Question

1. Consider a project whose net cash flow streams, F_n , are as follows

                                         n                E(F_n)                 Var(F_n)

                                        0                 -$10                    9

                                        1                     3                      4

                                        2                     8                     16

                                        3                    10                    25

In addition, the correlation coefficient among the F_n’s are known to be ρ₀₁ = ρ₀₂ = ρ₀₃ = 0.5 and ρ₁₂ = ρ₂₃ = ρ₁₃ = 1. Assuming i = 10%, compute the mean and variance of the PV for the project.

Answer 1

According to the given question the solution as follows Considering given project whose net cash flow streams that We realize that :

=> PV_{n} = F_{n}/1+r, where C is the net income and r is the pace of intrigue.

r = 10 % = 0.1

In this way, PV_{n} = F_{n}/1.1

We realize that, E[aX] = aE[X] and Var[aX] = a^{2}Var[X]

in this way, E[PV_{n}] = E[F_{n}/1.1] = E[F_{n}]/1.1

thus, E[F_{n}] = - 10, 3, 8, 10

thus, E[PV_{n}] = - 9.09, 2.72, 7.27, 9.09

Likewise, Var[PV_{n}] = Var[F_{n}/1.1] = Var[F_{n}]/(1.1)^{2} = Var[F_{n}]/1.21

Var[F_{n}] = 9, 14, 16, 25

Var[PV_{n}] = 7.43, 11.57, 13.22, 20.66

Therefore Complete Mean

= (- 9.09 + 2.72 + 7.27 + 9.09)/4 = 2.4975

Figuring covariance of each,

Cov(PV0, PV1) = p01 sqrt(Var(PV0) Var(PV1)) = 0.5 * sqrt(7.43*11.57) = 4.635

likewise, Cov(PV0, PV2) = 4.955, Cov(PV0, PV3) = 6.19

Cov(PV1, PV2) = 12.36, Cov(PV1, PV3) = 15.46, Cov(PV2, PV3) = 16.52

Therefore Difference of PV

= ( Var(PV0) + Var(PV1) + Var(PV2) + Var(PV3) + 2*Cov(PV0, PV1) + 2*Cov(PV0, PV2) + 2*Cov(PV0, PV3) + 2*Cov(PV1, PV2) + 2*Cov(PV1, PV3) + 2*Cov(PV2, PV3) )/4^{2}

= (7.43 + 11.57 + 13.22 + 20.66 + 9.27 + 9.91 + 12.38 + 24.72 + 30.92 + 33.04)/16

= 10.82