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Dear Mr Moffat,
I could not fully understand the answer provided by BBP for the following question and even though I got a slightly different answer I think my approach is correct. Could you please correct me if I am wrong.
Would you mind explaining the answer provided by the BBP?Paulo plans to buy a holiday villa in five years time for cash. He estimates the cost will be $1.5M. He plans to set aside the same amount of funds each year for 5 years, starting immediately and earning a rate of 10% interest per annum compound.
To the nearest $100, how much does he need to set aside each year?My approach:
As it starts immediately there is $300,000 (1.5M/5) @ 1
From 1-4 1,200,000.00 *0.683 (discount rate of 10% @ year 4) 819,600Therefore 819,000+300,000= 1,119,600 is the NPV in 5 years time which divided by 5 give the amount to set aside each year
223,920
Book answer:
Present value of holiday home 1.5M @ 0.621= 931,500 (PV of annuity)
931,500/ 4.170 (which is 1+3.170) = 223.381I believe is only matter or rounding, but still no clear the logic used by the book answer.
Thank you very much for you help
Gabriella
The difference is not due to rounding!!
They need 1.5M in 5 years time. If they set aside 300,000 each year then at the end of 5 years they will have much more than 1.5M in 5 years time (because of interest being earned).
The PV of the amount each year must be the same as the PV of 1.5M in 5 year time.
The PV of 1.5M in 5 years is 1.5M x 0.621 = 931,500.
The PV of $X per year from 0 to 4 is X x (1 + 3.170).
If you make this equal to 931,500 you will get X to be 223,381.Dear Sir,
Thank you for your reply. Now it is more clear.
I have another question about NPV which I have a doubt.AM Co will receive a perpetuity starting in 2 years time of $10,000 per annum, increasing by the rate of inflation (which is 2%).
What is the present value of this perpetuity assuming a money cost of capital of 10.2%?
Answer $115,740
I work out the answer as per below:
Nominal rate= Real rate* Interest Rate
Therefore1.102/1.02 = 1.080 = 8%
Perpetuity is 1/0.08 = 12.5
Less from year 0 – 1 0.926Equal 11.574
$10,000 *11.574 = 115,740.
Now, Am I correct if I say that when we calculate the perpetuity the inflation needs to be ignored therefore we should use only the real rate.
The reason is because the amount is constant in the future.
Thanks in advance for your help
Regards
Gabriella
Everything that you have done would be correct, if the $10,000 was quoted at current prices.
If it was, then the actual first receipt at time 2 would be 10,000 x 1.02^2.
However, if the actual first receipt is cash of 10,000 then this needs restating at current prices. That simply means dividing your answer by 1.02^2 – everything else is fine.
Sorry Mr Moffat,
I could not understand your answer.
What did you mean by “current price”?
What do you mean by ” That simply means dividing your answer by 1.02^2 – everything else is fine”My understanding is that when calculating the perpetuity the inflation needs to be ignored that why I use the real rate. I don t understand your calculation.
Could you please help me to clarify my confusion?
Thanks
Gabriella
You can only apply the real rate to flows at current prices.
Have you watched my free lectures on investment appraisal with inflation, because I do explain this?
Dear Mr Moffat,
Sorry for disturbing you with the same question. I watched the lecture and now the current price and real rate are more clear.
However, to make sure that everything clear I hope you won ‘t mind checking my consideration below:
When we calculate the perpetuity we should use the current price and real rate, therefore if the question gives receipt in actual money that the amount needs to be restarting at current price. Additionally we should use only the real rate.
The question did not say if $10K was at the current price or actual price.
When I answered the question I supposed $10K was at the current price therefore I had only to recalculate the real rate to get the present value of the perpetuity.Thanks again for your help
GabriellaWhat you have written is completely correct.
The question should have made it more clear that $10,000 is the actual cash amount in 2 years time (although the more I read it, the more I think that it does imply this – it would be strange for it to mean $10,000 at current prices without it actually having said that 🙂 )
Dear Mr Moffat,
In the question that was asked by Gabriella first could you please explain to me the timing of the cash flows. Why is it 0 to 4 and not 1 to 5?
Because the question says that the payments start immediately (i.e. time 0)
SIr, I wasn’t able to do this in the way you suggested, I did it like
X * (1.1^5+1.1^4+1.1^3+1.1^2+1.1)=1500000 and I found X.Pleeease please help me understand what you’ve said:
”The PV of the amount each year must be the same as the PV of 1.5M in 5 year time.” I really dont understand how 🙁
John Moffat wrote:The difference is not due to rounding!!
Talking about this.
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