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IF a question provide a discount factor, and cash flows at constant price. How the factor is to be determined real discount factor or nominal discount factor. Additionally, are discount factors done take into account inflation.
You use the nominal cost of capital (the actual cost of capital) to discount the nominal cash flows (the actual cash flows – including inflation).
You use the real cost of capital (the cost of capital without inflation – using the formula on the formula sheet) to discount the real cash flows (the cash flows at current prices, excluding inflation )
The discount factors themselves are nothing to do with inflation – you use the discount factors applicable to whichever cost of capital you are using (as explained above).
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