(a)  In order to obtain free cash flow to equity (FCFE), the two adjustments that Shaar must make to cash flow from operations (CFO) are

 i.   CFO does not consider the investing activities in long-term assets, especially the plant and equipment investments. All cash flows corresponding to those necessary investments are not available to stock holders and hence this must be subtracted from CFO in order to obtain FCFE.

 ii. CFO also does not account for the amount of capital supplied to the firm by debt holders or bond investors. The new borrowings, net of debt repayment, are cash flows which are available to stock holders and hence must be added to CFO to arrive at FCFE.

(b)  Let us look into each of the five supplemental notes one by one

Note 1: Rio National had $75 million in capital expenditures during the year.

Net Negative Adjustment: negative $75 million

The cash flows required for capital expenditures (-$75 million) are not available to the stockholders and must be subtracted from net income to get FCFE.

Note 2: A piece of equipment that was originally purchased for $10 million was sold for $7 million at year-end, when it had a net book value of $3 million. Equipment sales are unusual for Rio National.

Net Positive Adjustment: positive $3 million

In determining FCFE, only cash flow investments in fixed capital should be accounted. The selling price of equipment ($7 million) is a cash inflow currently available to stockholders and should be added to net income. But the gain over book value that was realized during the equipment sale ($4 million) is already included in the net income. Since the total sale is cash, the $3 million net book value must also be added to net income in addition to the gain. Therefore, the adjustment calculation is as follows $7 million cash received - $4 million gain recorded in net income = $3 million additional cash received added to net income to obtain FCFE.

Note 3: The decrease in long-term debt represents an unscheduled principal repayment; there was no new borrowing during the year.

Net Negative Adjustment: negative $5 million

The unscheduled debt repayment cash flow ($240 million - $245 million = -$5 million) is an amount not available to stockholders and must be subtracted from net income to get FCFE.

Note 4: On 1 January 2002, the company received cash from issuing 400,000 shares of common equity at a price of $25.00 per share.

No adjustment

Transactions between the firm and its shareholders do not have an effect on FCFE. Therefore, no adjustment to net income is required with respect to the issuance of new shares to get FCFE.

Note 5: A new appraisal during the year increased the estimated market value of land held for investment by $2 million, which was not recognized in 2002 income.

No adjustment

The increased market value of the land did not generate any cash flow and was not reflected in net income. Only when there is a real cash transaction involved, this will affect net income and hence FCFE. Hence no adjustment to net income is required to determine FCFE.

(c)   Rio National's Free cash flow to equity (FCFE) is calculated as follows:

FCFE = NI + NCC - FCINV - WCINV + Net Borrowing

Where NI - net income

NCC - non-cash charges

FCINV - investment in fixed capital

WCINV - investment in working capital

Calculation:

NCC = depreciation & amortization - gain on sale of equipment (note 2) = $71.17 - $4 = $67.17

FCINV = Capital expenditures (note 1) - cash on sale (note 2) = $75 - $7 = $68

WCINV = Increase in accounts receivable + Increase in inventory + decrease in accounts payable

                = ($30 - $27) + ($209.06 - $189.06) + ($26.05 - $25.05) = $24

Net borrowing = decrease in long-term debt = $240 - $245 = -$5

Hence FCFE = $30.16 + $67.17 - $68 - $24 + (-$5) = $0.33

Thus Rio National's free cash flow to equity for the year 2002 was determined to be $0.33 million.