In the previous two articles, we discussed the net present value of a series of future cash flows and how various discount factors are used to calculate the net present value. Now, we’ll reverse the calculation method. Let’s say you have an asset worth "X," which represents its cash value. You want to sell this asset, which could be real estate, a business, a car, or anything else. However, the buyer may wish to pay the amount in installments.
In this case, from a financial and economic perspective, the sum of installments should not be the same as the cash amount. So, how can you structure future financial flows whose net present value equals the value you initially set?
The Concept of Amortization
This is where the concept of Amortization (or debt repayment) comes in, along with the amortization schedule. To fairly divide the debt into equal payments over specific periods, it must follow somewhat complex mathematical calculations. Fortunately, there are functions in programs like Excel and calculators available on websites that perform all these calculations for you and generate an amortization schedule based on the following variables:
1. The required net present value (i.e., the cash amount you want to be paid in installments).
2. The required interest rate.
3. The period over which the amount will be paid in installments.
4. The number of installments.
5. The interest compounding rate.
Important Notes About Installment Payments
Although you won't be doing the mathematical calculations yourself, it’s important to understand the following:
- Downpayment: Installment payments often start with a down payment, which does not accrue any interest, and is deducted from the remaining principal amount.
- Installments: The first installment consists of two parts: a portion of the principal after deducting the down payment and the interest accrued on the debt up to the time of the first installment payment.
- Decreasing Interest Over Time: In the second installment, the principal (debt) will have decreased by the amount paid in the first installment. As a result, the interest on the remaining debt will decrease since the outstanding debt has been reduced.
- Gradual Adjustment: Over time, you will notice that although the installments are equal in amount, the interest portion decreases, and the portion applied to the principal increases until the full principal is repaid.
Installment Calculation Formula
When a debt of amount (P) is repaid through equal installments over a total of (n) payments at an interest rate (i), the formula to calculate the installment amount (A) is as follows:
A = (P * i) / [1 – (1 + i)^(–n)]
The interest portion of the first installment is the interest accrued on the full amount to be paid in installments up until the first installment is paid.
Using Online Calculators
You can use online calculators to generate the amortization schedule easily. These calculators allow you to input various variables such as the principal, interest rate, and number of installments to generate the amortization schedule. It’s also a good idea to consult a financial expert before agreeing to any installment plan, to avoid incurring invisible losses. An example of online loan calculator is found in this link:
https://www.calculatorsoup.com/calculators/financial/loan-calculator-advanced.php
Practical Example
For example, let’s say you want to pay $100,000 in installments over seven years, with equal payments made every three months at a 10% interest rate, and the interest is compounded monthly. Using the calculator above, we get the following amortization schedule:
- Number of Installments: 28 installments.
- Installment Amount: $5021.97.
Each installment consists of a portion of the principal and a portion of the interest. Over time, the principal will be fully repaid, reducing the debt to zero, as illustrated in the schedule, which you can download from the calculator.
By understanding these processes, you will be able to plan effectively to installment your dues in a way that ensures you achieve your target cash value without incurring hidden losses.