Approach
We used the APV approach to value the company under each of the three scenarios. To do so, we needed to find the free cash flow, debt tax shield, and the discount rate, which is ra. This rate should be applicable across all three scenarios, because it is not dependent on the operations of the company.
We then needed to value the present value of debt tax shield by finding the tax shield per year and the discount rate for that tax shield
Estimating the Asset Beta (0.73)
To find ra, we need to have the asset beta, the risk free rate (given), and the risk premium (given). We found the asset beta by de-leveraging the equity beta of the company in the last two years (1986 and 1987). The equity beta of the company is 1.24 in 1986 and 0.67 in 1987. We de-levered these equity betas by using the market value of the debt (notes payable + current portion of long term debt + long-term debt + redeemable preferred stock) and the market value of equity (price x shares outstanding). We found that the asset beta in 1986 and 1987 is 0.94 and 0.52, respectively. Averaging these two numbers gives us the asset beta of 0.73.
Estimating the ra (14.8%)
Using the asset beta of 0.73, risk free rate of 9%, and risk premium of 8%, we calculated the ra to be 14.8%
Estimating the cost of debt
We estimated the cost of debt using the average interest expense out of total debt.
Pre-bid: interest expense / (notes payable + current portion of long-term debt + long-term debt) = 10.3%
Management Group: interest expense / (principal debt payments + total year-end book value of debt) = 12.5%
KKR: interest expense / (principal debt payments + total year-end book value of debt) = 12.8%
As we can see, the cost of debt is higher in both Management Group and KKR scenarios than the pre-bid scenario because more debt is taken on by