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Residual Income (from CFAI Qbank)

From the vignette, “Raman collects additional data for valuing PBRI using the multistage RI model. For this model, he assumes an annual growth rate of residual income of 15% during the forecast horizon of 5 years (Years 1 to 5) and discounts the terminal year’s residual income as a perpetuity.” The question asks for the discounted value of terminal RI in Year 5.

I am not sure what year to use to discount the terminal RI back to the present. PV of cont. RI in year T-1 = RI in year T/(1+r-w)

I thought T was 5, hence the discounting year of 4. But the answer discounted RI back 5 years. What am I missing here?

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Should be just like discounting CF’s with free cash flow model / Gordon growth model. You calculate the terminal value off of the last year of projected CF when long-term growth is expected to be achieved. Then you discount back using a discount factor based on the time period you determined the terminal value, in the case of your example, year 5.