Question

An increase in the market risk premium is likely to increase WACC?

Answer 1

Yes, An increase in market risk premium increases WACC.

As shown below, the WACC formula is:

WACC = (E/V x R_e) + ((D/V x R_d) x (1 – T)) -> 1

The Value of Re is calculated using the formula R_e = r_f + (r_m – r_f) * β_e-> 2

& The Value of R_d is calculated using the formula R_d = r_f + (r_m – r_f) * β_d-> 3

Where,

E = market value of the firm’s equity (market cap)

D = market value of the firm’s debt

V = total value of capital (equity plus debt)
E/V = percentage of capital that is equity
D/V = percentage of capital that is debt
Re = cost of equity (required rate of return)
Rd = cost of debt (yield to maturity on existing debt)
T = tax rate

r_f = Risk-Free rate of interest

r_m = Market Risk rate of interest

r_m-r_f is the Market Risk Premium. (i.e The extra return rate obtained over the risk-free rate by taking up the market risk)

β_{e &} β_d are the Beta's of Equity & Debt respectively

From Equations 2 & 3, It is clear that both the Cost of Equity & Cost of Debt are directly proportional to the Market risk premium. This implies that an increase in market risk premium increases both the cost of equity & debt.

However, From Equation 1; it is further clear that WACC is directly proportional to both the Cost of Equity & Cost of Debt. i.e they are positively correlated. Therefore, an increase in Market Risk Premium increases Cost of Equity & Cost of Debt which further increases the WACC as all of these three are directly proportional to each other.