According to CFA book, when valuing a target company using discounted cash flow method, FCFF is used. But when acquiring a company’s stock, do we suppose to discount FCFE to get the value of the target equity, not to discount FCFF to get the value of the whole firm? Because you are only acquiring the equity of the firm, not the whole firm (debt + equity).
You can calculate the value of the whole firm using FCFF, then deduct the market value of debt (properly: liabilities) to get the value of equity.
FCFF or FCFE valuation approach are preferable when sufficient data for accurate forecasts is available, for example, when valuing mature companies. Both methods should give you the same equity value, so you can use either. Calculating debt value is somewhat straightforward (depending on the complexity of the debt structure), so calculating FCFF and then subtracting the market value of debt should give a value very similar to the one obtained from the FCFE approach.
When acquirers purchase the stock of the target, they should value the target equity using FCFE discount method.
When acquirers purchase the asset of the target, they should value the target as a whole using FCFF discount method.
Is that right?
Yup, it is right. However, nothing prevents me to use FCFF to calculate the equity value of a company, just make the necessary adjustments.
Thank you all !
It’s our pleasure 
Indeed, it is.