I am given values for the AC voltage, AC frequency, the load in kW, and a lagging power factor of 0.6 and I am told to calculate the value of capacitor I would need to add to change the power factor to 0.9. I'm following the steps below but when I use the values I come up with to check my work it comes out wrong and I don't know what I'm doing wrong.

Here's what I'm doing;

1) I am assuming since the value of the load is given in kW and not VA that the value is real power (P). Using this and the power factor I am calculating apparent power S, reactive power Q, and the power factor angle.

2) I am assuming as the real power P is a component of the resistive inductance of the load that it will not change when a capacitor is added.

3) I am using the required power factor value 0.9 to calculate the power factor angle and using that along with the real power P value to calculate new values for apparent power (S2) and reactive power (Q2).

4) I am subtracting the new reactive power Q2 from Q1 to obtain the reactive power (Q3) that the capacitor will need to provide.

5) Using Q3 I am then calculating the impedance and then the capacitance of the capacitor placed in parallel.

6) As a sanity check I am calculating the impedance of the load and using that value to calculate total P, S, and R of the circuit and I get completely different results.

My suspicion is that I'm messing up my sanity check somewhere but I'm really not sure.

Any help would be most appreciated.