Open Ended Question for Practice

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bean

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Alex is considering a venture capital investment. He has estimated the payoff after 5 years will be $7 million if the firm survives and that the conditional failure rate is 15%. If the initial investment is $1 million and he requires a return of 25% on the investment, the NPV of the venture is:
 
P(Fail) = 0.15 and P(Not Fail) = 0.85
NPV(Fail) = -$1,000,000
NPV(Not Fail) = -$1,000,000 + $7,000,000/(1.25)^5 = $1,293,760

NPV(Total) = NPV(Fail) * P(Fail) + NPV(Not Fail) * P(Not Fail) =
= -$1,000,000 * 0.15 + $1,293,760 * 0.85 = $949,696.
 
P(Fail) = 0.15 and P(Not Fail) = 0.85
NPV(Fail) = -$1,000,000
NPV(Not Fail) = -$1,000,000 + $7,000,000/(1.25)^5 = $1,293,760

NPV(Total) = NPV(Fail) * P(Fail) + NPV(Not Fail) * P(Not Fail) =
= -$1,000,000 * 0.15 + $1,293,760 * 0.85 = $949,696.
 
P(Fail) = 0.15 and P(Not Fail) = 0.85
NPV(Fail) = -$1,000,000
NPV(Not Fail) = -$1,000,000 + $7,000,000/(1.25)^5 = $1,293,760

NPV(Total) = NPV(Fail) * P(Fail) + NPV(Not Fail) * P(Not Fail) =
= -$1,000,000 * 0.15 + $1,293,760 * 0.85 = $949,696.
 
Here is the answer:
7(1 � .15)5 (1/1.25)5 � 1 = 7(0.85/1.25)5 � 1 = 0.017753 million or $17,753
 
That 15% if is the chance that in any one year the venture will fail. The chance that the firm will last until year 5 is (1-0.15)^5 = 0.444 an therefore the probibility of the venture failing is 1-0.443705 = 0.556. The next step is assessing the NPV if it suceeds:

-1m + 7m/1.25^5 =
1.294 m = NPVs

NPV for a fail is -1m

Next is the expected value of the NPV's=

.444 * (1.294m) + .556 * (-1m) = 18,536

So it should be taken.

Bean you are a little off because you are not taking the expected value of the NPVs, you are taking the future discounted amount and adjusting it downward by the probability without adjusting any of the other figures for their probabilities. That was my mistake the first time I did a question like this on my own.



Edited 1 time(s). Last edit at Thursday, April 27, 2006 at 10:21AM by jamespucyk.
 
Whoa, whoa, whoa boys...

these are three VERY different methods/answers that are being presented.

At first I thought Lev's answer was right, but Pucyk's look like it's on the money. Bean, is that the official answer given? If so, we're all a little off.
 
Sorry, I ran out of time on the edit.

Anyways, I consulted my notes here and Pucyk's spot on again (great job dude...throw some of the knowledge my way).

Due to rounding, I get a final NPV = $18,415.

On second thought, if it is in fact the way they worded the question saying that the 15% is the "conditional" rate meaning for ALL five years, then we are wrong. This could just be an issue of interpreting what "conditional" means for mine and James' answers. If that's the case, this is BS, cuz all the examples in Schweser that I came across actually spelled out the success/failure rates per year, so you simply multiplied them together to find the total. Thoughts?



Edited 1 time(s). Last edit at Thursday, April 27, 2006 at 11:34AM by zimzim78.
 
I posted the 'offical' answer from Schweser.
 
bean Wrote:
-------------------------------------------------------
> I posted the 'offical' answer from Schweser.

Cool, thanks Bean. Looks like Pucyk and I misinterpreted the question. Apparently they were giving the total expected probability for ALL five years as being the 15%.
 
bean Wrote:
-------------------------------------------------------
> I posted the 'offical' answer from Schweser.

Okay...I'm royally confused now. I just worked out this question as you have typed the answer and it def does not come out to what they have as the final NPV???

James...can you help me out here, I thought we had the right answer, but for some reason, Schweser's got if f*cked...unless it was just typed incorrectly, but I've tried it three different ways, and it's not coming even close to what they have, using that solution that Bean posted??? WTF>?

I'm still sticking to the way you (and I) understand it, as was taught previously in Schweser.
 
I don't understand Bean's notation, but James' solution looks good to me if "conditional" means the probability of failure in year k = 15% conditional on having survived through year (k-1). If we leave out the word conditional, I like Lev's first solution. His second solution is only so-so and his third is really off the mark ;-p
 
Well I cross reference, what I know to be true with this type of problem, with the course material and with the Schweser online question bank LOS summary and they both use the expected NPV formula. If schweser's answer in the question review is different it even contridicts what I have seen on their LOS summary.
 
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