# Weighting and Cost of Capital Calculation  Aswath Damodaran discusses the importance of using market values in calculating the cost of capital, debunking three common arguments for using book values instead.

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## About Weighting and Cost of Capital Calculation

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1. Aswath Damodaran 1 Session 8: Weights and Cost of Capital Dynamics

2. Aswath Damodaran 2 Weights for Cost of Capital Calculation The weights used in the cost of capital computation should be market values. There are three specious arguments used against market value Book value is more reliable than market value because it is not as volatile : While it is true that book value does not change as much as market value, this is more a reflection of weakness than strength Using book value rather than market value is a more conservative approach to estimating debt ratios: For most companies, using book values will yield a lower cost of capital than using market value weights. Since accounting returns are computed based upon book value, consistency requires the use of book value in computing cost of capital: While it may seem consistent to use book values for both accounting return and cost of capital calculations, it does not make economic sense.

3. Aswath Damodaran 3 Disney: From book value to market value for debt In Disney s 2008 financial statements, the debt due over time was footnoted. Disney s total debt due, in book value terms, on the balance sheet is \$16,003 million and the total interest expense for the year was \$728 million. Assuming that the maturity that we computed above still holds and using 6% as the pre-tax cost of debt: Estimated MV of Disney Debt = No maturity was given for debt due after 5 years. I assumed 10 years.

4. Aswath Damodaran 4 And operating leases The pre-tax cost of debt at Disney is 6%. Debt outstanding at Disney = MV of Interest bearing Debt + PV of Operating Leases = \$14,962 + \$ 1,720= \$16,682 million Year Commitment Present Value 1 \$392.00 \$369.81 2 \$351.00 \$312.39 3 \$305.00 \$256.08 4 \$265.00 \$209.90 5 \$198.00 \$147.96 6 & 7 \$309.50 \$424.02 Debt Value of leases = \$1,720.17 Disney reported \$619 million in commitments after year 5. Given that their average commitment over the first 5 years of \$302 million, we assumed two years @ \$309.5 million each.

5. Aswath Damodaran 5 Current Cost of Capital: Disney Equity Cost of Equity = Riskfree rate + Beta * Risk Premium = 3.5% + 0.9011 (6%) = 8.91% Market Value of Equity = \$45.193 Billion Equity/(Debt+Equity ) = 73.04% Debt After-tax Cost of debt =(Riskfree rate + Default Spread) (1-t) = (3.5%+2.5%) (1-.38) = 3.72% Market Value of Debt = \$ 16.682 Billion Debt/(Debt +Equity) = 26.96% Cost of Capital = 8.91%(.7304)+3.72%(.2696) = 7.51% 45.193/ (45.193+16.682)

6. Aswath Damodaran 6 Dealing with Hybrids and Preferred Stock When dealing with hybrids (convertible bonds, for instance), break the security down into debt and equity and allocate the amounts accordingly. Thus, if a firm has \$ 125 million in convertible debt outstanding, break the \$125 million into straight debt and conversion option components. The conversion option is equity. When dealing with preferred stock, it is better to keep it as a separate component. The cost of preferred stock is the preferred dividend yield .

7. Aswath Damodaran 7 Decomposing a convertible bond Assume that the firm that you are analyzing has \$125 million in face value of convertible debt with a stated interest rate of 4%, a 10 year maturity and a market value of \$140 million. If the firm has a bond rating of A and the interest rate on A-rated straight bond is 8%, you can break down the value of the convertible bond into straight debt and equity portions. Straight debt = (4% of \$125 million) (PV of annuity, 10 years, 8%) + 125 million/1.08 10 = \$91.45 million Equity portion = \$140 million - \$91.45 million = \$48.55 million

8. Aswath Damodaran 8 Debt ratios for private businesses While the temptation is to go with book values for debt and equity, you should steer away from them. There are three alternatives you can employ. Use the industry average market debt ratio, obtained by looking at publicly traded companies in the sector, to estimate the cost of equity and capital. Use an estimated market value of equity, based upon applying a multiple (say a PE ratio) to your private company s earnings to arrive at a debt to equity ratio. Use your DCF estimates of equity and debt value to compute your cost of capital. Since you will need the cost of capital to arrive at these estimates, this will create circularity in your valuation. If you are willing to use the iteration function in Excel, you should be still able to work with the circularity.

9. Aswath Damodaran 9 Target versus Actual Debt Ratios The actual debt ratio for a firm reflects what the current management of the firm has chosen as the appropriate debt ratio. To the extent that the managers have either been too conservative or too extreme in the use of debt, the right debt ratio for the firm may be different from the actual. To estimate this right or target debt ratio, analysts use one of three choices: An arbitrary number, based upon gut feeling and experience An industry average for the industry in which your company operates An optimal debt ratio that minimizes your cost of capital

10. Aswath Damodaran 10 Computing an optimal debt ratio

11. Aswath Damodaran 11 Should you value your business using the target or optimal? If you are valuing a business for a sale or acquisition, it does make sense to use the target debt ratio, since the acquirer can reset the debt ratio at the time of the acquisition. If you are valuing a business as a passive investor or observer, you may be better off using the actual debt ratio, since the existing managers will continue to run the firm (and presumably keep intact their views of debt). If you are uncertain about who will be running the business in the future (existing managers or a new owner), you can either Change the debt ratio gradually over time from the actual to the optimal Do two valuations, one with the actual and one with the optimal, and take an expected value.

12. Aswath Damodaran 12 Changing risk profiles & changing costs of capital When valuing young, growth firms, the cost of capital at the start of your valuation should reflect the high risk of the firms (high costs of equity) and their inability to borrow money (low or no debt). As a result, your cost of capital will be high. As you bring down the growth rate of the firm over time and make it a more mature business (with higher revenues & profits), you should expect The cost of equity to change over time, as your risk moves towards the average for the sector or the market. The debt ratio to rise, as earnings and cash flows go up The cost of capital to drift down towards the average for the market (or the sector).

13. Aswath Damodaran 13 Back to the beginning