- Schweser notes book5, P287, Q10, the probabilities that a venture capital investment will fail, given that it has survived all prior periods, are: 1st year 15% 2nd year 18% 3rd year 10% 4th year 8% an investment of 1.5 million is expected to return 9 million if the venture survives until the end of 4th year. The expected annual compound rate of return on this investment is closest to : A. 36% B. 33% C. 31% D.28% Answer is A. the probability that the venture survives 4 years is (1-15%)(1-18%)(1-10%)(1-8%)=57.7% expected payoff is 57.7%*9million=5,194,044 expected return is [5,194,044/1,500,000]^1/4 -1=36.4% --my question is why not consider the project failure affects the expected return. My calculation is 57.7%*9million+42.3%*(-1.5million)=4,559,940 expected return is [4,559,940 /1,500,000]^1/4 -1=32.04%
I think your answer corresponds to calculation of NPV of the project. What is being calculated here is the Compound Growth rate of return.
cpk123 Wrote: ------------------------------------------------------- > I think your answer corresponds to calculation of > NPV of the project. > > What is being calculated here is the Compound > Growth rate of return. --------------------------------------------------------------- I know the Compound Growth rate of return is the question. to have a right NPV is a necessary step. I don’t agree their NPV calculation which didn’t consider the effect of project failure.
Annexguy- Project failure is incorporated in the pay off calculation. Thats why for investment of $1.5MM pay off is ===> (1-p(fail))*$9.0MM = $5.19MM (as in the solution) So if you invest 1.5mm in a project it is expected to give you $5.19 at the end of year 3 (and not $9.0mm), so, 1.5(1+g)^4 = 5.19
For Compound Growth Rate of return – I am pretty confused. Why would you need NPV of the project? NPV is a present time value. How does dividing two #s at exactly the same point in time give you a Compound growth rate? Maybe I am missing something real big, and I am pretty sure this was not a topic in the L1… (Compound growth rate for Venture capital projects). CP
acctually, my calculation follows a sample in CFAi curriculum volume6, P206. CPK, since you don’t have the curriculum, I type a simplified version here. ------------------------------------------------------------------------- investor invests 1million in a venture capital project will pay 16million at end of 7 years if it succeeds, his cost of capital for this project’s risk level is 18%. the following table are probabilities of failure. year//////////1/////2//////3/////4//////5/////6////7 P(failure)//0.25// 0.22// 0.2// 0.2// 0.2// 0.2// 0.2 Q1. detemine probability that project survives to end of 7th year (1-0.25)(1- 0.22) (1- 0.2) (1- 0.2) (1- 0.2) (1- 0.2) (1- 0.2) =19.2% Q2. detemine the expected NPV of the project when it survives to end of 7th year and earn 16million, NPV=-1million+16million/1.18^7=4.02 million; when it fails, NPV=-1million. thus project’s expected NPV is a probability-weighted average of 2 amounts, 19.2%*4.02million+80.8%*(-1million)=-36,160. based on its negative NPV, investor will decline the project. ----------------------------------------------------------------------------- in above sample, the project’s failure (-1million) is also added per probability weighting to project’s expected NPV. my calculation follows this method.
That is exactly what I was saying as well. For the NPV for the project, what is done is right. All the cashflows are being reduced to the CURRENT TIME PERIOD for NPV. For Compound growth rate: You spent X amount at time 0. (Initial Investment). You get back Y amount at time T (Cashflow * Probability of Success). Now Y/X ^ 1/t is your compound growth rate. If you calculated NPV – it is also at time 0. (Because it is PRESENT VALUE). And then what “Compounded growth rate” are you looking at? You seem to be getting confused between NPV of the project and the Compound Growth rate for the project. CP
cpk123 Wrote: ------------------------------------------------------- > All the cashflows are being reduced to the CURRENT > TIME PERIOD for NPV. > > For Compound growth rate: > > You spent X amount at time 0. (Initial > Investment). > > You get back Y amount at time T (Cashflow * > Probability of Success). > > Now Y/X ^ 1/t is your compound growth rate. > > If you calculated NPV – it is also at time 0. > (Because it is PRESENT VALUE). And then what > “Compounded growth rate” are you looking at? > > You seem to be getting confused between NPV of the > project and the Compound Growth rate for the > project. > > CP -------------------------------------------------------- in above example, 15% discount rate is used to get PV of 5th year payoff, and plus CF0 , equal NPV when project succeeds, no survive Probability invovled at this step. in my Q, the " expect annual compound rate of return" actually is IRR when project succeeds. thus we don’t need us survive Probability 57.7% to discount the 4th year payoff 9million ,either. my calculation is (9million/1.5million)^1/4
CPK, I think I got it now. this is a basic Quan Q, but looks like Alternative Q. I messed them up.