The Cost of Capital is the cost of a company’s funds (both debt and equity), or from an investor’s point of view is “the required rate of return on a portfolio company’s existing securities”. It is used to evaluate new projects of a company. It is the minimum return that investors expect for providing capital to the company, thus setting a benchmark that a new project has to meet.

When companies borrow funds from outside lenders, the interest paid on these funds is called the cost of debt.

**Cost of Debt=Kd*(1-Tax)**

The cost of equity – the investors expect a certain return from their investment, and the company must pay this amount in order for the investors to be willing to invest in the company. It is commonly computed using the capital asset pricing model formula:

Cost of equity = Risk free rate of return + Premium expected for risk

** Cost of equity = Risk free rate of return + Beta × (market rate of return – risk free rate of return)**

where Beta = sensitivity to movements in the relevant market.

**How to Calculate Beta of a private limited Company?**

Beta is a measure of stock’s Volatility in relation to the overall market. Stocks with betas higher than 1.0 can be interpreted as more volatile than the S&P 500.

A stock with a beta of

• zero indicates no correlation with the chosen benchmark (e.g. cash or treasury bills)

• one indicates a stock has the same volatility as the market

• more than one indicates a stock that’s more volatile than its benchmark

• less than one is less volatile than its benchmark

• 1.3 is 30% more volatile than its benchmark

• Beta data about an individual stock can only provide an investor with an approximation of how much risk the stock will add to a (presumably) diversified portfolio.

A beta of 1.2 indicates that if the market moves up by 10% then the stock price will move by 10*1.2=12%

How to compute Beta:

A beta can be computed through Regression Analysis.

A regression analysis of Stock return against the market return would give the following equation:

**Ks= As + Bs Km + Es**

Ks=Stock price movement

Km=Market price Movement

Bs=Beta of the stock return i.e., movement of stock that relates with market return

As=movement in stock irrespective of market movement

Es=residual error term that indicates the movement that cannot be explained.

Mathematically, Beta is calculated as:

**Beta Formula = Covariance ( Re , Rm)/ Variance (Rm)**

**•** Re = Stock Return

• Rm = Market Return

Since private companies do not have stock prices, we can calculate an approximate Beta:

First step: Find beta of the listed company that are similar to private company.

Second step: Un-lever this beta to remove the effect of Debt equity ratio

Third step: Re lever the beta using the private company’s debt equity ratio.

Let’s understand this with an example:

AB steel private limited company is a large private limited company and is contemplating raising funds. The company has assigned you to value the company. The company counts Tata steel, JSW steel and Sail among its peers. It expects the target equity would be Rs. 35000 Crore and Debt would be Rs.27000 Crore.

The 10 year Govt Bond is yielding 6.07% and the Long-Term Market return would be 15.4%.

The company can borrow fund at a rate of 10% and the applicable tax rate is 27%.

Assess the WACC of the company.

Answer: So in this question, we have with us:

WACC= (Cost of equity* weight of equity) + (cost of debt(1-tax) * weight of debt)

Cost of debt=10%

Tax rate=27%

Weight of debt = 27000/ (35000+27000) = 0.435

Weight of equity=35000/ (35000+27000) = 0.564

Cost of equity= Rf+(Rm-Rf) *Beta

Rm=15.4%

Rf=6.07%

Beta=?

After Calculation we have:

**Tata Steel JSW SAIL Company**

Beta(1 Yr) as compared to sensex 1.169 1.289 1.359

Equity 70454.71 35393 38151.57 35000

Debt 26651.19 26517 30802.66 27000

D/E ratio 0.38 0.75 0.81 0.77

Average Beta of all the companies = (1.169+1.289+1.359)/3

=1.272

Average D/E ratio = (0.38+0.75+0.81)/3

=.64

To un-lever the Beta = Beta/(1+(1-tax)(D/E ratio))

= 1.272/(1+(.64)(1-27%))

= .86

To re-lever the beta of Company= Unlevered Beta*((1+D/E)(1-tax))

= .86*[1+.77(1-.27)]

=1.35

~ The cost of equity= Cost of equity= Rf+(Rm-Rf) *Beta

= 6.07+(15.4-6.07) *1.35

=18.667

~Cost of Debt=Cost of Debt*(1-Tax rate)

= 10(1-27%)

= 7.3%

~**WACC**= (Cost of equity* weight of equity) + (cost of debt(1-tax) * weight of debt)

= (18.667*35000/62000) + (7.3*27000/62000)

= 10.54+3.18

= 13.72%.

This is how we can calculate the beta and cost of Capital of the company.

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