Corporate Finance 001: Time Value of Money

Definition

Simply put, corporate finance is the study of how corporations make decision, any kinds of decision from investment, purchasing, operations and marketing. It provides a framework to quantify the costs and benefits of any endeavours, so that corporation, or even individuals at a personal level, can make financially sound decisions.


Time Value of Money

This is an intuition, fundamental to any finance course, that money obtained or expended (Cash Flows) at different time period has a different value with respect to a chosen point in time. The value is calculated based on a Rate of Return offered by investment alternatives in the capital markets of equivalent risk.

Here are some examples from the lesson of the next best alternative investment in the capital markets and the rate of return. Therefore, depending on the alternatives chosen for comparison, the rate used in valuing money will differ. This also interestingly point out that with higher risk of investment, rate of return will also be higher.


Discounting and Compounding

If we are interested in finding the Present Value of a series of future cash flows, we would discount the cash flows with a selected rate of return.

Discounting

If we are interested in finding the Future Value of a series of cash flows that occured before the chosen point in time, we would compound the cash flows with a selected rate of return.

Compounding


Annuity and Perpetuity

Instead of discounting or compounding the cash flows, there are simple formulas to calculate the value of common cash flow streams. Here are some examples:

Annuity

  • A finite stream of cash flows
  • Cash flows of identical magnitude
  • Cash flows are spaced out equally in time

To find the present value of annuity, simply use:

PV of Annuity = [CF / R] * [1 – (1+R)^-T]

When dealing with Growing Annuity, which is annuity with cash flows that grow at a constant rate, the formula is as follows:

PV of Growing Annuity = [CF / (R-g)] * (1 – [ (1+R) / (1+g) ]^-T )

Perpetuity

Perpetuity is very similar to annuity. A perpetuity does not have an expiry for the stream of cash flows. Some coupon bonds, company stocks that give dividends, or insurance with payouts, are assumed to be perpetuity as the stream of cash flows is theoretically infinite.

To find the present value of perpetuity, simple use:

PV of Perpetuity = CF / R

For Growing Perpetuity, which has cash flows that grow at a constant rate, the formula is:

PV of Growing Perpetuity = CF / (R-g)

These concepts of present values of cash flows intuitively explain why the stock prices of dividend stocks rise or fall when there are changes in the amount of dividend payout.

 

(Reference: Coursera Wharton Online Introduction to Corporate Finance)

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