# Case averaged out to a market risk premium

### Case averaged out to a market risk premium

Case questions • What is the cost of capital for Marriott’s as a whole at the prevailing capital structure vs. at the target capital structure. ? Be prepared to defend your specific assumptions about the various inputs adopted into equations.

For example, the team is expected to suggest the proposed market risk premium. ? WACC should be estimated for the overall firm ? CAPM – equity beta vs. asset beta – see Section F • Compute a separate cost of capital (WACC) for the lodging business, contract services business and restaurant business. How was cost of debt measured of each division? Should the cost of debt differ across three divisions? Why? ? What is/are suitable comparables? Why? ? What cause each divisional WACC differ? ? What is the appropriate method of estimate cost of capital of each division? ? using comparables to get divisional betas – See Section F The Marriott’s prevailing weighted cost of capital (WACC) is 10. 48%.

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The first step to finding the prevailing WACC was to calculate the capital asset pricing model (CAPM).First, a risk free rate must be determined; this was done by taking the average return of the Long-Term U. S. government bonds and averaging it for the years 1987, 1986, 81-85, and 80-76. This came out to be a risk free rate of 9. 14%. Next, the market risk premium needed to calculated, this equation is the spread between expected market return and the risk free rate.

The same method to find the risk free rate was used to find the market risk premium, by taking average return of the spread between the the S&P 500 Composite returns and long-term U. S. overnment bond returns and averaging it for the years 1987, 1986, 81-85, and 80-76; this averaged out to a market risk premium of 3. 11%.

The last factor of the CAPM model is the beta for the company, the given beta of 1. 11 was used in this calculation. When the rates and betas are all calculated, the CAPM came out to be 12. 59%.

Once the CAPM has been calculated, the next step to determining the WACC is to figure out the required rate of return for debt, which was found by adding the debt rate premium above government for Marriott from Table A, 1. 30% and the 10 year U. S.Government interest rates from Table B, 8. 72%. The 10 year rate was chosen to be consistent with time lengths. Then the value for equity, debt and the firm need to be calculated, this is a simple step.

The market price of the shares is multiplied by the number of outstanding shares to find the value of equity and the book value of long term debt is used for the value of debt and the value of both equity and debt are added together to come up with the value of the firm. The weight of the equity and debt can now be calculated by dividing the value of equity or debt by the value of the company.Lastly, the tax rate was calculated by using the balance sheet, given in exhibit 1, to determine income taxes paid and dividing it by earnings before interest and taxes for each of the last ten years then by taking the average of the ten years tax rates. Once the prevailing WACC rate was found, the target WACC was calculated to be 9. 00%. Again the CAPM model was used but a new the required rate of return on equity needed to be calculated. Since there is a change in the capital structure an unlevered beta needed to be determined.

The Hamada equation was used to unlever the beta, which had a debt to equity ratio of . 70, then to re-lever it again with a debt to equity ratio of 1. 5; this changed the beta from 1. 11 to 1. 48. The new required rate of return on equity came out to be 13. 74%.

The required rate of return for debt remained the same as in the prevailing calculation. The weight of equity and debt for the firm did not need to be calculated because they are given in Table A, debt 60%, and weight of equity, 40%. The same tax rate is also used in calculating the target WACC.

The WACC for each of the three divisions of Marriott is also calculated as if they were separate entities. The first to be calculated will be Lodging, followed by Restaurants, then Contract Services. Each of the three divisions has a different WACC, this is due to different weights of debt and equity, rates of return on debt, and betas of the tree divisions, which lead to different WACCs for each division. Lodging’s WACC came out to be 7. 95%. This was calculated using the same methods as the overall Marriott’s WACC.

Starting with the CAPM model, the risk free rate and market risk premiums were the same as that for the firm. The significant difference was calculating the division’s beta. The beta was figured out by taking the average of all the proxy hotels’ betas’, in exhibit 3, then using the hamada equation to unlever that average.

Finally, re-levering that beta in accordance with the target debt to equity ratio of 2. 85 found in Table A. With this new levered beta we found our required rate of return for equity to be 14. 25% for the lodging division.

The required rate of return was then calculated by adding the debt rate premium above the government from Table A, 1. 10% and the 10 year U. S.

government interest rate from Table B, 8. 72%. The weight of the debt was taken from Table A, 74%, and the weight of equity was taken from one minus the weight of debt. The same tax rate for the entire Marriott company was used in the Lodging calculation. Lastly, the weight of lodging division in Marriott is 86.

59%, this weight was found by dividing the amount of capital expenditures for lodging by the sum of capital expenditures for lodging, restaurants and contract services.This method of determining the weight of the divisions was chosen because the amount of money the company chooses to invest in each division should determine its weight not the amount of sales each division generates, but how much capital each division needs to generate. The restaurants division’s WACC was calculated in the same way as the lodging division’s, it came out to be 9. 26%. The CAPM and required rate of return of debt were calculated to be 12. 28% and 8. 70%, respectively.

The same procedures were taken to get the restaurant division’s beta, 1. 4, weight of equity, 58%, weight of debt, 42%, and the weight of the division, 5. 55%, the only difference was in finding the required rate of return of debt, instead of adding the 10 year U. S.

government interest rate, the 1 year rate was added to the debt rate premium about government. The 1 year rate was used instead, because of the shortened asset life associated with this division. Contract services was most challenging division to calculate WACC for, because there were no proxies to compare it to and little information to go y; therefore, the calculations had to be estimated by using what was found from the other two divisions. The WACC estimation for Contract Services was calculated to be 13.

93%. First the beta was calculated by taking the unlevered target beta of Marriott as a whole, then subtracting the sum of each division’s unlevered beta times the weight of that division to firm then dividing by the weight of contract services to the firm. This unlevered beta is then levered by using the same tax rate calculated for the Marriott, 41. 3% and the debt to equity ratio based on the debt percentage in Table A, this comes out to a levered beta of 3. 48. This newly calculated levered beta is plugged into the CAPM model with the same risk free rate and market risk premium, to get a required rate of return of equity of 19. 98%.

The required rate of return of debt is 8. 30%, using the 1 year U. S. Government interest rate (Table B) and the weight of debt and equity come from Table A.

Finally, the weight of the contract services division is the calculated in the same way as the other divisions, making it 7. 86% of Marriott.