Using market value to calculate cost of debt for WACC

Hello sir, my question is why we use the current market value of debt in order to calculate our cost of debt. I understand as I remember in you F9 lectures you mentioned that it represents our cost of rasing new debt which makes sense to me but when we use this cost of debt in our WACC calculation surely, we can underestimate our actual cost of debt or interest payments because let’s say if I issued a debt at nominal value of 100 with 10% interest payments with maturity of 5 years and redemption at the nominal value. My interest payments or cost of debt would be 10% but if the market value changes to say 110 the IRR or cost of debt would come to 7.53%.
Now it is mentioned in the study hub and as I recall in one of your lectures as well that the reason we do not include our interest payments in Investment appraisal is because it is reflected in our WACC. But if we look at the above example that I gave discounting at WACC would understate our cost of debt and I have not seen anywhere a satisfactory explanation for this. Hopefully you can clear up the confusion. Thank u!