2. Before we calculate the discount rate, we need to make the following assumptions: a. Since Ms. Zhang wanted to keep things simple by assuming a stock purchase using the maximum amount of leverage available and a debt to value ratio not exceeding 50%, so we calculate the initial D/E=100% which is the maximum leverage for AirThread under this scenario. b. AirThread neither rebalanced its capital structure during 2008 and 2012, nor did it keep its debt at a fixed level. It repays its debt monthly. However, the amount of debt repaid before the end of 2012 is small compared with the total amount of debt and the total bullet payment. So when we calculate debt cost of capital from 2008 to 2012, we assume that the debt maintains at a fixed amount till the end of 2012 and the periodic payments will not have effect on the debt cost of capital.
In order to use APV method to value the company from 2008 to 2012, we need to figure out the unlevered cost of asset-R(U) and cost of debt at initialization-R(D08-12) to discount the FCF back to 2007. According to Rubinstein & Ross the interest rate of the bond should be 5.5% at the initial leverage, so RD08-12=5.5%. And we expect to use the market multiples to estimate RU. We can calculate Beta(D08-12) at the initial leverage by using CAPM model. So Beta(D08-12)=1.25%/5%=0.25, at D/E=100%. However, when the capital structure of AirThread is in line with the industry, the D/E ratio is approximately 40.1%, which is less than 100%, indicating less risk in debt after 2012 when the company was in line with the industry leverage.
So we assume that AirThreads debt beta after 2012-Beta(D12-)=0.125, also we can get equity beta-Beta(E12-)=1.00 from the market multiples. Since the D/E=40.1% in market multiples, we can get Beta(U)= 0.125*40.1%/(1+40.1%)+1*1/(1+40.1%)=0.75, R(U)=(5.5%-1.25%)+0.75*5%=8%. Finally we can use R(U) to discount the FCF and use R(D08-12) to discount the interest tax shield. A detail list of inputs can be found in Sheet1. In terms of the terminal value, the discount rate=WACC-G. G is the growth rate in perpetuity, which cannot exceed the long term growth rate of US economy. The WACC is the weighted cost of capital when AirThreat keeps rebalancing the capital structure in line with the industry, the assumptions are very different from what we have made when calculating the discount rate from 2008 to 2012. So we cannot use the same discount rate to value the terminal value.
3. Compute the unlevered free cash flow and the interest tax shields from 2008 to 2012 based on estimates provided in Exhibit 1 and Exhibit 6. Based on the data provided by the case we can calculate estimated FCF which can be found in Sheet2. In calculating the ITS, we think only the interest payment can be used to calculate the ITS instead of the total payment each year. The calculation of ITS can be found in Sheet3. Free Cash Flow = EBIT—(1-tax rate) + Depreciation & Amortization change in Net Working Capital Capital Expenditure EBIT = Revenue Operating Expense COGS SG&A Depreciation & Amortization Among the inputs listed above, only changes in Net Working Capital is not projected with explicit figures, and assumptions concerning net working capital accounts and important related notes are listed in Sheet4.Based on our above sheets can calculation, we can arrive at the results. (in million dollar)
| 2008| 2009| 2010| 2011| 2012|
Free Cash Flow| 227.07| 347.38| 319.73| 326.04| 322.24| Interest Tax Shield| 80| 73| 66| 59| 56|
4. A companys long-term growth rate is a function of return on capital and reinvestment rate, and should not exceed long-term macro economy growth rate. The return on capital represents the investment return and the reinvestment rate represents the proportional amount of capital reinvested to fulfill future growth of the company. So a better to estimate the long term growth rate is to return on capital multiplied by reinvestment rate. So, g=return on capital—reinvestment rate. A detailed disaggregation of this function can be fond in Function 1 in appendix. We need the long term growth rate of AirThread when its capital structure is in line with the industry and reflect the most recent performance after the merger event. So it is better to estimate the long term growth rate by using the 2012 year end projected financial statements.
As we have computed the Î” NWC in Q3 and got other necessary inputs from the exhibits in case material, the only unknown data is the Total Assets of 2012. To project this number in 2012, we need to use the formula of Asset Turnover ratio. Asset Turnover ratio = Total revenue/ Total asset The total revenue of 2012, combining the Service Revenue and Equipment Revenue of 2012 in Exhibit 1, should be 6806.50. Then we compute the average growth rate of the Asset Turnover Ratio based on Table 2 and use the result to estimate the Asset Turnover Ratio of 2012, which is 1.58. Now we can estimate the total asset of 2012 with the Asset Turnover Ratio of 1.58. Total asset= 6806.50/ 1.58â‰ˆ4311.1(in million). With the total asset of 2012, we can calculate the long-term growth rate=2.61%.
The inputs and detailed result is list in Sheet5. Based on the 30-year GDP data of U.S (Dec.1976-Dec 2007), average nominal GDP growth rate is 7.3%, average real GDP growth rate is 3.3%, and inflation growth rate is 0.9%, so projected Future Growth Rate of AirThread should be between 0.9% and 7.3%, which support our estimate result of 2.61%. 5. A companys total assets can be expressed as the sum of operating assets and interest tax shield assets.
Under the assumptions that from 2008 to 2012 the total debt is fixed and in perpetuity the company keeps rebalancing the leverage ratio to be in line with the industry, we should use unlevered discount rate (Ru) to discount the FCF back to 2007. Terminal Value of FCF in perpetuity is estimated with the long-term growth rate calculated in Q4 and unlevered discount rate calculated in Q3: Terminal Value at 2012=FCF2012—(1+g)Ru=322.24—(1+2.61%)8%-2.61%=6,134.52 (million dollar) Value of operating assets=15FCFt(1+Ru)t+Terminal Value(1+Ru)5=5,176.58 (million dollar)