Real domestic return

I would like to calculate the real domestic return of a foreign asset

What I know

Real price is $$P_{Real, t} = \frac{P_{Nominal, t}}{CPI_t}$$

where CPI is consumer price index.

And I know that the nominal domestic return of a foreign asset is calculated as follows:

$$R_{Nominal, Domestic, t} = \frac{(P_{Nominal, Domestic, t}) \times E_t}{(P_{Nominal, Domestic, t-1}) \times E_{t-1}}$$

Then, when I want to calculate the real domestic return of a foreign asset, would I do as follows?

$$R_{Nominal, Domestic, t} = \frac{((P_{Nominal, Domestic, t}) \times E_t )/ CPI_t}{((P_{Nominal, Domestic, t-1}) \times E_{t-1}) /CPI_{t-1}}$$

where E shows the exchange rate.

Is this way true? How can I calculate?