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Hi Sir.
Can you help with the below please?
A wealthy business man wished to invest a sum that will guarantee his descendants a sum of 20,000 annually in perpetuity adjusted for inflation with payments starting in one years time. the sum will be invested at a rate of 10% per year. inflation is expected to average 4% per year.
how much will the business man need to invest today in order to fund this payment?
I have watched this lecture and tried to follow the steps.
https://opentuition.com/acca/f9/discounted-cash-flow-annuities-and-perpetuities/
First thing I did was..
inflate the year 1 cash flow by 4%= 20800
then calculated the perpetuity= 20,800 divided by1/r where r= 10%
=200,800since the payment starts in one year time and the perpetuity if from 1 to infinity no need to remove previous years.
I then discounted 200,800 with 0.909 (10% D.F)=189,072
Which is wrong. Can you explain where I have gone wrong.
thanks
You need to discount the current price flow at the real (or effective) discount rate.
What you have done is discount at 10% which is ignoring the fact that the cash flow will continue to inflate each year.The current price flow is 20,000, and the real rate is calculated using the fish formula on the formula sheet.
ok got it.
So I needed to have used this formula
(1+m%)= (1+r%)*(1+I%)
Where M= 10% and I = 4%
therefore r= 5.76%Therefore when using the real rate we get 20,000* 1/r …. 20,000 divided by 1/5.76%
= 347,222ok got you. thanks sir. so trying to review where I went wrong here.. effectively since there is inflation you discount at the real rate and not the money rate. If there was no inflation it would be fine to use the 10%.
Dear John,
On the Formulae sheet
(1+i)= (1+r)*(1+h) is the formula, above he states this rather differently.
Is this just a random set of letters or do they actually stand for something?
Have you watched my free lectures on this? (The lectures are a complete free course for Paper F9 and cover everything needed to be able to pass the exam well).
The reason I ask is that although I will tell you what the symbols mean, this is a formula that is better understood and remembered (because it is so often relevant in the exam) rather than having to look at the formula sheet and waste time.
In this formula, ‘i’ is the nominal (actual/money) cost of capital; “r” is the real (effective) cost of capital; and ‘h’ is the general inflation rate.
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