Basic Concepts of Finance: Cashflows and Discounting
We are starting with some of the most important concepts in finance: cash flows and discounting. These, along with a few other tools we will introduce later, are essential in understanding personal finance, investment, planning, banking, insurance or any other advanced topics. In fact, these concepts come up repetitively, so understanding the basics will better position you for the future.
Cash Flows
Cash flow is the movement of money - for example, the payments you make for your Netflix subscription or the salary you get from your employer. Cash flow can be regular, like monthly paychecks, or irregular, like earnings from online sales.
In finance, cash flows also include regular payments made to policyholders, such as regular annuity ( or structured settlements ) payments under and insurance contract to a policyholder claiming disability, or regular bond coupon on a fixed income investment.
Here is an example of an annuity paying $ 100 yearly at the start of each year for the next 10 years.
| Installments | Date of payment | Annual Installment | Cumulative Amount Paid |
|---|---|---|---|
| Column number: (0) | (1) | (2) | (3) |
| 1 | 1/1/2025 | $ 100 | $ 100 |
| 2 | 1/1/2026 | $ 100 | $ 200 |
| 3 | 1/1/2027 | $ 100 | $ 300 |
| 4 | 1/1/2028 | $ 100 | $ 400 |
| 5 | 1/1/2029 | $ 100 | $ 500 |
| 6 | 1/1/2030 | $ 100 | $ 600 |
| 7 | 1/1/2031 | $ 100 | $ 700 |
| 8 | 1/1/2032 | $ 100 | $ 800 |
| 9 | 1/1/2033 | $ 100 | $ 900 |
| 10 | 1/1/2034 | $ 100 | $ 1 000 |
In total $1,000.
Discounting
Now let's explore time value of money using 2% annual rate of return. How should we adjust our schedule?
Let's look at this from another angle. Assume you invest $ 100 on January 1st, 2025 at a 2% interest. Ignore taxes and transaction costs.
- After one year, on January 1st, 2026, your investment would be worth $ 102. That is $ 100 * ( 1 + 2% ).
- After two years, on January 1st, 2027, it would earn another 2%. This time $ 100 * ( 1 + 2% ) * ( 1 + 2% ).
- After three years, on January 1st, 2028, it would be $ 100 * ( 1 + 2% ) * ( 1 + 2% ).* ( 1 + 2% ).
The cash flow schedule would be updated as below.
| Installments | Date of payment | Annual Installment | Cumulative Amount Paid | $ 100 invested on 1/1/2025 at 2% annual interest |
|---|---|---|---|---|
| (0) | (1) | (2) | (3) | (4) |
| 1 | 1/1/2025 | $ 100 | $ 100 | $ 100.00 |
| 2 | 1/1/2026 | $ 100 | $ 200 | $ 102.00 |
| 3 | 1/1/2027 | $ 100 | $ 300 | $ 104.04 |
| 4 | 1/1/2028 | $ 100 | $ 400 | $ 106.12 |
| 5 | 1/1/2029 | $ 100 | $ 500 | $ 108.24 |
| 6 | 1/1/2030 | $ 100 | $ 600 | $ 110,41 |
| 7 | 1/1/2031 | $ 100 | $ 700 | $ 112,62 |
| 8 | 1/1/2032 | $ 100 | $ 800 | $ 114,87 |
| 9 | 1/1/2033 | $ 100 | $ 900 | $ 117,17 |
| 10 | 1/1/2034 | $ 100 | $ 1 000 | $ 119,51 |
Comparing columns (2) and (4) above, shows the effect investment has on our money. The deal however is to pay our policyholder $ 100 each year and not the higher amounts from column (4). Also, the total amount we will pay out is $ 1,000 so we need more than $ 100.
The trick would be to structure our cash flows in a way that generates $ 100 every year on January 1st for the next 10 years, but no more.
Year 1 is straightforward. We pay $ 100 on January 1st, 2025 so all that is needed is $ 100.
Year 2 is slightly more comples. We need to generate $ 100 on January 1st, 2026. Another words, investing enough so that the principal (amount invested) plus interest earned will amount to $ 100. That would be $ x * ( 1 + 2% ) = $ 100. Solving for $ x would give $ 98.04.
Every subsequent year would follow the same principle, resulting in a schedule such as the one below.
| Value on 1/1/2025 | $ 100.00 | $ 98.04 | $ 96.12 | $ 94.23 | $ 92.38 | $ 90.57 | $ 88.80 | $ 87.06 | $ 85.35 | $ 83.68 |
|---|---|---|---|---|---|---|---|---|---|---|
| 1/1/2026 | $ 100 on 1/1/2026 | |||||||||
| 1/1/2027 | $ 100 on 1/1/2027 | |||||||||
| 1/1/2029 | $ 100 on 1/1/2028 | |||||||||
| 1/1/2029 | $ 100 on 1/1/2029 | |||||||||
| 1/1/2030 | $ 100 on 1/1/2030 | |||||||||
| 1/1/2031 | $ 100 on 1/1/2031 | |||||||||
| 1/1/2032 | $ 100 on 1/1/2032 | |||||||||
| 1/1/2033 | $ 100 on 1/1/2033 | |||||||||
| 1/1/2034 | $ 100 on 1/1/2034 |
In practice, however, we would set aside one large amount and draw from it as needed. In the example above, the sum of all the values in the first row would add up to $ 916.22. We call this the "present value." That amount would allow for withdrawals to meet the $ 100 payment each year, while still generating enough to continue those payments for the full ten years.
| Installments | Date of payment | Amount of money in the pot before drawdown | Payment | Amount of money in the pot after drawdown |
|---|---|---|---|---|
| (0) | (1) | (3) | (2) | (4) |
| 1 | 1/1/2025 | $ 916.22 | $ 100 | $ 816.22 |
| 2 | 1/1/2026 | $ 832.55 | $ 100 | $ 732.55 |
| 3 | 1/1/2027 | $ 747.20 | $ 100 | $ 647.20 |
| 4 | 1/1/2028 | $ 660.14 | $ 100 | $ 560.14 |
| 5 | 1/1/2029 | $ 571.35 | $ 100 | $ 471.35 |
| 6 | 1/1/2030 | $ 480.77 | $ 100 | $ 380.77 |
| 7 | 1/1/2031 | $ 388.39 | $ 100 | $ 288.39 |
| 8 | 1/1/2032 | $ 294.16 | $ 100 | $ 194.16 |
| 9 | 1/1/2033 | $ 198.04 | $ 100 | $ 98.04 |
| 10 | 1/1/2034 | $ 100.00 | $ 100 | $ 0.00 |
What happens in the schedule above is the following:
- we start with $ 916.22 present value on January 1st, 2025.
- then withdraw $ 100 to make the first payment. This leaves us with $ 816.22.
- $ 816.22 earns 2% interest and on January 1st, 2026 it is worth $ 832.55.
- we withdraw $ 100 to make the second payment. This leaves $ $ 732.55.
- $ 732.55 earns interest and increases to $ 747.20 on January 1st, 2027.
- the schedule continues in similar fashion.
And there you have it—a peek into the fascinating world of finance. Want to dive deeper? Try calculating different scenarios or see how changes in interest rates affect the present value. You can use this for all sorts of scenarios - your future university financing, your childern’s investments, gap year planning etc. Possibilities are endless.
It's all about understanding the numbers to make smart financial choices!
Until next time !
M | K