Time Value of Money (Part 2)

Earlier we discussed about compounding by which we found out the future value of an amount deposited now.
Similar is the concept of discounting where we calculate the present value of a cash that is going to come in future.

PV - Present Value of an amount that will be received in the future, calculated after discounting. FV - Future Value of an amount invested now at a given rate of interest.

The rate used for compounding is the interest rate offered by the instrument in which the money is invested.
For discounting rate generally the cost of capital rate is used. This can be the rate which your money can grow with you.

Till now we had considered cash flow at one point of time and discussed ways to find its value at some other point of time. This kind of cash flow is known as lump-sum. What if the cash flow is divided and keeps on coming at different times. Four new terms are introduced for these:

Annuity - It is a regular cash flow for a fixed period of time.
Annuity Due- Cash flow occurs at the start of the period.
Annuity Ordinary- Cash flow occurs at the end of the period.
Perpetuity - It is a regular cash flow for a infinite period of time.

Generally, Annuity and Perpetuity are used for equal cash flows in each period.
If the cash flows are unequal it is called mixed stream.

The formula for future value of an ordinary annuity (FV) is:
where FVA(due) is future value of annuity due, A is equal cash flow per period for n periods compounded at interest rate r.
Similar formulae for present value are:
Present Value of a growing stream of cash flow:
Gordon Growth Model
g is growth rate of cash flow and if g < onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7awFDFtnkqy-wTbUDBR2FLJDdcQDpfcIUeReymZnyAO7IqGLC2X9YeJaksDZ10WIrby-Y9zs9Rgzpeg7r-_1rQL8uTAoG2Jl1GS2CeQb6KHWTQuO3Uzu3lf-6ACKTsRaLejJAnCV8Ez0k/s1600-h/AnnuityGrow.jpg">
Change in Compounding interval

Time Value of Money

Like most of the things money also loses its value if kept idle. Its mainly because of inflation, which increases the cost of goods and the purchasing power of money decreases.

Its better to invest money in something which can give an interest which is more than inflation. Generally the safest place to keep your money is the banks. They give an interest on your deposit. Most of the time the interest is compounded. Compounding makes a big difference in the long run. Compounding essentially means that you will get interest on 'interest earned' besides the usual interest on the initial amount (principal). It keeps on accumulating period after period. Generally the interest rates are compounded annually - meaning the interest you will earn after the end of a year will start fetching you more interest from year end onwards.

Power of Compounding
Compounding creates a big difference in long run. The table shows the the Future Value of Rs 100 after several years.
One may ask that who has seen 200 years and from the table it appears that it doesn't make that big a difference during a short span, say of 10 years. But what happens if you get 20% interest rate.
Now certainly the difference cannot be neglected.
The formula used for calculating Future Value (FV) is pretty simple.

where FV is Future Value, PV is Present Value, r is rate of interest compounded periodically (generally compounded annually), n is the number of periods (eg. number of years if interest rate is compounded annually)
Next article we will discuss about Annuities.

Capital Budgeting

This Article tells us about what Capital Budgeting is and what are the various methods used to evaluate projects.

Capital Investment is spending on long-lived assets.
Capital Budgeting is choosing which project to put money. Its not just choosing best project. It involves identifying potential projects, choosing best out of alternatives and implementing it.

Key parameter for decision making:

1. Simplicity of method of arriving at decision
2. Cash Flows from project
3. Accounting for time value of money
4. Risk-return management
5. Stockholder's value

Methods used for decision making:

1) Payback Period: In this method we choose between the projects based on the time taken to recover the initial investment. We choose the project which has the shortest time period.
Limitations with this method is that it does not take into account the time value of money. also, it is not dependent on the initial investment and ignores the cash flow occurring after the payback period

2) Accounting rate of return(ARR): In this method, we find the ratio of accounting profit, i.e. EBIT and average assets. Whichever project has higher ARR, we take that project.
Limitations with this method is that it also ignores time value of money. Moreover, accounting profit is an ambiguous term. It can vary as per the accounting principles followed.

3) Net Present Value(NPV): In this method, we bring all the cash flows to occur in future at the present value.(discounting them using cost of capital) If the net cash flow comes out to be positive, then project is accepted. Project having higher NPV is selected.
Advantage of this method is that it takes into account the time value of money

4) Internal rate of Return(IRR): this is one of the most widely used method. In this we find out the rate or the cost of capital, at which NPV becomes zero. This rate is known as IRR. In normal cases, i.e. positive cash flows occurring in future, if IRR is higher than present cost of capital, project is accepted. Project having higher IRR is selected.
Limitation of this method is that in case, cash flows sign changes, we get multiple values of IRR which creates problem in taking decisions

5) Profitability Index: this is the ratio of present value of cash inflows to cash outflows.