basics of capital budgeting 2: WACC

1) How does a change in the D/E ratio impact returns on equity? 2) what is the formula for return on equity?

1) An increase in leverage increases equity returns 2) r_E = r_A + (D/E) * (r_A - r_D) →Think about it as return on investment. Assuming you get the same amount at the end of the project, if you invest less to start you will get a higher % return

debt capacity (D_t) 1) what is the definition of debt capacity (D_t) 2) what is the formula for debt capacity (D_t)

1) Debt capacity (D_t) = the amount of debt the firm must add/subtract at each time period t in order to maintain its target D/V ratio (d) 2) D_t = V_L_t * d

debt to equity ratio what is it? what does it indicate?

1) Debt to equity ratio = D/E 2) indicates how much debt a firm is using to finance its assets relative to the amount of value represented in shareholders equity

1) What is the debt to value ratio (d) equation? *****Q: I actually dont know if the debt to value ratio and the debt to equity ratio are the same thing***** CHECK --FIGURED out that they're not the same thing, but beware of changes you might have made and not spotted / fixed after figuring it out

1) Debt to value ratio (d): → d = D/V_L OR →d = D/D+E

Computing levered firm value and the value of equity using WACC: 1) What are the 2 high level steps required and what does each step give you? 2) what does the formula you use in the last step depend on?

1) estimate FCFs to an unlevered firm (or project) →FCF = NOPLAT - ∆NWC - CapEx + depreciation 2) discount the unlevered FCFs with the WACC: --> gives you the value of the levered firm (V_L) NOTE: formula you use to discount the FCFs depends on if project is finite or infinite (i.e. has a terminal value)

What are the components of the WACC formula? 1) r_D 2) 1-t_C 3) (D/V) 4) r_E 5) (E/V)

1) r_D = the required return on the firm's debt financing →should reflect the current market rates the firm pays for debt →r_D = total interest payments / firm's avg debt over the last year →I think ERWIN just took weighted avg of required returns for different debt levels of the firm??? 2) 1-t_C = the tax adjustment for interest expense →interest paid on debt reduces NI, and therefore reduces tax payements →The value of this interest tax shield depends on the tax rate 3) D/V = debt to value ratio →The % of firm value comprised of debt 4) r_E = cost of equity →calculate using CAPM 5) E/V = equity to value ratio →The % of firm value comprised of equity →based on (stock price * shares outstanding)

What is the relationship between unlevered return and WACC when D/V ratio (d) is constant: 1) formula for WACC as a function of unlevered return 2) unlevered return (r_U) as a function of WACC 3) alternative formula for unlevered return (r_U)

1) r_WACC = r_U - d * r_D * c OR 2) r_U = r_WACC + d * r_D * c NOTE: C = the corporate tax rate 3) r_U can also be calculated as follows: r_U = d * r_D + (1-d) * r_E

Keeping the D/E ratio constant: implications for how total debt will change with new investment

1) undertaking a project adds new assets to the firm with initial market value equal to V_L_0 2) to maintain a constant D/V ratio (d), the firm will need to raise new debt, by using cash and/or borrowing at the initial time of the project 3) Throughout the life of the project, the value of the firms assets will change as the project delivers its CF's. 3b) As the value of the firms assets change, the firm must change its debt level to maintain its constant D/V ratio (d)

WACC 1) what does WACC stand for? 2) what is the assumption required for WACC to work? 2b) what does this assumption imply that makes it ok to use WACC?

1) weighted average cost of capital 2) WACC only works under the assumption that the firm maintains a fixed debt to value ratio (d) 2b) This assumption implies that the risk of the firms debt and equity (and thus its WACC) will not change over time due to leverage changes. Since under this assumption r_WACC remains the same through time, it is ok to use WACC

Discounting unlevered FCFs to find V_L 1) what factor determines which formula you use to discount FCFs? 2) what is the formula to discount the unlevered FCFs of a finite project that ends at time T 3) What are the two formulas that one could use to discount the unlevered FCFs from an infinitely lived project?

1) you use a different formula to discount the unlevered FCFs of a project if the project is finite (ends at some time T) or infinitely lived 2) for a finitely lived project that stops at time T, the levered value of the project at time 0 is: V_L_0 = ∑ _T_t=1 = [ (FCF_t) / (1+r_WACC)^t ] 3) In the case of an infinitely lived project, you can do one of two things: 3a) Project all future CFs and then discount them: V_L_0 = ∑ _T_t=1 = [ (FCF_t) / (1+r_WACC)^t ] →formula is the same as for a finite project 3b) Project FCFs up to some time T and compute the TV separately V_L_0 = ∑ _T_t=1 = [ (FCF_t) / (1+r_WACC)^t ] + [ TV_T / ((1+r_WACC)^T ]

return on equity calculation 1) CAPM

Cost of equity CAPM formula: r_E = r_f + beta(r_M - r_f) →r_f = the risk free rate →B = the firm's beta (correlation between firm's returns and the markets) →r_M = the historical market return

Debt capacity formula

D_t = (V_L_t) * d --> need to compute levered continuation value for each time period before you can solve for debt capacity

Using D/E to solve for % of debt and equity (i.e. D/V and E/V)

Example: D/E = .75 1) take your given D/E ratio 2) add 1 to the D/E ratio and solve for the inverse →In excel, use the =MINVERSE function →the output is the proportion of equity (E/V) →Calculate the proportion of debt by subtracting the proportion of equity from 1 3) Check your answer by dividing the proportion of debt by the proportion of equity →answer should = the given D/E ratio

Calculating debt capacity

To calculate a project's debt capacity: 1) start with the project's FCF's and compute the LEVERED CONTINUATION VALUE at each date by discounting the future FCFs at r_WACC 1b) Levered continuation value formula: V_L_t = [ (FCF_t+1) + (V_L_t+1) ] / (1+r_WACC) 2) Once you have computed V_L_t, you can compute the debt capacity at each date using the debt capacity formula: D_t = V_L_t * d

Levered continuation value (V_L_t)

V_L_t = (FCF_t+1 + V_L_t+1) ÷ (1 + r_WACC)

what is the CAPM formula for WACC?

WACC = r_D*(1-t_C)*(D/V)+r_E*(E/V)

why can you use the same WACC to discount all CF's throughout the life of the project?

You can use the same WACC throughout the life of the project because the debt-to-equity ratio is held constant and thus the risk of the equity remains constant →if the debt to equity changes, so does the return on equity because an increase in leverage increases equity returns

unlevered return (r_U) alternative formula

r_U = d * r_D + (1-d) * r_E

what does the terminal value (TV) in the final year of the forecast period capture?

the terminal value in the final year of the forecast period captures the PV of the CF's beyond the forecast period