Question

Robotek Ltd. Sti. The Humanoid Robot Production Project, whose net cash flows and possibilities are given below; Calculate the expected value, standard deviation and coefficient of variation in terms of risk and calculate the probability of the project's NPV to be greater than 150 million TL.

                 Humanoid Robot Production Project  

            (000.000,00)                         (%)                                                                              

Net Cash Flow (A_i)                        Possibility (P_i)

   180                                         25

   240                                         65

   300                                         10

Equations You May Need:

NPV = ∑n Rt / (1+k)t - C                t=1       ∑m Ct / (1+r)t = ∑n Rt / (1+r)t t=1                       t=1
profitability index = {∑n Rt / (1+k)t + H / (1+k)n} / {C0=∑n Ct / (1+k)t}                                   t=1                                                 t=1
E (A) = ∑k Ai * Pi                i=1 S = √ ∑k [Ai – E (A)]2 * Pi             i=1 DK = S / E (A) Z = X – E (NPV) / S

Answer 1

Expected value = E(A) = =

= 180*0.25 + 240*0.65 + 300*0.10 = 45 + 156 + 30 = 231

= 231 million

Standard deviation = s =

s² = 0.25(180 - 231)² + 0.65(240 - 231)² + 0.1(300 - 231)² = 0.25*51² + 0.65*9² + 0.1*69² = 0.25*2601 + 0.65*81 + 0.1*4761 = 1179

s = 1179^0.5 = 34.33657 million

Hence approximately

s = 34.34 million

Coefficient of variation = s/= 34.34/231 = 0.148658 = approximately 14.87%

Coefficient of variation = DK = 14.87%

Note: For calculating NPV, we first need the rate of interest r, which is not given in the question. Please provide it for further answers about NPV.