Bank Loans vs. Bonds: Debt Financing in Infrastructure Projects
Debt financing is the most important source of finance for infrastructure projects. In most infrastructure projects, the majority of the project is funded using debt-based financial instruments. Equity holders invest a significantly smaller amount. However, they bear all the risks. The size and scale of debt financing make it an important decision for any company […]
Gold vs. Bitcoin
Gold has always been the alternative asset class. Whenever people lose faith in the value of the stocks that they are holding or even in the value of any currency, they typically sell their holdings and invest the proceeds in gold. However, of late, Bitcoin has burst onto the scene. Gold is no longer the […]
Will The Fiat Money System Collapse?
In 1971, Richard Nixon single-handedly took the world off the gold standard. Ever since, many commentators have been of the opinion that the monetary system of the world will face a complete collapse. These fears get exaggerated every time there is a crisis. For instance, during the 2008 crisis, many people felt that the dollar […]
Disadvantages of Bootstrapping
In the previous article, we have learned about what self-financing i.e. bootstrapping is. We have also learned about what are the various advantages of using the bootstrapping technique. However, despite the advantages listed in the previous article, relatively few startup founders actually go the bootstrapping route. This is because of the fact that bootstrapping also […]
How Ultra Long Term Bonds Work?
In September 2018, Austria became the latest developed country to issue ultra-long-term bonds. As per the deal, Austria raised a total of $4.2 billion which have to be paid back after 100 years! The interest rates on this bond were 2.11%. This deal is being called the largest ever issue of bonds which have a […]
In the articles on present value, we learnt that the value of a dollar today is not the same as it will be 10 years from now. Then, we came across annuities which are a powerful mechanism that ensure that the nominal value of the payments remain the same throughout the years whereas its internal components i.e. interest and principal keep on changing. Annuities, therefore give a very useful way to work with a schedule of payments. There are various types of payment schedules possible while working with an annuity. Here are some of the important types:
Annuities can convert a lump sum payment today into a series of future cash flows which will have the exact same value as of today. This is useful in business because usually the outlays required have to be done immediately in a lump sum whereas the benefits arrive at a later date and they arrive in installments. Annuities therefore enable us to draw a comparison between these values and decide if they are beneficial to us.
Example: Assuming a 12% rate of return for the next 5 years, an annual payment of $27.74 has the same present value as a $100 payment today. So we can choose between making a $100 payment upfront or choose a 5 year annuity of $27.74
The reverse of the above calculation is also true. Annuities help us to take a series of future equal payments that will be made at equal periodic intervals and come up with a lump sum present value that is equal to those payments. This too is very useful. Let’s say that you are scheduled to make mortgage payments for the next 5 years. But instead you choose to pay upfront and close the loan. What is the amount that you should pay to the lender? Annuity calculations will help us come up with that amount.
Example: Assuming a 14% interest rate for the next 5 years and an annual payment of $100, the present value of this stream of payments is $343.31
Now, in the above cases we were converting lump sums into equal payments or equal annuity payments into lump sums. Annuity calculations can be used to arrive at the calculation of the two as well. The payment maybe partially made in equal installments and partially paid in a lump sum. For instance, if you owed the bank $500, you could pay $200 upfront and convert the balance into an annuity.
Annuity calculations allow you to convert any lump sum or stream of cash flows into any other lump sum or stream of cash flows or a combination of both. These calculations form the backbone of finance and it is difficult to imagine the financial world without them.
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