The Risk-Free Rate

Most risk and return models in finance start off with an asset that is defined as risk free and use the expected return on that asset as the risk-free rate. The expected returns on risky investments are then measured relative to the risk-free rate. But what makes an asset risk free? And what do we do when we cannot find such an asset? These are the questions we will deal with next.

The Cost of Equity

Firms raise money from both equity investors and lenders to fund investments. Both groups of investors make their investments expecting to make a return. The expected return for equity investors would include a premium for the equity risk in the investment. We label this expected return the cost of equity. In other words, the cost of equity is the rate of return investors require on an equity investment in a firm.
As you may know, the risk and return models need a riskless rate and a risk premium. They also need measures of a firm’s exposure to market risk in the form of betas. These inputs are used to arrive at an expected return on an equity investment:

Expected return = Riskless rate + Beta(Risk premium)

This expected return to equity investors includes compensation for the market risk in the investment and is the cost of equity.

In the Capital Asset Pricing Model (CAPM), the beta of an investment is the risk that the investment adds to a market portfolio. There are three approaches available for estimating these parameters: one is to use historical data on market prices for individual investments; the second is to estimate the betas from the fundamental characteristics of the investment; and the third is to use accounting data. We will look at all three approaches next.

Calculating the Cost of Debt

The cost of debt measures the current cost to the firm of borrowing funds to finance projects. In general terms, it is determined by the following variables:

•   The riskless rate. As the riskless rate increases, the cost of debt for firms will also increase.

•   The default risk (and associated default spread) of the company. As the default risk of a firm increases, the cost of borrowing money will also increase.

•   The tax advantage associated with debt. Since interest is tax deductible, the after-tax cost of debt is a function of the tax rate. The tax benefit that accrues from paying interest makes the after-tax cost of debt lower than the pre-tax cost. Furthermore, this benefit increases as the tax rate increases:

After-tax cost of debt = Pre-tax cost of debt(1 – Tax rate)

Estimating the Default Risk and the Default Spread of a Firm

The simplest scenario for estimating the cost of debt occurs when a firm has long-term bonds outstanding that are widely traded. The market price of the bond in conjunction with its coupon and maturity can serve to compute a yield that is used as the cost of debt. For instance, this approach works for a firm like AT&T that has dozens of outstanding bonds that are liquid and trade frequently.

Many firms have bonds outstanding that do not trade regularly. Since these firms are usually rated, we can estimate their costs of debt by using their ratings and associated default spreads. Thus, Boeing with an AA rating can be expected to have a cost of debt approximately 1.00 percent higher than the Treasury bond rate, since this is the spread typically paid by AA-rated firms.

Some companies choose not to get rated. Many smaller firms and most private businesses fall into this category. While ratings agencies have sprung up in many emerging markets, there are still a number of markets where companies are not rated on the basis of default risk. When there is no rating available to estimate the cost of debt, there are two alternatives:

1.     Recent borrowing history. Many firms that are not rated still borrow money from banks and other financial institutions. By looking at the most recent borrowings made by a firm, we can get a sense of the types of default spreads being charged the firm and use these spreads to come up with a cost of debt.

2.     Estimate a synthetic rating. An alternative is to play the role of a ratings agency and assign a rating to a firm based on its financial ratios; this rating is called a synthetic rating. To make this assessment, we begin with rated firms and examine the financial characteristics shared by firms within each ratings class. For instance, the Altman Z score, which is used as a proxy for default risk, is a function of five financial ratios that are weighted to generate a Z score. The ratios used and their relative weights are usually based on empirical evidence on past defaults. The second step is to relate the level of the score to a bond rating.

What is Debt?The answer to this question may seem obvious since the balance sheet for a firm shows the outstanding liabilities of a firm. There are, however, limitations with using these liabilities as debt in the cost of capital computation. The first is that some of the liabilities on a firm’s balance sheet, such as accounts payable and supplier credit, are not interest-bearing. Consequently, applying an after-tax cost of debt to these items can provide a misleading view of the true cost of capital for a firm. The second is that there are items off the balance sheet that create fixed commitments for the firm and provide the same tax deductions that interest payments on debt do. The most prominent of these off-balance sheet items are operating leases. Consider what an operating lease involves. A retail firm leases a store space for 12 years and enters into a lease agreement with the owner of the space agreeing to pay a fixed amount each year for that period. We do not see much difference between this commitment and borrowing money from a bank and agreeing to pay off the bank loan over 12 years in equal annual instalments.

There are therefore two adjustments we can make when we estimate how much debt a firm has outstanding.

1.     We can consider only interest-bearing debt rather than all liabilities. We would include both short-term and long-term borrowings in debt.

2.     We can also capitalise operating leases and treat them as debt.

Weighted Average Cost of Capital (WACC) or Cost of Capital

Since a firm can raise its money from three sources – equity, debt, and preferred stock – the cost of capital is defined as the weighted average of each of these costs. The cost of equity (k_e) reflects the riskiness of the equity investment in the firm, the after-tax cost of debt (k_d) is a function of the default risk of the firm, and the cost of preferred stock (k_ps) is a function of its intermediate standing in terms of risk between debt and equity. The weights on each of these components should reflect their market value proportions, since these proportions best measure how the existing firm is being financed. Thus, if E, D, and PS are the market values of equity, debt, and preferred stock, respectively, the cost of capital can be written as follows:

Cost of Capital = k_e[E/(D + E + PS)] + k_d[D/(D + E + PS)] + k_ps[PS/(D + E + PS)]

Changes in the distribution of banks’ reserve balances are important since they may impact conditions in the federal funds market and alter trading dynamics in money markets more generally. In this post, we propose using the Lorenz curve and Gini coefficient as a new approach to measuring reserve concentration. Since 2013, concentration, as captured by the Lorenz curve and the Gini coefficient, has co-moved with aggregate reserves, decreasing as aggregate reserves declined (such as in 2015-18) and increasing as aggregate reserves increased (such as at the onset of the COVID-19 pandemic).
— Read on libertystreeteconomics.newyorkfed.org/2020/11/how-bank-reserves-are-distributed-matters-how-you-measure-their-distribution-matters-too.html

Is there anything cultural that should be preserved? An artifact perhaps? Or a dance style? What about food, or norms and practices (like ilobolo) etc.?
I suppose the answer depends on your definition or understanding of what culture is. I guess a simple definition is that culture is a way of life of a people, be it a nation, an ethnic group or a tribe. But it is clearly deeper than that, and encompasses a whole lot of things – language, technology and tools, indeed norms and behaviours, ‘education’/learning, etc. Technology and tools and ‘education’/learning play very significant roles.
In a sense I would see a river as a good metaphor for culture. Sometimes people talk about “traditions” as culture, and vice versa. In a deeper and stricter sense, this is incorrect. Traditions, which is what people usually mean by ‘preserving our culture’, are almost akin to a dam or stagnant water, to culture’s flowing river. Just as a river flows, culture may at times flow fast or slow, go over rocky terrain, have flotsam and jetsam, have deep or shallow points, etc. The key, however, is that it keeps flowing forwards. Because people sometimes fear the discomfort of change, or vested interests find certain current practices to their advantage, from time to time there is pressure and agitation to keep or preserve certain aspects of current culture. Although there may be some limited value in this, hanging on for dear life to practices that are centuries old may be inimical to cultural progression.
To hark back to old dress styles in the name of tradition, when newer and current methods are clearly vastly superior is foolhardy. Or to perpetuate practices that come from a time when women were regarded as inferior and akin to children or property, is also demeaning and outrightly dangerous. These traditions may suit certain vested interests, but are ultimately out of their time and should be discarded forthwith.

www.newyorkfed.org/medialibrary/media/research/staff_reports/sr945.pdf

www.federalreserve.gov/econres/feds/files/2020094pap.pdf

www.newyorkfed.org/medialibrary/media/research/staff_reports/sr946.pdf