What is the top price (per share) that Kennecott should pay for Carborundum? (Show calculations)
The top price per share that Kennecott should pay is $53/share at a valuation of $428M. Details on this calculation are found below.
What Cashflows are being discounted in Exhibit 7? What cashflows should be discounted?
First Boston is Discounting the Wrong Cashflows
It appears as though First Boston is discounting the wrong set of cash flows in their analysis. The cash flows to Kennecott listed in Exhibit 7 do not reflect that free cash flow. Rather, it subtracts out the profit retentions that Corborundum will keep to support its growth even though Kennecott will own 100% of the equity in Carborundum. Additionally, to get to the FCF that should be used in an APV analysis, one must take Net Income and add back tax-adjusted interest expense minus interest income, add back depreciation and add back goodwill. Additionally, change in networking capital should be removed and capital expenditures should be subtracted. Therefore, the cashflows being discounted are inappropriate. For example, if you take the share price that First Boston thought they could justify of $85 and multiply by the 8M outstanding shares, you get a market capitalization of $680M. If you discount the cashflows from Exhibit 7 using a discount rate of 10% (another First Boston assumption), then you get $679M. Therefore, it appears that their entire analysis is based on a false set of cashflows and a flawed DCF analysis.
How to get from the cashflows in Exhibit 7 to the cashflows you actually want to discount
To value Carborundum using the APV method requires calculating free cash flow to an all equity firm. Since Exhibit 7 does not have EBIT, we must use the formula for calculating FCF that uses Net Income.
FCF = Net Income + (Interest Expense – Interest Income)*(1-Tc) + Depreciation + Goodwill – Capital Expendiures – Increase in Working Capital + Tax-loss Carryforwards
Goodwill and Depreciation – goodwill is added back because it is amortized over 40 years and acts similar to depreciation in that it is a non-cash expense that reduces net income but does not reduce free cash.
Increase in Net working Capital: increase in networking capital means that the ratio of current assets/current liabilities is getting larger. This suggests that more cash is being wrapped up in receivables and inventory rather than cold, hard cash. Therefore, these increases must be removed from net income in this calculation.
Tax-loss carryforwards: the tax loss carryforwards are also added back to cash flow because they are a form of cash flow that is relevant for an all equity firm and are not included in the other cash flows.
Which unlevering formula?
To calculate the appropriate discount rate, we can use rUe = rf + βU*(rm - rf) where rUe is the appropriate discount rate for an all equity firm, βU is the unlevered (or asset) beta for the firm, and rm - rf is the market premium over the riskfree rate. To use this equation requires calculating βU. However, there are two common unlevering formulas, one in which debt is set proportionally to equity so that the company continuously rebalances, and the other which assumes perpetual constant debt. In this case, Carborundum projects a relatively constant debt from 1977 to 1982 between $83.4M and $91.7M. Using Carborundum’s estimates in Exhibit 5, therefore, we would use the following unlevering formula.
Unlevering Formula #1:
βA = [D*(1-Tc)*βD + E*βE]/[E+D*(1-Tc)] where:
Tc = 50% (given)
βD= 0.31[2]
βE = 1.16[3]
D= 186.2M[4]
E= 410[5]
βA = [D*(1-Tc)*βD + E*βE]/[E+D*(1-Tc)] = [75.8*(1-.5)*.31 + 424.5*1.16]/[424.4+75.8*(1-.5)] = 1.00.
βA = 1.00
However, Kennecott’s projected estimates in Exhibit 7 suggest a relatively constant balance of debt/assets of 26.5% or a debt/equity ratio of 53.8%. First Boston presumably created these estimates believing that after the acquisition they would continually rebalance to attempt to maintain a relatively stable debt/equity ratio of 54%. This would suggest that we should use the following unlevering formula:
Unlevering Formula #2:
βA = [D/(D+E)]*βD + [E/(D+E)]*βE] where:
Tc = 50% (given), βD = 0.31, βE = 1.16
D= 186.2M[6]
E= 410[7]
βA = .89
I have used the Asset Beta from the first unlevering formula because I assume that the 35% assumed by First Boston were based on assumptions and discussions with Kennecott managers and that this represents their intention to have a constant debt/equity ratio moving forward.
At what rate should the cash flow be discounted?
rUe = rf + βU*(rm - rf) where
βU = βA = .89
rf = 6.3%[8]
rm - rf = 8%[9]
rUe = 6.3% + .89*8% = 13.5%
This is substantially higher than the 10.5% discount rate that Kennecott’s internal group used to justify a price up to $85/share.
What is terminal value should we use?
First Boston has assumed a terminal value using the multiples method. They assume a value based on 10% of earnings, presumably from looking at the multiples from Exhibit 8 which all had tender offers above 9 times net income. Therefore, using the multiples method this seems to be an appropriate number to use.
However, using a cash flow/perpetuity approach, this terminal value becomes less substantial. For example, I calculated the terminal value using the equation:
(FCF1987*(1+g)/(rUe-g) where g represents the growth rate in steady state. I used a growth rate of 5%. It is important to note that NWC is estimated by First Boston to be growing at 9% up through 1987, which seems high at steady state and therefore could skew the results.
Calculating the Debt Tax Shield
Using the APV valuation method requires calculating the value of the debt tax shield. We have been given a rate on Carborundum debt of 10%. This is probably appropriate because it reflects the risk of the debt that is throwing off the tax shields. This will generally lead to slightly high estimates. We could also use the return on assets which would lead to a lower debt tax shield. This value reflects the risk that the firm will generate profits and you need profits to use the tax shields. In this case, there is a strong history of profits for Carborundum so I have chosen to use iD=10% as the discount rate for the tax shield. This represents an optimistic choice given that making profits is certainly riskier than just being able to make the interest payment.
What is the actual Adjusted Present Value of the Company?
After outlining all the assumptions above, the adjusted present value of Carborundum has been calculated to be $428M or a maximum of $53/share.
Please identify the main assumptions or other factors that are the most critical in arriving at your estimate of your maximum price you are willing to pay.
There are a number of assumptions that were critical to arriving at this estimate.
Tax Rate: First, we were given an effective tax rate of 50%. If this assumption is incorrect it can drastically change the value of the debt tax shield and therefore the valuation. For example, a tax rate of 30% reduces the valuation by $60M.
Debt Beta: I assumed a debt beta of .31 believing that the long-term debt was not investment grade. However, if the debt is higher quality and the debt beta is reduced to .10, the valuation of the company goes up about $25M.
Equity Beta: I used the equity beta calculated in 1977 of 1.16. However, using the 60 month range from 1.04 to 1.26 can change the valuation by as much as $50M.
Unlevering Formula: I chose the unlevering formula assuming that Carborunda would maintain a constant debt/equity ratio moving forward rather than a constant level of debt. This affected the calculation of the asset beta. Using the other formula reduces the valuation by about $40M
Choosing Risk Free Rate: I chose a risk free rate of 6.3% for the reasons outlined above (7.8%-1.5%). However, if I simply use the long-term bond rate of 7.8% as is and still maintain the equity premium of 8% as stated in the problem, my valuation is reduced by $65M holding everything else constant.
Growth Rate: In calculating the terminal value, I assumed a growth rate of 5%. If you use a more conservative 2%, the valuation decreases by $70M. If you increase the growth rate to the projected growth in NWC of 9%, you get a valuation very close to the $85/share (gross increase in valuation of $220M) that First Boston claimed would still be valuable. However, it is pretty unrealistic to believe that the company, in steady state, will grow forever at 9%.
Cost of Debt: The 10% cost of debt for Carborundum did not effect the valuation substantially when reduced to the risk free rate or increased to as much as 15%. This was not a critical assumption compared to many of the others.
As a non-management director of Kennecott, how would you vote on the resolution at the end of the cases? What do you think of the advice tendered by the investment bankers?
I would vote against making a cash tender offer to shareholders at $66/share. There do not appear to be substantial synergies between these two businesses, and the core financial analysis suggests that Carborundum is not worth more than $53/share unless some of the assumptions above are loosened. Therefore, I consider the advice of the investment bankers to be poor. I think the investment bankers were encouraging this deal to get through so that they could take a percentage and increase their fees. This deal appears dilutive to me.
[1] Peabody had negative profit in 1970, 1971 and 1973 which clearly did not help smooth out Kennecott’s wide swings. See Exhibit 1.
[2] According to “A Note on Discounted Cash Flow Valuation Methods” by Steven Kaplan, .2 is a good estimate of βD for long-term debt in a company with an investment grade rating and .3-.4 is a good estimate for non-investment grade long-term debt. Here, it is unclear whether Carborundum’s debt is investment grade. I have assumed a corporate lower grade debt beta of .31.
[3] See Exhibit 5.
[4] This is the Carborundum’s long-term debt as of 1977, adjusted to reflect the acquisition by Kennecott per Exhibit 7.
[5] There is a choice between using the shareholder’s equity at historical cost or shareholder’s equity based on replacement cost. Given that replacement cost is a better indication of the actual market value, it might make sense to have used the replacement costs. However, as they were not readily available for 1977 I used the adjusted shareholder equity based on historical costs.
[6] Used same debt value to be consistent with prior unlevering formula.
[7] Id.
[8] The long-term T bonds is 7.8%. However, ordinarily if I used the long-term T-bond rate for the riskfree rate, I would use a risk premium of about 6.5% because that is the return by which the market exceeded T-bonds over the last 50 years according to Kaplan’s article. However, in this case we are told to use a market premium of 8% which is generally used when a with a short rate on a T-bill. Therefore, I am using the market premium of 8% but I have chosen to drop the long-rate by 1.5% to use a final rf of 6.3%.
[9] Since the return on the market exceeded T Bonds by about 6.6% per year, a risk premium of about 6.5% is reasonable.