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Hello John,
A Co will receive a perpetuity starting in 2 years time of $10,000 per year, increasing by the rate on inflation (which is 2%)
What is the present value of this perpetuity assuming a money cost of capital of 10.2?
1. The answer is $115,175
2. In the question the money rate was converted to real rate and hence was used to obtain the answer. Could you please explain why so?Thanks
In questions where it is not a perpetuity, we inflate the flows to get the nominal cash flows and then discount at the nominal/money cost of capital.
However this is not possible to do when it is a perpetuity and so we discount the real cash flows (without inflation) at the real cost of capital (without inflation).
Hello Sir, can you please tell me when can Labour be considered as a Relevant cost and when not?
As in all NPV calculations, if doing the new project will mean that the total labour cost to the company will increase, then the increase is relevant. If the total cost to the company is not going to change then there is no relevant cash flow.
If you are asking this because of something that has puzzled you in a past exam question (or a question in the BPP Revision Kit) then say which question and I will explain 🙂
This question is from the BPP workbook: if a team of workers, costing $300,000 per year, is diverted to work on a new Project then they will stop work on existing products which earn contribution (ie sales revenue less variable cost) of $500,000, this contribution will therefore be lost (note that this assumes that labor is a variable cost).
Calculate the relevant cost associated with using the team of workers on the new project.In the Solution, they have considered both the opportunity cost and the labor cost, although the labor was already engaged on another work. Can you please tell me why have they considered labor as a relevant cost?
Hi John
Sorry to piggy back in here. In relation to the perpetuity question that adarsh raised.
How did the $115,175 come about. If the real cost was used, I thought it would have been
real = 10.2/2 =5.10. $10000/5.1= $196,078/1.859 (discounted back by 2 years) = $105,475Thanks
Grahamjatingupta:
Consider this simple example.
Suppose a company currently makes a product that has a selling price of $20, a materials cost of $4, and a labour cost of $5. So a contribution of $12.
Suppose the labour is taken for a new product (and so the current product is not made).
As a result they will lose the revenue of $20, but they will save the materials of $4. (They will still be paying the labour and so no change there). So they will lose a net $16. This is the same (and will always be the same) as the lost contribution of $12 plus the labour of $4.Grahamega:
Using the Fisher Formula, the real cost of capital = (1.102 / 1.02) – 1 = 0.080392 (or 8.0392%)
(I do suggest that you watch my free lectures where I explain this – it is certainly not 10.2/2 !!!)
Therefore the PV is (10,000 / 0.080392) x (1/1.080392) = 112,262
(The difference from the answer that adarsh quoted is due to the fact that the answer he has quoted has used 8% instead of 8.0392% and so used the tables for the extra years discounting, which is fine in the exam.)We discount the perpetuity for 1 extra year and not 2 years, because the perpetuity starts 1 year late – at time 2 instead of time 1.
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