Is there a way to solve without iteration?

Given that a firm’s current dividend is $2.00, the forecasted growth is 7% for the next two years and 5% thereafter, and the current value of the firm’s shares is $54.50, what is the required rate of return?

You can just use common sense to solve it. The terminal value at the end of year 2 P2 is $2*1.07^2*1.05/(k-.05)

D1 = $2*1.07, D2 = $2*1.07^2.

P0 = D1/(1+k)+D2/(1+k)^2+P2/(1+k)^2.

Then plug a few values of k - 9% is the solution. I don’t think it’s possible to solve the problem without iterations because you are dealing with a cubic equation. There are formulas for roots but it’s better to assume that those formulas are way outside of the scope of the CFA exams.

There is no iterative process involved here. Assuming maratikus’ solution is correct (I didn’t really look at it), it’s just a multivariable function. There is no way to solve the problem without solving two equations, but that’s not iterative.

it is a cubic equation. you have a r^3 term on the denominator.

so you could do - take value 1, find RHS

take another value 2 - find RHS

perform a crude linear interpolation to arrive at a “approximate” answer. Approximate because it is a cubic equation.

Equation: 2.14/(1+r) + 2.14*1.07/(1+r)^2 + 2.14*1.07*1.05/(r-0.05)(1+r)^2

r = 7% Equation evaluates to: 2 + 2 + 105 = 109

r = 10% RHS = 45.84

so linear interpolation: (54.5 - 45.84)/(109-45.84)*(10-7) + 7 = 9.59