You are considering buying a new house that costs $300K. With probability 0.2 th

Question

You are considering buying a new house that costs $300K. With probability 0.2 the roof will have to be replaced immediately. With probability 0.5 it will have to be replaced in 10 years. Otherwise it will last 20 years. A new roof costs $20K and will last 20 years. An alternate house costs $310K, but has just had a new roof put in. You have a discount rate of 10%. You are indifferent between the houses, so you want the house with the lowest expected cost.

a. If you are risk neutral, what is the value of information on the state of the roof?

b.If you have utility ln (w) and current wealth equal to $500K, what is the value of information on the state of the roof?

Explanation / Answer

Net Present Value of the House if you need to replace the roof now = $300 + $23.49 = $323.49

If you replace house in 10 years, then NPV fo House = $300+$9.06 = $309.06

If you replace house in 20 years, then NPV of the House = $300 + $3.49 = $303.49

So Expected NPV if you buy first House = 0.2*323.49 + 0.5*309.49 + 0.3*303.49 = $310.27

Now, calculate NPV for the second House = ?

NPV for Second House = $310 + $3.49 = $313.49

Thus you want a house with lowe Expected Cost, so House 1 or first option must be availed.(Without Info).

Now Assume you hve information before you decide

Best option if you need to replace roof now = Cpmpare $323.49 and $313.49 (So second House)

Best option if you need to replace roof 10 years later so buy first house in both cases(lower values $309.06 and $303.49 respectively).

SO ENPV1 =0.2*$313.49 +0.5*$309.06 +0.3*$303.49 = $308.27

So EPVI = $310.27 - $308.27 = $2

if we have wealth work $500k, then value of information = $2*1000 = $2000

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