A ﬁrm has a WACC of 12%. It is ﬁnanced with 40% debt and 60% equity. The ﬁrm's cost of debt is 10% and its tax rate is 40%. If the ﬁrm's dividend growth rate is 8% and its current stock price is $40,
What is the value of the next dividend the ﬁrm is expected to pay?

Question

Quizplus · Accepted Answer

We can use the Gordon growth model to find the value of the next dividend:
D1 = D0(1 + g)
where:
D0 = current dividend = ?
g = dividend growth rate = 8%
Assuming a constant growth rate, we can use the formula for constant growth perpetuity to calculate the present value of all future dividends:
P0 = D1/(r - g)
where:
P0 = current stock price = $40
r = WACC = 12%
To find D1, we need to solve for it by rearranging the formula:
D1 = P0*(r - g)
D1 = $40*(12% - 8%)
D1 = $1.60
However, this is the value of the dividend before considering the effect of taxes on the cost of debt. Since interest payments on debt are tax-deductible, the cost of debt is effectively reduced by the tax rate. Thus, the after-tax cost of debt is:
after-tax cost of debt = cost of debt*(1 - tax rate)
after-tax cost of debt = 10%*(1 - 40%)
after-tax cost of debt = 6%
To calculate the WACC, we need to find the weighted average of the after-tax cost of debt and the cost of equity:
WACC = (1 - tax rate)*weight of debt*after-tax cost of debt + weight of equity*cost of equity
WACC = (1 - 40%)*40%*6% + 60%*r
12% = 24%*6% + 60%*r
r = 15%
Now we can use the formula to find D1 again:
D1 = P0*(r - g)
D1 = $40*(15% - 8%)
D1 = $2.80
Therefore, the answer is B, between $3.01 and $3.50, inclusive.

A ﬁRm Has a WACC of 12