Examples 1, 2, 7 and 8 in Ch. 12 and example 1 in Ch. 13. For examples 1 and 2 in Ch. 12, assume the net cash flow is $2,000,000, the tax rate is 40% and the cost of common equity is 10% which is computed using the CAPM equation.

You do not have to do any calculations for this HW assignment. You only need to explain, in a few sentences, what each example means; hence, this HW assignment is strictly qualitative. However, you should be familiar with the calculations since there will be quantitative questions, on the final exam, based on these examples.

- After making debt service payments and paying taxes, the firm pays dividends to distribute any remaining free cash flows to the equity shareholders each year. - The cost of equity capital is 10 percent. Example 1: Value of Common Equity in an All-Equity Firm Assume that the common equity shareholders have financed the asset entirely with $10 million of equity capital. We can determine the value of the common equity investment to the shareholders using the present value of free cash flows for common equity shareholders. The free cash flow to common equity shareholders each year will be as follows: The value to the shareholders of the common equity in the firm is $12,000,000 (=$1,200,000/0.10). Dividing by the discount rate is appropriate because the $1.2 million annual free cash flow for common equity is a perpetuity with no growth. This investment is worth $12 million to those shareholders (a gain of $2 million over the original investment of $10 million) because of the present value of the free cash flows the investment will generate and that will in turn be paid out as dividends to the shareholders. Therefore, we would determine the same value for the investment using the dividends-based valuation model as shown in Example 5 in Chapter 11. Example 2: Value of Common Equity in a Firm with Debt Financing For this example, we will make the same assumptions as in the preceding example, except we will now make the following additional assumptions to use both debt and equity financing: - The equity shareholders finance a portion of the investment in the asset with $4 million of equity capital. - The firm finances the remainder of the asset using $6 million of debt capital. - This amount of debt in the firm's capital structure does not alter substantially the risk of the firm to the equity investors, so they continue to require a 10 percent rate of return. - The debt is issued at par, and it is less risky than equity; so the debtholders demand interest of only 6 percent each year, payable at the end of each year. - Interest expense is deductible for income tax purposes. We can again determine the value of the common equity investment using the present value of free cash flows for common equity shareholders. Note that this example is essentially the same as Example 6 in Chapter 11, except that the valuation focus changes from dividends to free cash flows. The free cash flow available to common equity shareholders each year is as follows: The value of the common equity to the shareholders in the firm is $9,840,000 (=$984,000/0.10). Dividing by the discount rate is appropriate because the $984,000 annual free cash flow for common equity is a perpetuity with no growth. Note that inthis example, the present value of the gain to the common equity sharehorders in excess of their initial investment is $5,840,000(=$9,840,000$4,000,000). The gain to the shareholders is $3,840,000(=$5,840,000$2,000,000) larger in this example than in the previous example because (1) the debt capital is less expensive than the equity capital ( 6 percent rather than 10 percent on $6,000,000 of financing), creating $2,400,000 of value for equity shareholders from capital structure leverage [=($6,000,000{0.100.06})/0.10], and (2) the net tax savings from interest expense creates $1,440,000 of value for equity shareholders [=($800,000$656,000)/0.10, or, alternatively, =($360,000 interest deduction 0.40 tax rate)/0.10]. Example 7: Nominal versus Real Free Cash Flows A firm owns an asset that it expects to sell one year from today for $115.5 million. The firm expects the general price level to increase 10 percent during this period. The real interest rate is 5 percent. The nominal discount rate should be 15.5 percent to measure the compound effects of the real rate of interest and inflation [0.155=(1.101.05)1]. Discounting nominal or real free cash flows, the present value of the asset to the firm is $100 million, as shown: In both computations, we derived the value of the equity of the firm by computing the present value of the free cash flows to common equity shareholders. As a practical matter, analysts usually find it more straightforward to discount nominal free cash flows using nominal discount rates than to adjust nominal free cash flows to real free cash flows and then discount real free cash flows using real interest rates. Discount rates derived from the CAPM are nominal because the risk-free rate component incorporates expected inflation. Further, stated and effective interest rates on long-term debt also are nominal because they incorporate expected inflation rates. Thus, readily available or easily estimable discount typically deduct the costs of debt capital but cannot deduct mic cosss or equity capital. Example 8: Tax Effects on Free Cash Flows Suppose the firm faces the following costs of capital: Assume that this firm expects to generate $90 million of pretax-free cash flows and \$54 million of after-tax free cash flows [ =(10.40)$90 million] one year from today. This firm would be valued using pretax and after-tax amounts (assuming a one-year horizon) as follows: These values are not equivalent because cash inflows from assets are taxed at 40 percent and cash outflows to service debt give rise to a tax savings of 40 percent. However, the cost of equity capital does not provide a tax benefit. The appropriate valuation in this case is $47.37 million. Thus, the analyst should use after-tax free cash flows and the after-tax cost of capital. Selecting a Forecast Horizon The analyst will need to project periodic free cash flows over the remaining expected life of the resource to be valued. This life is a finite number of years for a resource with a finite physical life, such as a machine or a building, or a financial instrument with a finite stated maturity, such as a bond, a mortgage, or a lease. But an equity security is a resource that has an indefinite life; therefore, the analyst must project future periodic free cash flows that, in theory, could extend to infinity. As a practical matter, the analyst cannot precisely predict a firm's free cash flows very many years into the future. Therefore, analysts develop specific projections of income statements and balance sheets for the firm and use them to derive forecasts of free cash flows over an explicit forecast horizon (for example, five or ten years) depending on the industry, the maturity of the firm, and the expected growth and predictability of the firm's cash flows. After the explicit forecast horizon, analysts then use general growth assumptions to project the future income statements and balance sheets and use them to derive the free cash flows that will persist each period to infinity. Therefore, the - After making debt service payments and paying taxes, the firm pays dividends to distribute any remaining free cash flows to the equity shareholders each year. - The cost of equity capital is 10 percent. Example 1: Value of Common Equity in an All-Equity Firm Assume that the common equity shareholders have financed the asset entirely with $10 million of equity capital. We can determine the value of the common equity investment to the shareholders using the present value of free cash flows for common equity shareholders. The free cash flow to common equity shareholders each year will be as follows: The value to the shareholders of the common equity in the firm is $12,000,000 (=$1,200,000/0.10). Dividing by the discount rate is appropriate because the $1.2 million annual free cash flow for common equity is a perpetuity with no growth. This investment is worth $12 million to those shareholders (a gain of $2 million over the original investment of $10 million) because of the present value of the free cash flows the investment will generate and that will in turn be paid out as dividends to the shareholders. Therefore, we would determine the same value for the investment using the dividends-based valuation model as shown in Example 5 in Chapter 11. Example 2: Value of Common Equity in a Firm with Debt Financing For this example, we will make the same assumptions as in the preceding example, except we will now make the following additional assumptions to use both debt and equity financing: - The equity shareholders finance a portion of the investment in the asset with $4 million of equity capital. - The firm finances the remainder of the asset using $6 million of debt capital. - This amount of debt in the firm's capital structure does not alter substantially the risk of the firm to the equity investors, so they continue to require a 10 percent rate of return. - The debt is issued at par, and it is less risky than equity; so the debtholders demand interest of only 6 percent each year, payable at the end of each year. - Interest expense is deductible for income tax purposes. We can again determine the value of the common equity investment using the present value of free cash flows for common equity shareholders. Note that this example is essentially the same as Example 6 in Chapter 11, except that the valuation focus changes from dividends to free cash flows. The free cash flow available to common equity shareholders each year is as follows: The value of the common equity to the shareholders in the firm is $9,840,000 (=$984,000/0.10). Dividing by the discount rate is appropriate because the $984,000 annual free cash flow for common equity is a perpetuity with no growth. Note that inthis example, the present value of the gain to the common equity sharehorders in excess of their initial investment is $5,840,000(=$9,840,000$4,000,000). The gain to the shareholders is $3,840,000(=$5,840,000$2,000,000) larger in this example than in the previous example because (1) the debt capital is less expensive than the equity capital ( 6 percent rather than 10 percent on $6,000,000 of financing), creating $2,400,000 of value for equity shareholders from capital structure leverage [=($6,000,000{0.100.06})/0.10], and (2) the net tax savings from interest expense creates $1,440,000 of value for equity shareholders [=($800,000$656,000)/0.10, or, alternatively, =($360,000 interest deduction 0.40 tax rate)/0.10]. Example 7: Nominal versus Real Free Cash Flows A firm owns an asset that it expects to sell one year from today for $115.5 million. The firm expects the general price level to increase 10 percent during this period. The real interest rate is 5 percent. The nominal discount rate should be 15.5 percent to measure the compound effects of the real rate of interest and inflation [0.155=(1.101.05)1]. Discounting nominal or real free cash flows, the present value of the asset to the firm is $100 million, as shown: In both computations, we derived the value of the equity of the firm by computing the present value of the free cash flows to common equity shareholders. As a practical matter, analysts usually find it more straightforward to discount nominal free cash flows using nominal discount rates than to adjust nominal free cash flows to real free cash flows and then discount real free cash flows using real interest rates. Discount rates derived from the CAPM are nominal because the risk-free rate component incorporates expected inflation. Further, stated and effective interest rates on long-term debt also are nominal because they incorporate expected inflation rates. Thus, readily available or easily estimable discount typically deduct the costs of debt capital but cannot deduct mic cosss or equity capital. Example 8: Tax Effects on Free Cash Flows Suppose the firm faces the following costs of capital: Assume that this firm expects to generate $90 million of pretax-free cash flows and \$54 million of after-tax free cash flows [ =(10.40)$90 million] one year from today. This firm would be valued using pretax and after-tax amounts (assuming a one-year horizon) as follows: These values are not equivalent because cash inflows from assets are taxed at 40 percent and cash outflows to service debt give rise to a tax savings of 40 percent. However, the cost of equity capital does not provide a tax benefit. The appropriate valuation in this case is $47.37 million. Thus, the analyst should use after-tax free cash flows and the after-tax cost of capital. Selecting a Forecast Horizon The analyst will need to project periodic free cash flows over the remaining expected life of the resource to be valued. This life is a finite number of years for a resource with a finite physical life, such as a machine or a building, or a financial instrument with a finite stated maturity, such as a bond, a mortgage, or a lease. But an equity security is a resource that has an indefinite life; therefore, the analyst must project future periodic free cash flows that, in theory, could extend to infinity. As a practical matter, the analyst cannot precisely predict a firm's free cash flows very many years into the future. Therefore, analysts develop specific projections of income statements and balance sheets for the firm and use them to derive forecasts of free cash flows over an explicit forecast horizon (for example, five or ten years) depending on the industry, the maturity of the firm, and the expected growth and predictability of the firm's cash flows. After the explicit forecast horizon, analysts then use general growth assumptions to project the future income statements and balance sheets and use them to derive the free cash flows that will persist each period to infinity. Therefore, the