Session 1: Principles of Time Value of Money and the Discount Rate

There are three ways to compute time value of money problems:

1. The algebraic (or formula) method
2. The financial table method
3. The financial calculator method

Compound Interest Rate
Compound interest results when the interest paid on the investment during the first period is added to the principal sum and during the second period the interest is earned on the original principal sum plus the interest earned during the first period.

Present Value
Present Value is the value in today's dollars of a sum of money to be received in the future, which involves nothing other than inverse compounding. The differences in these techniques come about merely from the investor's point of view.

Present value results when the opportunity cost of having to wait for future consumption is factored into the amount to be received in the future.
Present value reflects the discounting of a sum of money to be received in the future.

Mathematically, the present value of a sum of money to be received in the future can be determined with the following equation:

The present value of a future sum of money is inversely related to both the number of years until the payment will be received and the opportunity rate.

At a positive rate of interest, present value will be less than future value with the difference reflecting the opportunity cost of funds given up.

Future Value
Future value reflects appreciation of a present lump sum over time so as to return to the lender principle plus interest.
Money has future value because resources relinquished today will grow at the real rate lenders require to forego present consumption.

Annuity
An annuity is a series of equal dollar payments for a specified number of years.
A. Ordinary Annuity
This assumes that payments are paid or received at the end of the period.

Note: Both FVIFA and PVIFA tables assume ordinary annuities where payments are paid or received at the end of the period.

B. Annuities Due
Assumes that payments are made/received at the beginning of the period

Note: The number of payments, n, is the same as an ordinary annuity

Perpetuities
A perpetuity is an annuity with an infinite number of payments (PMT)
or
A perpetuity is an annuity that continues forever, that is every year from now on this investment pays the same dollar amount.

Present Value of Uneven Cash Flows (PVUCF)
Note: Unless we can find an "embedded annuity" in a stream of uneven cash flows, each cash flow must be discounted separately in order to obtain the present value. The FVIFA and PVIFA tables assume equal cash flows and will not work. These problems are best handled via calculator or the use of spreadsheets. Just enter the cash flows, the interest rate, and request the present value.

Spreadsheets and the Time Value of Money
While there are several competing spreadsheets, the most popular one is Microsoft Excel. While working with Microsoft Excel, you can easily perform most common financial calculations. Listed below are some of the most common functions in Excel for calculating the elements of an annuity:

Exercises

1. Would you rather have a savings account that pays 5% annual interest rate compounded semi-annually or one that pays 5% annual interest compounded daily? Explain why?
2. Among the telecommunication companies operating in your country two had came up with different investment proposals which you want to evaluate. Both the proposals have the same maturity but the proposal for company A pays a 6% return and that of company B yields 5% per annum. Which investment is preferably riskier? Explain briefly using the time value of money concept.
3. A new mobile operator has just come up with a proposal that its growth rate is 8% if allowed to operate in the country. The regulators think that to be fair, it would offer a license when the sum of the projected returns doubled. How many years of licensing operation are you going to offer to this company?
4. A strategic mobile investment company in US buys a note for US $12,835,000 from a mobile operator in your country. The funds received from the note will enable the local company to make new investments to facilitate the expansion of mobile services in the rural areas. The local company is supposed to make ten equal annual payments to the US based company of US $2,000,000. According to the signed contract, the first payment should be made one year from the date of the receipt of the funds. You are required to calculate the rate of return on the note offered.