What is the relation and composition of interest rate, discount rate and cap rate?

Question

I want to understand the what are constituents of discount rate, Interest rate and cap rate? How do they behave in relation to each other?

Answer 1

The discount rate is different from a more normal interest rate. The two are separate concepts in financial mathematics. The discount rate is based on the future cash flow in lieu of the present value of the cash flow. The divisor, for the discount rate, is the resulting future value, including the income. The divisor in the calculation of interest is the original investment.

Assume I have $80, and I buy a government bond that pays me $100 in a year's time. The discount rate represents the discount on the future cash flow:

(100-80)/100 = 20%

The interest rate on the cash flow is calculated using 80 as its base:

(100-80)/80 = 25%

It should become apparent that for every interest rate, there is a corresponding discount rate, given by the following formula:

d = i/(1+i)

Another way to think of a discount rate is to consider that the discount rate tells you how much of your future value is interest and how much is principal. For example, if you deposit $100 into an account that pays 50% interest, the amount that you will subsequently withdraw will be $150. Your discount rate is 0.5/(1+0.5) = 1/3 or 33.3%. Based on this, you can say that 33.3% of your $150 is interest and the other 66.7% is principal.

A contraction of capitalization rate, the cap rate is the assumed rate of return on an investment in real estate. The cap rate is commonly used in the valuation of commercial and investment property because it directly links the value to the income produced by the property.

To determine the cap rate of a property divide the net operating income by the sales price. From an income standpoint, the higher the cap rate, the better the deal.

To determine the value of a particular real estate asset, divide the net operating income or the net cash flow on the asset by the assumed cap rate(value=NOI/cap rate). Effectively, this values the real estate as a perpetuity.

An alternative use of the concept is to take the net income or net cash flows, and divide it by the purchase price in a sales transaction, to determine the implied cap rate. Used in this fashion, the cap rate indicates rising or falling demand for real estate investments.

Note that a higher cap rate results in a lower value. Thus, newer properties in upscale areas will tend to show lower cap rates than their less desirable counterparts