## DCF Example

The following post is related to the analysis of the DCF example provided with the book Investment Banking by Rosenbaum and Pearl. The example analyse a private company ValueCo,  for which we are provided historical information but no future projections. Through the analysis we learn how professional bankers define their assumptions and which type of financial data sources they use to reinforce them.

Following some notes related to the DCF process:

• Step 1, study the target and determine key performance drivers
• Step 2,  project free cash flow: from the historical analysis and the analysis of public comparables, we can build 2 excel sheets with the assumptions. The assumptions are related to: 1) Sales Growth, 2) COGS (Cost of Goods Sold), 3) SG&A (Selling, General, and Administrative), 4) D&A (Depreciation and Amortization), 5) CAPEX (capital expenditure), 6) DSO (Days Sale Outstanding), 7) DIH (Days Inventory Held), 8) PEO (Prepaid and Other Current Assets), 9) DPO (Days Payable Outstanding), 10) AL (Accrued Liabilities), 11) OCL (Other Current Liabilities). All variables are a percentage of sales or days in the case of DSO, DIH, and DPO. Using the previous assumptions we can project the NWC=AR+I+PEO-AP-AL-OCL, and the FCF=EBIT(1-T)+DA- ∆NWC- CAPEX (AR=DSO*Sales/365, I=DIH*COGS/365, AP=DPO*COGS/365).  The projections are normally done over 5 years for companies with more predictable results, 10 years otherwise. The current year and future assumptions are estimated considering the historical performances and comparing them with companies in the peer group of traded companies. Note that only the sale growth varies in the different years, the other assumption are constant
• Step 3, calculate the WACC using the standard formula: Ke*(E/Ev)+Kd*(1-T)*(D/Ev). The D/Ev value (Ev, is the enterprise value) is the target debt to total capitalization ratio. This value is set to 30% considering the mean average of the peer companies. Kd is assumed to be the same of the current one: LIBOR+300bps, or 6%. Ke is calculated using the CAPM formula Re=Rf + βL * (Rm-Rf) + SP (SP, size premium). Rf is assumed to be 4% using the interpolated yield on 20-year U.S. Treasury. Rm-Rf is obtained from Ibbotson SBBI Valuation Yearbook using the period 1927-2007. βL is calculated using the βL of peer companies. These companies are traded and from Barra we can obtain the predicted levered beta. From the βL values, we can calculate the βu and finally the maean is used to obtain the βL for the targeted capital structure. The βL value is 1.2 and the βu is 0.95. In these calculations the Tax rate used is 38%. The Ke value is 14.1%. Finally we obtain the WACC including a size premium of 1.65%. This is the Low-Cap decile size premium based on market capitalization, as per Ibbotson. The WACC obtained from the previous assumptions is 11%. To have a perception on how the WACC can change, we can define a table with different WACC values obtained changing the debt-to-total capitalization ratio and the debt cost
• Step 4, calculate the terminal value (TV) using the EMM (Exit Multiple Method) approach. The EBIDTA of the last year projections is multiplied by an exit multiple. The multiple used is 7 because the peer companies tend to trade in a range of 6.5-7.5 x LTM EBIDTA (LTM: last twelve months). From the TV we can calculate the implied growth rate. In this case we obtain a TV of 1326.3\$ using a multiple of 7 (implied growth rate is 3%). With this assumption the present value of the TV represents the 69.4% of the enterprise value. Note that the TV is discounted using the factor 1/(1+WACC)^5
• Step 5, calculate the equity value from the Ev subtracting the debt and adding the cash. From this value we can evaluate the share price knowing the number of shares outstanding

Now that we have a very detailed valuation framework we can use it to understand why analyst are valuing Apple shares at 635\$, or Google shares at 670\$. We can compare our results with the Damodaran valuation that we can find in the following post for Apple and in the following one for Google.

Are you ready to crunch numbers?