Cigno Co WACC Question

Dear Sir,
For Cigno Co, they valued the cash flows of Antara Co using the combined company’s wacc. I found this strange as how are they discounting using combined companies WACC when the cash flows are only for Antara Co.

In my answer that I drafted, I took the kd as the interest ÷ Book value of debt, and then discounted the cash flows with Antara’s WACC.

My answer matches with rest of the answer in the suggested solution.
However, I do realize that interest ÷ debt may not give the correct Kd, as it would be possible interest may involve interest paid on current liabilities (such as bank overdraft). However, I would have mentioned this in my assumptions

Is my answer wrong? because i think its wrong to discount using WACC of combined company when the cash flows are only of Antara