Corporate Finance 003: Yield and Term Structure

Terminology of Rates

It is pretty confusing if you are unsure of the terms used when quoting interest rates. Here is a simple introduction based on U.S. examples.

The Rate or APR or Annual Percentage Rate is the simple interest earned without compounding in a year. It is therefore not accurate and quoted for convenience. However, many bank products sold commercially are quoted in terms of APR.

The APY or Annual Percentage Yield or EAR or Effective Annual Rate is the actual amount of interest accumulated in a year, taking into effect compounding.

Therefore to calculate actual values using compounding or discounting, we need to use EAR. However, APR is usually quoted instead, therefore we would need to calculate the EAR using the following formula before finding the actual value:

EAR = [ 1+ (APR / k) ]^k  – 1
EAR = ( 1+ i)^k  – 1

k is the number of compounding period within a year. i is the periodic interest rate.

Term Structure

Term Structure is the relation between the investment term and the interest rate. A Yield Curve is a graph representing that relation. The yield typically differs between different maturity terms. The curve conveys the market expectation of interest rates movement in future. If the yields of longer maturity loans are higher, then the market is expecting interest rate to move higher in the future.

Spot Rate (on the Spot) is the interest rate for a loan made today. The rate can be derived from the yield curve using


(Reference: Coursera Wharton Online Introduction to Corporate Finance)


Corporate Finance 002: Taxes and Inflation

Effects of Taxes on Rates

If the cash flows from a certain investment is subjected to tax, then the rate of return need to be adjusted to reflect the effect of tax. This generally lowers our returns from investments.

On the flip side, the interest payment for certain types of loan are exempted from tax. This effectively reduces the interest rate of our loans in proportion to the tax rate.

It is important to keep the effects of taxes in mind for any forms of investments. For example as a Singaporean investing in U.S. company stocks, any dividends that I receive is subjected to a 30% tax. Therefore, I would have an additional consideration when making investment decisions as compared to a U.S. investor.

Effects of Inflation on Rates

Inflation does not directly impact our returns on investments, but it reduces the purchasing power of our money over time. Therefore, there is a distinction between real value and nominal value, where real value had taken into account inflation.

To calculate the real value of an investment, the cash flows have to be discounted with real interest rate. Relationship between real interest rate, nominal interest rate and inflation is captured by this formula:

real rate formula.JPG

RR is the Real Rate. Sum with 1 prevents division by zero error.

And as a rule of thumb, always find real value with real rate, and nominal value with nominal rate. Never mix them up when dealing with inflation.

In my opinion, it is important to understand and take note of the effects of inflation when investing for the long term, for example retirement funds. The medical costs and costs of living may have increased quite a bit due to inflation by the time you start drawing out your retirement funds, resulting in you not being able to meet your daily needs. It is therefore necessary to plan ahead carefully.


(Reference: Coursera Wharton Online Introduction to Corporate Finance)

Corporate Finance 001: Time Value of Money


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.


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.


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:


  • 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 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)