Suppose a venture fund wishes to base its required return (used in dis- counting future terminal values) on its historical experience and suggests merely averaging the rates on the last three concluded deals

Given
For Deal 1
return r =-67%
time n = 2 years
For Deal 2
return r =50%
time n = 5 years
For Deal 3
return r =70%
time n = 3 years

A.
Formula to calculate Annualized rates = (1+r)^1/n -1
Deal 1:
Annualized rate = (1+r)^1/n -1 = (1 - 0.67)^(1/2) - 1 = -42.55%
Deal 2:
Annualized rate = (1 + 0.50)^(1/5) - 1 = 8.45%
Deal 3:
Annualized rate = (1 + 0.70)^(1/3) - 1 = 19.35%

B.
Equally weighted average annualized return = Sum of (weight of each deal *annualized rate ) = [(1/3) *-0.4255) ]+ [(1/3) *0.0845)] + [(1/3) *0.1935)]= -4.92%

C.
It does not make sense to use this as a single discount rate to apply across scenarios involving different durations
This is because the different deals have different years of maturities. The rate depends on the maturity period and also the risk which is different for different deals.