Question

Identify and record an average person's cash flows. Which cash flows function as annuities or perpetuities? Calculate the present value of each. Then calculate the future value. Which cash flows give you the greatest liquidity or value?

Answer 1

The cash flow statement is about actual money going in and out of your wallet or account. Unlike the income statement, you don’t need to allocate your expenses to specific months, because what you are looking at now is WHEN you spend the money. For example, if Aiman prepays for a 5-month gym membership this month, his cash flow statement would show the complete amount as a cash outflow while his income statement would only show the amount that relates to that specific months as an expense.

This might be a difficult concept to grasp. With the cash flow statement, you always have to think about how it affected your cash balance, while with the income statement you want to show the most reliable picture of your profitability.

Imagine if you would record the whole gym membership payment in the income statement. Your income statement for the first month would show a lower profit than the next 4 months, even though nothing changed in your basic activities. Similarly, if you would record only parts of the payment in your cash flow statement, the statement would no longer show what actually happened to cash.

•An annuity is a finite stream of cash flows received or paid at specified intervals, whereas Perpetuity is sort of Ordinary Annuity which will last forever, into perpetuity.

•An annuity can further be defined in two types i.e. Ordinary Annuity and Annuity Due. An Ordinary Annuity means, payments are required to be made at the end of each period, eg. Plain Vanilla Bonds make their coupon payments at the end of each period till the life of the Bond. Whereas in Annuity Due, payments are required to be paid at the beginning of the period eg. Rent paid in advance for every month until the let out period.

•Due to its stringent time period, Perpetuity is not utilized for many financial assets, as compared to Annuity.

•There are no further types of Perpetuity and Consols i.e. Bonds issued by UK Government which will make the coupon payments till the infinity or stocks paying a constant dividend are the best examples of Perpetuity.

•As an Annuity has a specified time period, it uses the compound interest rate to calculate the future value of a stream of cash flow. It means, while deriving the value of an Annuity, it’s required to compound cash flow and interest rate which is earned every year, till the life of Annuity. Whereas Perpetuity has an infinite time period, it uses simple interest rate or stated interest rate only. The Perpetuity owner will receive a constant amount of cash flow forever.

•One can calculate the present value of Annuity by discounting annuity cash flows and future value of Annuity by compounding annuity cash flows at the specified interest rate. While the future value of Perpetuity is indeterminable due to its perpetual nature of cash flow, its present value can be calculated and which is equal to sum of the discounted value of each periodic cash flow.

•The formula for calculating the present value of Ordinary Annuity, Annuity Due and Perpetuity are as below – •Present Value of Ordinary Annuity = A * [{1 – (1 + r)-n} / r ]

•Present Value of Annuity Due = A * [{1 – (1 + r)-n} / r ] * (1 + r)

•Present Value of Perpetuity = A / r

Where, A = Annuity Amount, r = Interest Rate per Period and n = Number of Payment Periods

the Perpetuity is perpetual Annuity. The only difference between Annuity and Perpetuity is their time period. At a one hand, Annuity has finite set of sequential cash flows and at the other hand, Perpetuity don’t have any specified existence and it’s payment frequency extends indefinitely. While calculating the present value or future value of Annuity, you must have to consider cash flow, cash flow frequencies, interest rate and the time at which the first payment is made i.e. at the beginning of period or at the end of the period. But calculation of perpetuity is quite simple and while calculating the present value of the perpetuity, you only need to consider the cash flow and the stated interest rate

Liquidity is valuable, and the liquidity of an asset affects its value: all things being equal, the more liquid an asset is, the better. This relationship—how the passage of time affects the liquidity of money and thus its value—is commonly referred to as the time value of money, which can actually be calculated concretely as well as understood abstractly.

Suppose you went to Mexico, where the currency is the peso. Coming from the United States, you have a fistful of dollars. When you get there, you are hungry. You see and smell a taco stand and decide to have a taco. Before you can buy the taco, however, you have to get some pesos so that you can pay for it because the right currency is needed to trade in that market. You have wealth (your fistful of dollars), but you don’t have wealth that is liquid. In order to change your dollars into pesos and acquire liquidity, you need to exchange currency. There is a fee to exchange your currency: a transaction cost, which is the cost of simply making the trade. It also takes a bit of time, and you could be doing other things, so it creates an opportunity cost (see Chapter 2 "Basic Ideas of Finance"). There is also the chance that you won’t be able to make the exchange for some reason, or that it will cost more than you thought, so there is a bit of risk involved. Obtaining liquidity for your wealth creates transaction costs, opportunity costs, and risk.

In general, transforming not-so-liquid wealth into liquid wealth creates transaction costs, opportunity costs, and risk, all of which take away from the value of wealth. Liquidity has value because it can be used without any additional costs.

One dimension of difference between not-so-liquid wealth and liquidity is time. Cash flows (CF) in the past are sunk, cash flows in the present are liquid, and cash flows in the future are not yet liquid. You can only make choices with liquid wealth, not with cash that you don’t have yet or that has already been spent. Separated from your liquidity and your choices by time, there is an opportunity cost: if you had liquidity now, you could use it for consumption or investment and benefit from it now. There is also risk, as there is always some uncertainty about the future: whether or not you will actually get your cash flows and just how much they’ll be worth when you do.

The further in the future cash flows are, the farther away you are from your liquidity, the more opportunity cost and risk you have, and the more that takes away from the present value (PV) of your wealth, which is not yet liquid. In other words, time puts distance between you and your liquidity, and that creates costs that take away from value. The more time there is, the larger its effect on the value of wealth.

Financial plans are expected to happen in the future, so financial decisions are based on values some distance away in time. You could be trying to project an amount at some point in the future—perhaps an investment payout or college tuition payment. Or perhaps you are thinking about a series of cash flows that happen over time—for example, annual deposits into and then withdrawals from a retirement account. To really understand the time value of those cash flows, or to compare them in any reasonable way, you have to understand the relationships between the nominal or face values in the future and their equivalent, present values (i.e., what their values would be if they were liquid today). The equivalent present values today will be less than the nominal or face values in the future because that distance over time, that separation from liquidity, costs us by discounting those values