsf{Present\;value} = \frac{\mathsf{future\;cash\;flow}}{(1 + \frac{\mathsf{discounted\;rate}}{\mathsf{compounding\;periods}})^{(\mathsf{number\;of\;years}\,\times\,\mathsf{compounding\;periods})}}$$
For example, if you wanted to save $3 000 by the end of four (4) years with half-yearly discount rate of 5 %, what would be the present value that you have to set aside today?
$$\begin{aligned}\mathsf{PV} &= \frac{3\,000}{(1 + \frac{0.05}{2})^{(4\times2)}} \\&\\ &=\frac{3\,000}{(1 + 0.025)^{8}}\\&\\ &=\frac{3\,000}{1.218402898}\\&\\&=$2\,462.24\end{aligned}$$
The following figure shows the difference between present value of one dollar and its future value, depending on the interest rates and the time period given. However, if there is no interest (zero interest) involved, both present and future values remain constant.
Annuity
An annuity is a sequence of equal payments or receipts, which are setup to arise within a set time frame.
Future value of annuity
Future value of annuity refers to the sum of the payment sequences at a future date. There are two (2) types of future value of annuity, calculated depending on when the payment occurs within the time period (Thakur n.d.):
- Future value of the ordinary annuity
- Future value of an annuity due.
Future value of the ordinary annuity
If the payment occurs at the end of the period, it will be considered as ordinary annuity. The future value of the ordinary annuity is calculated according to the following formula:
$$\mathsf{FVA\;ordinary}=\mathsf{P} \times \frac{[(1+i)^n – 1]}{i}$$
Where:
- P = periodic payment
- n = number of periods
- i = effective rate of interest.
Future value of an annuity due
If the payment occurs at the beginning of the period, it is considered as annuity due. The future value of an annuity due is calculated according to the following formula:
$$\mathsf{FVA\;due}=\mathsf{P} \times [(1+i)^n - 1]\times \frac{(1+i)}{i}$$
Where:
- P = periodic payment
- n = number of periods
- i = effective rate of interest.
Present value of annuity
Present value of annuity is today’s value of a future payment required. The formula to calculate the present value of annuity is as follows:
$$\mathsf{P}=\mathsf{PMT} \times \frac{1- (\frac{1}{(1+r)^{n}})}{r}$$
Where:
- P = Present value of your annuity stream
- PMT = Dollar amount of each payment
- r = Discount or interest rate
- n = Number of periods in which payments will be made.
Determining periodic annuity payments, interest rates and time requirements for annuities
To determine either the future or present value of annuity, interest rate or time requirements for annuities, you need to select the correct formula and know the values of the other variables. These variables include:
- PV = present value
- FV = future value
- r = interest rate
- n = number of periods
- PMT = periodic payments.
Key takeouts
Congratulations, we made it to the end of the fifth topic! Some key takeouts from Topic 5:
- It is important to understand the time value of money because one dollar ($1) today is worth more than one dollar ($1) tomorrow.
- Opportunity cost is the key concept behind time value of money.
- Annuity is a sequence of equal payments or receipts, which are set up to arise within a set period.
- To calculate the present value or future value, all other variables need to be aligned into the same time period (for example, monthly, quarterly or semi-annually).
Welcome to your seminar for this topic. Your lecturer will start a video stream during your scheduled class time. You can access your scheduled class by clicking on ‘Live Sessions’ found within your navigation bar and locating the relevant day/class or by clicking on the following link and then clicking 'Join' to enter the class.
Click here to access your seminar.
The following learning tasks will be completed during the seminar with your lecturer. Should you be unable to attend, you will be able to watch the recording, which can be found via the following link or by navigating to the class through ‘Live Sessions’ via your navigation bar.
Click here to access the recording. (Please note: this will be available shortly after the live session has ended.)
In-seminar learning tasks
The in-seminar learning tasks identified below will be completed during the scheduled seminar. Your lecturer will guide you through these tasks. Click on each of the following headings to read more about the requirements for each of your in-seminar learning tasks.
Watch the video, What is Time Value of Money – Time Value of Money Formula from Learn to Invest (2018), to help your understanding of why time value of money is important to an organisation. The video focusses on several examples to clarify how the calculations are done. These will be discussed during the seminar.
Working in a breakout room team assigned by your lecturer during the scheduled seminar, discuss the following concepts with your teammates. Your lecturer will request that you present the findings back to the class.
- Simple interest and the compounding interest
- Opportunity cost
- Discount rate versus interest rate.
- Working in the same breakout room as previously, visit the Climax Business Valuations website and learn about what they do.
- Share and discuss your findings with your teammates. Use the following questions to guide your discussion:
- Why are business valuations needed?
- Briefly explain the quantitative and qualitative facts that can be used in a business valuation.
- What can you do to increase your business valuation?
Welcome to your post-seminar learning tasks for this week. Please ensure you complete these after attending your scheduled seminar with your lecturer. Your lecturer will advise you if any of these are to be completed during your consultation session. Click on each of the following headings to read more about the requirements for each of your post-seminar learning tasks.
Knowledge check
Complete the following three (3) tasks. The following questions have been adapted from p. 229 of Melicher, RW & Norton, EA 2017, Introduction to finance: Markets, investments, and financial management, 16th edn., John Wiley & Sons, Inc.
Click the arrows to navigate between the tasks.
The following question has been taken from page 245 of Melicher, RW & Norton, EA 2017, Introduction to finance: Markets, investments, and financial management, 16th edn., John Wiley & Sons, Inc.
Identify the Rule of 72 and how can it be used to determine how long it will take for an investment to double in value?
Add your answers to your reflective journal.
Knowledge check
Complete the following three (3) tasks. The following questions have been adapted from page 244 of Melicher, RW & Norton, EA 2017, Introduction to finance: Markets, investments, and financial management, 16th edn., John Wiley & Sons, Inc.
Click the arrows to navigate between the tasks.
Complete the following calculations in your reflective journal.
Part A: Review the table
You have three (3) type of repayment options at end of every year, as shown in the following table:
| Investment types | |||
|---|---|---|---|
| Year | A | B | C |
| 1 | $50 000 | $30 000 | $10 000 |
| 2 | $40 000 | $30 000 | $20 000 |
| 3 | $30 000 | $30 000 | $30 000 |
| 4 | $20 000 | $30 000 | $40 000 |
| 5 | $10 000 | $30 000 | $50 000 |
| Totals | $150 000 | $150 000 | $150 000 |
Part B: Present value
In your reflective journal complete the following questions.
- Find the present value of each stream, using a 15 % discount rate.
- If there is a difference in value as shown in the table above:
- explain the reasons for the discrepancy
- identify the stream you would choose to make your repayments
- justify your choice.
Part C: Explanation
In your reflective journal complete the following questions.
- Identify the relationship between discount rate and the present value. Explain your answer using examples.
- Identify the relationship between compounding rate and the future value. Explain your answer using examples.
Please ensure you complete Assessment 2, Quiz 4 by the nominated time and date. You can access this quiz by clicking on “Assessment 2” in the navigation bar for this subject, then selecting “Quiz 4 – Week 5”.
Each week you will have a consultation session, which will be facilitated by your lecturer. You can join in and work with your peers on activities relating to this subject. These session times and activities will be communicated to you by your lecturer each week. Your lecturer will start a video stream during your scheduled class time. You can access your scheduled class by clicking on ‘Live Sessions’ found within your navigation bar and locating the relevant day/class or by clicking on the following link and then clicking 'Join' to enter the class.
Click here to access your consultation session.
Should you be unable to attend, you will be able to watch the recording, which can be found via the following link or by navigating to the class through ‘Live Sessions’ via your navigation bar.
Click here to access the recording. (Please note: this will be available shortly after the live session has ended.)
- Diamond, DW & Dybvig PH 2000, ‘Bank Runs, Deposit Insurance, and Liquidity’, Federal Reserve Bank of Minneapolis Quarterly Review, 24(1):14–23.
- Kerin, J 2021, Buffett vs. Soros: Investment strategies, Investopedia.
- Netflix 2020, Explained | The Stock Market | FULL EPISODE | Netflix, Streaming Video, YouTube
References
- Elkins, K 2020, This simple formula tells you how long it will take for your money to double—while you sit back and relax, CNBC, https://www.cnbc.com/2020/01/28/what-the-rule-of-72-is-and-how-it-works.html
- Gitman, LJ & Zutter, CJ 2012, Principles of managerial finance, 13th edn., Prentice Hall.
- Graham, JR, Smart, SB, Adam, C & Gunasingham, B 2017, Introduction to Corporate Finance, 2nd edn., Cengage Learning.
- Lewin, P & Cachanosky, N 2015, 'The time-value of money and the money-value of time: Duration, roundaboutness, productivity and time-preference in finance and economics', SSRN Electronic Journal, https://www.researchgate.net/publication/314415825_The_Time-Value_of_Money_and_the_Money-Value_of_Time_Duration_Roundaboutness_Productivity_and_Time-Preference_in_Finance_and_Economics
- Melicher, RW & Norton, EA 2017, Introduction to finance: Markets, investments, and financial management, 16th edn., John Wiley & Sons, Inc.
- McCamish, B 2020, Future value (FV), Investing Answers, https://investinganswers.com/dictionary/f/future-value-fv
- Pritchard, J 2022, What is compound interest?, Investopedia, https://www.thebalance.com/compound-interest-4061154
- Sharpe, F 1964, 'Capital asset prices: A theory of market equilibrium under conditions of risk', The Journal of Finance, 19(3):425-442.
- Thakur, M n.d., Future value of an annuity formula, EDUCBA, https://www.educba.com/future-value-of-an-annuity-formula/.
- Thakur, M & Vaidya, D n.d., Present value vs future value, WallStreetMojo, https://www.wallstreetmojo.com/present-value-vs-future-value/
- Vaidya, D n.d., Time vs money, WallStreetMojo, https://www.wallstreetmojo.com/time-vs-money/
