# Risk and return relationship in capital budgeting we use cash

### Capital Budgeting Techniques, Importance and Example

Capital budgeting: the process of planning expenditures on assets with cash (2 ) Internal rate of return (IRR): rate of return a project earns (a discount rate that NPV profile: a graph that shows the relationship between a project's NPV and . Risk-adjusted cost of capital: use the beta risk to estimate the required rate of. Capital budgeting (or investment appraisal) is the planning process used to In order to discuss this further, we should look into defining the concept or risk. and it might also attempt to forecast financial market returns (for bonds, stocks, and cash) The institution can also calculate the scenario-weighted expected return. Applications of the CAPM to Capital Budgeting; Determination of the appropriate In order, therefore, to value risky cash flows, we need to know two things: The variance of returns can be used as a measure of risk if we are evaluating the entire portfolio of . Consequently, we can write the risk-return relationship as.

It is expressed in years with two decimals, such as 4. In general, shorter payback periods are more attractive because the cash is recovered in a shorter period of time. If the cash is expected to be recovered in a time period shorter than the useful life of the investment, it is tentatively deemed acceptable.

If the shortcut method is used to calculate the PBP, the results may indicate a payback period that is greater than the useful life of the asset. It is not possible to have a useful life greater than the payback period because the 'end' of the useful life indicates the asset will no longer be used in the production of income.

When it is no longer used, it no longer brings in economic resources. As such, when the numerical result using the shortcut method appears to have a payback period that exceeds the useful life, the interpretation is 'the investment will never be recovered. First, it does not consider the total stream of cash flows. It ignores those after the end of the recovery period. The cash flow in year 3 is ignored.

Hence, project A is superior to B. Accounting rate of return method ARR: This method helps to overcome the disadvantages of the payback period method.

The rate of return is expressed as a percentage of the earnings of the investment in a particular project. It works on the criteria that any project having ARR higher than the minimum rate established by the management will be considered and those below the predetermined rate are rejected. This method takes into account the entire economic life of a project providing a better means of comparison. It also ensures compensation of expected profitability of projects through the concept of net earnings.

The discounted cash flow technique calculates the cash inflow and outflow through the life of an asset. These are then discounted through a discounting factor. The discounted cash inflows and outflows are then compared. This technique takes into account the interest factor and the return after the payback period.

This is one of the widely used methods for evaluating capital investment proposals. The appropriate measure of risk of an individual asset, then, is the marginal contribution of that asset to the variance of the market portfolio.

The risk measure that is used in practice is this covariance normalized by the total variance of the market portfolio, which works fine if we are interested in the risk of an asset, relative to other assets.

### Internal Rate of Return (IRR) - A Guide for Financial Analysts

This measure is denoted by the greek letter beta and is written: The Risk-Return Tradeoff for Individual Securities Now that we have derived a common risk measure for all investors, we can specify the equilibrium risk-return tradeoff in the market. The expected return on an asset can be divided into two parts: The return for deferring compensation is, of course, simply rf, the return on the risk-free asset. Hence the return for bearing risk is E ri - rf.

Mean-variance analysis implies that the return for bearing risk is proportional to the risk. Consequently, we can write the risk-return relationship as: This equilibrium relationship has several desirable features: The expected return on a security with a beta of zero is equal to the riskfree rate, rf.

Since such a security contributes nothing to the market portfolio risk, it is effectively riskless even though its return variance may be positive. An asset with a beta of one is equivalent to the market portfolio and earns the expected rate of return on the market portfolio.

If two assets are priced to satisfy the above risk-return pricing equation, then so will their combination.

## Internal Rate of Return (IRR)

Portfolio Diversification The risk of an asset, if held alone, is given by its variance. However, as we add other assets to the investor's portfolio, the variance decreases, in general, until it reaches a minimum level, which depends upon the covariances of the asset returns with each other. This is seen in the following figure, where the portfolio variance is depicted as a function of the number of securities in the portfolio, where the securities are chosen randomly for inclusion in the portfolio.

Real and nominal return - Inflation - Finance & Capital Markets - Khan Academy

The curve shown in the figure is actually an average of the different curves that might result in a large number of such simulations. Note that the portfolio variance decreases steadily until it reaches an asymptotic level. Excel file with example Figure: Behavior of portfolio return variance, as we increase the number of securities in a portfolio.

If we consider that the average investor holds the market portfolio, we can use the above picture to obtain another perspective on why the beta of an asset is the correct measure of its risk.