Suppose an investor has an opportunity to invest $3 million in a venture investment that is expected to pay $30 million at the end of 4 years if it survives. The cost of capital for a project with this risk level is 30%. However, the project may not survive the full 4 years and has an expected failure rate shown in the probability table shown below. The likelihood of failure in the first year is 25% , with the likelihood of failure in the second year being 20% ( assuming it survives the first year) and so on.
A．Year
B．1
C．2
D．3
E．4
F．Failure Probability
G．25%
H．20%
I．15%
J．10%
参考答案：C
解析：The NPV of this project is a weighted average of the NPV if the project survives and is successful, combined with the probability and NPV if the project is a failure. If the project is successful it will have an NPV of $7.5 million ( PV of 30 million in 4 years discounted at 30% p. a. is $10.5 million; from this reduce the initial outlay of $3 million) with a likelihood of success at 45.9%. If the project is a failure, it will lose the initial outlay of $3 million with a probability of 54.1% ( 1 - 45.9% ). The weighted average of both success and failure is: $1.82 mil. [ (7.5 ×0.459) - (3 ×0.541 ) = 1.82]. Since the weighted average NPV of the project has been determined to be a positive value ( e. g. $1.82 mil. ) the implication is that this project is worthwhile to pursue given the net investment, potential return, implied risk level and likelihood of default. Investors will receive a positive risk adjusted return with this project.