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Hello John
In this question, cash flows are given for years 1 to 5. In year 5, it mentions that the cash flow is 125,000. The question also mentions at the end, “cash flows are expected to grow at a rate of 3% per year after year five to infinity. Assume a discount factor of 14%.”
In the working of the answer, there’s a line which states the following:
PV 6 to infinity (125,000 X 1.03)/(0.14-0.03)=1,170,454>>>>1,170,454 X 0.519 =607,466While I know that PV=FV/(1+r) n which in this case involves the 0.519, I do not understand why the inflated amount is divided by (0.14-0.03). Kindly explain.
You have not said which question you are referring to.
However, to get the present value of any inflating perpetuity we use the dividend valuation formula (it doesn’t matter whether it is dividends we are discounting – it applies to any inflating perpetuity) That is why they multiply by 1.03 (3% growth) and divide by 0.14 – 0.03 (14% discounting, 3% growth).
However that gives the PV if the first flow is in 1 years time. If the first flow is in 5 years time, then because it starts 4 years later, we have to discount our answer by 4 years at 14% (using the discount factor from the tables).
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