# Valuation of a Firm Free Cash Flow and Residual Income Model

Calculating a company's firm price via the free cash flow model and via the residual income model. Please show work in Excel spreadsheet. Thank you!

Assume Co. began operations on January 1, 2001 with $100 cash and $100 equity. On January 1, it purchased a machine for $60 cash and inventory for $40 cash. During 2001 it sold half the inventory for $50 cash. On December 31, it purchased $30 more inventory in cash and paid a $10 dividend.

During 2002 the company sold inventory costing $40 for $70 cash. It purchased $20 more in inventory and paid out a $10 dividend.

During 2003, it sold the remaining inventory for $60 cash. At the end of 2003, the machine had no further value and was scrapped. Co. decided to cease operations and to pay out a liquidating dividend equal to cash on hand. Please ignore the effect of income taxes.

I. Assuming that the machine is depreciated on a straight-line basis over 3 years with no salvage value, calculate the following (show your work):

2001 2002 2003 Beginning equity Net income Dividends Ending equity Residual income

Assume that on January 1, 2001 you were able to forecast Co.'s future transactions perfectly.

(a) Calculate the firm's price as of January 1, 2001 using the free cash flow model. Use a 10% discount rate (cost of capital).

(b) Calculate the price using the Residual income model. Use a 10% cost of capital. You should get the same price as in (a).

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#### Solution Preview

The calculation are in the attached file. The income statement is made as per the data given. There is no chnage in the equity since the net income is given out as dividend. The residual income is the amount left after accounting for the cost of equity. This is given as 10%. the cost of equity on book value of 100 is 10. Subtracting this from the net income, we get the residual income as zero. The residual ...

#### Solution Summary

The solution explains the valuation of a firm using the free cash flow model and the residual income model