pv of the expected payoff

CFA Level I Ethics
#1

If the survival probability of project is 0.3672 then the pv of the expected payoff is (20k × 0.3672)/1.25^5 Can you help me wich formula is this? the 20k is the payoff if the project succeeds 25% is the rate of return

#2

The basic formula is the present value of a future cash flow.

PV = CF / [(1 + r)^n]

Is that what you’re asking?

#3

Where does 0.3672 fits in your formula?

#4

The 0.3672 is the probability of the future value occuring. It’s an independent calculation of the Present Value formula. While you combined the two in your initial question, the future cash flow is equal to the probability of the future payoff --> future CF = prob x payoff. You then take this answer and plug it into the equation in my earlier resonse.

#5

Now that I think about it, I’m not so sure about where we’re applying the probability. Is there more context? There is a possibility that it would be more appropriate to find the PV of the future cash flow, THEN apply the probability.

Perhaps you could provide additional detail and someone could help here.

#6

An analyst has been hired to evaluate a high-risk project. The analyst estimates the probability that the project will fail in the first year as well as the conditional probability of failure for each of the remaining four years of the project, as follows: year                         1                2                  3                 4                5 failure probability   0.25          0.20              0.20            0.15           0.10 The project will have no payoff if it fails, but will have a payoff of $20,000 at the end of the fifth year if it succeeds. Because of its high risk, the required rate of the return for an investment in this project is 25%. Based on this information, the expected present value of the project is closest to : a 2400 b 3010 c 5900 d 6550

#7

Any idea plz

#8

Multiply the probability of success which is 1-probability of failure as given in this question. Since it is a condition probability we use the multiplication rule. Probability of (AB)= Probability (A) x Probability (B).

Therefore the probability of success of the project is equal to: (1-0.25)x(1-0.2)x(1-0.2)x(1-0.15)x(1-0.1)= 0.3672 Multiply the probabilty of success by the payoff which will give you the expected payoff five years from now (0.3672 x 20000= USD7344).

Now we need to discount this figure to t=0 using the 25% required rate of return to get the expected present value of the project. 7344/(1.25^5) to get 2408. Therefore the answer is A.