You bought a small painting by Picasso for poundsign1, 200,000, following the re

Question

You bought a small painting by Picasso for poundsign1, 200,000, following the recommendations of your financial advisor He believes you could rent the piece to museums or collectors to earn a net income of poundsign35,000 each year. Based on your advisor's estimations, what is the internal rate of return of this investment? If the real interest rate on your savings account is 3%. is this a good investment? Some information emerges raising doubt about the authenticity of your painting. You are told that there is 20% chance that it is a fake, in which case its true value would be poundsign1,000. What is the expected value of the painting? No museum would ever agree to exhibit a fake and rental agreements are suspended until the authenticity of the piece is confirmed. Experts from Musee d'Orsay in Paris are offering to assess the authenticity of the piece for a fee of poundsign80,000. A courier agrees to organise and insure the delivery from London to Paris. The one-way cost is poundsign60,000 if the painting is worth over a million, but only poundsign60 if the painting is fake. What is the expected cost of carrying out the authenticity check? Is it rational to pay for the expert assessment to take place?

Explanation / Answer

Hi,

The correct answer is as follows:

Let the discount rate be i

At IRR the NPV is = 0

Hence, the present value of painting = 35000/i

NPV => (35000/i)-1200000 =0

=> i = 35000/1200000

=> 2.92% is the IRR

Since the IRR is less than the expected return, this is not a good investment

Expected value of the painting = 20%*1000+80%*1200000

= 960200

Expected cost = 80000+20%*60+80%*60000

=128012

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