Corporate Finance – Time Value of Money

Subject :- Corporate Finance

Date : 12-Jul-2008

Time Value of Money

Key Principle :- The valuation of money depends on time. A rupee today is worth more than a rupee tomorrow or years to come, the simple reason being the rupee (in hand today) could be used to earn interest if invested today (also factors like Inflation comes to play).

The concept of value of money deals with the elementary concepts covered in Mathematics (8th, 9th Std), of Interest (Simple and Compound). In a real life scenario, simple interest is not used much, as the returns on Simple interest are fractional compared to Compound Interest for a specific period of time.

Hence two key things to consider are 1. Compounded Rate 2. Discounted Rate

Present Value of Money is the Discounted Vaue of Future Value

Future Value of Money is Compounded Value (As the rate is compounded) of the Present Value

Image Source – Courtesy :- Investopedia.com

Instead of doing complex calculations around 1+i to the power n, we can arrive at the compounded interest factor for FV (FVIF), and the discounted interest factor for PV(PVIF), using the tables.

The valuation of money is key to making decisions around investments and project, which will derive future value. Of course these needs to be seen in conjunction with the Opportunity costs.

PVIF, and FVIF are used when we receive a fixed cash flow in the future. However in case of Annuity, the fixed payments paid over a period of time has to be considered and factored as well.

Annuity refers to a fixed payment paid which will terminate after a specific period of time.  It differs from Perpetuity in that the period is Infinite.

Annuity is of 2 types

Ordinary Annuity – Paid at the end of each period/term (Interest on Deposits etc)

Annuity Due – Paid at the begining of each period/term (Fees, Rent etc)

 

Why these two are seen differently is because of the payout involved during a different time scale, which in turn affects the calculation of the value.

Future Value of Annuity Due = Future Value of Ordinary Annuity * (1+i)

Money Doubler Formulae:

As discussed in class, if we quickly have to figure out in what period of time, our money will double given an interest rate, we should use the rule of 72.

Years = 72/Rate of Interest

A more precise formula would be Years = 0.35 + 69/Interest Rate

In all the formulae above, the frequency of compounding was considered to be a year. It can be half-yearly, quarterly etc, and the calculations will change based on the compounding frequency.

A depiction of the cashflow using a time line is a good way to approach the problems involving Time Value of Money. Also the cash flows can sometimes be inflows or outflows, and constant or variables.

More on Risk/Returns & CAPM to follow in the next recap….