Introduction:
The time value of money is the most important concept in the valuation of assets. Almost all the cash-generating assets are valued using the present value of forecasted cash flows.
The time value of money deals with equivalence relationship between cash flows with different dates. The cash flows at different dates can be compared by comparing their time values at a particular date. That date can be any date. If this date is today, then it is referred to as present value. If it is some future date, then it is referred to as future value.
Suppose you have two options: $100 today or $100 after one year. Which one would you prefer? Obviously, everyone would like to take $100 today than at some future date. Now, suppose the options are $100 today or $200 after one year. Now, most of the people would prefer $200 after one year. There must be one price in the future at which there will not be any preference, and both options will be equally preferable. Or there must be one price in the today's date that would make both the payment equivalent.
Suppose the risk-free rate for one year is 5 percent. Now, $100 invested today for one year will become $105 after one year because we will get $5 (=0.05*100) as interest and $100 as principal at the end of one year. Thus, $105 after one year (if the payment is certain i.e. without any risk) is equivalent to $100 today.
Now, the payment after one year can have some amount of risk as well. For taking that risk, you would want to have an additional return. Suppose you settle for a return of 8 percent (5 percent risk-free rate plus 3 percent risk premium). For this payment, $108 after one year will be equivalent to $100 today.
We can write the equivalence equation between the cash flows at different dates as:
FV = PV(1+r)T or PV = FV(1+r)-T
where:
FV = Future value of the investment
PV = Present value of the investment
r = Periodic interest rate
T = Number of periods
Use of financial calculator:
To solve for the present value, future value, the number of periods, periodic interest rate, or annuity payment, we can take help from the financial calculator as that makes the calculation easier.
CFA Institute allows only two types of financial calculators for the exam - TI BA II PlusTM (including the TI BA II PlusTM Professional) and HP 12C (including the HP 12 C Platinum).
We will discuss the working of TI BA II PlusTM here. However, you are free to use HP 12C as well.
In the third row of the financial calculator, you will find five buttons - N, I/Y, PV, PMT, and FV where:
N - Number of periods
I/Y - Periodic interest rate
PV - Present value
PMT - Annuity (We will discuss it later in this reading)
FV - Future value
In any problem of TVM (time value of money), you will be given 3 out of 4 or 4 out of 5 values, and you will be asked to calculate the 4th or 5th value.
The operation of the calculator is very easy. But you need to feed the inputs in the calculator with appropriate signs. PV and FV have opposite signs. N and I/Y will almost always be positive. PMT can have same or different sign than PV or FV.
The best way to solve the issue is to use positive signs for the inflows and negative signs for the outflows. You can take exact opposite signs as well. But the signs of inflows and outflows has to be different. After choosing the signs, it is very simple to operate the calculator. You just need to press the input value on the calculator and then press the appropriate button, and once all input values are put into the calculator, you need to press CPT and then the missing value.
For example, you are asked to calculate the future value of $100 after two years if the annual discount rate is 6 percent. Then, you need to enter $100 and then press PV. Then press 6 and I/Y. Then press 2 and N. These can be entered into any order i.e. N can be entered before PB and I/Y as well. There is no mention of PMT here. So, you can skip that or can press 0 and PMT. Then press CPT and FV to get the future value.
In the above example, we have taken PV to be positive. So, the answer (the FV) will come with a negative sign. If you had put PV as -$100 then the FV would have come with a positive sign. To put the PV as -$100, we need to press these buttons in the order: 100, +/-, and PV. We will discuss more examples later on and then you will become proficient in the usage of the calculator.
Interest rates: Two things are required to calculate the time value of money: Timing and amount of cash flows and interest rate. Rest everything is simple basic mathematics. We can think of interest rates in three ways: First, required rates of return - the minimum rate of return required by an investor for investment. Second, discount rates - the rate used to discount the cash flows. The terms "discount rate" and "interest rate" are used interchangeably. Third, opportunity cost - the return that an investor forgoes to make this investment. For example, an investor could have deposited money in a bank rather than investing in stock. By investing in the stock, he forgoes the return from the bank and vice versa.
Exam Alert: You don't need to spend too much time here. For the exam, if you find any of above three classifications, then you need to use that as the interest rate for discounting the cash flows.
Next LOS: Components of an interest rate
