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a project is expected to earn $5000p.a(current price) in perpetuity. inlfating at 4% per year. the first receipt will be in one year time. cost of cap. is 12%. what is the present value of receipts.
i tried several times but couldnt get the correct solution. please help.
Because it is an inflating perpetuity you have to discount the real cash flow (the current price flow) at the real cost of capital (the effective rate).
(This is explained in our free Lecture Notes and lectures).Using the Fisher formula, the real cost of capital is 1.12/1.04 – 1 = 0.0769231 (or 7.69231%)
Discounting the perpetuity in the normal way gives 5,000 / 0.0769231 = $65,000
Alternatively you can use the dividend valuation formula on the formula sheet (it works for any inflating perpetuity, not just dividends).
So PV = (5,000 x 1.04) / (0.12 – 0.04) = 65,000
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