Question

Telluride Tours is currently evaluating two mutually exclusive investments. After doing a scenario analysis and applying probabilities to each scenario, it has determined that the investments have the following distributions around the expected NPVs.

probability	NPV a	NPV b
0.1	-39,780	-14,918
0.2	-9945	2486
0.4	19890	19890
0.2	49725	37294
0.1	79560	54698

a). calculate the expected NPV for both projects. Can the question be resolved with this information alone?

b). calculate the variance and standard deviation of the NPVs for both projects. Which project appears to be riskier?

c). calculate the coefficient of variation for both projects. Does this change your opinion from part b?

d). calculate the probability of a negative NPV for both projects.

e). Which project should be accepted and why?

Answer 1

a) Expected NPV of a = (0.1*-39780) + (0.2*-9945) + (0.4*19890) + (0.2*49725) + (0.1*79560) = -3978 -1989 + 7956 + 9945 + 7956 = 19,890

Expected NPV of b = (0.1*-14,918) + (0.2*2486) + (0.4*19890) + (0.2*37294) + (0.1*54698) = -1491.8 +497.2 + 7956 + 7458.8 + 5469.8 = 19,890

The question cannot be resolved with this information alone because the expected NPV is the same for both

b)

p1 = 0.1

p2 = 0.2

p3 = 0.4

p4 = 0.2

p5 = 0.1

S1 = NPV1 for a = -39,780

S2 = NPV2 for a = -9945

S3 = NPV3 for a = 19890

S4 = NPV4 for a = 49725

S5 =  NPV5 for a = 79560

ES = Expected NPV of a

Variance for a = p1*(S1-ES)² +  p2*(S2-ES)² +  p3*(S3-ES)² +  p4*(S4-ES)² + p5*(S5-ES)²
Variance for a = 0.1*(-39,780 - 19890)² +  0.2*(-9945 - 19890)² +  0.4*(19890 - 19890)² +  0.2*(49725- 19890)² +  0.1*(79560 - 19890)² = 1068152670

Standard deviation of a = (variance of a)^(1/2) = (1068152670)^(1/2) = 32682.60501

similarly for b

Variance of b =

0.1*(-14918 - 19890)² +  0.2*(2486 - 19890)² +  0.4*(19890 - 19890)² +  0.2*(37294- 19890)² +  0.1*(54698 - 19890)² = 363479059.2000

Standard deviation of b = (variance of b)^(1/2) = (363479059.2000)^(1/2) = 19065.12678

Comparing the standard deviations and variance , project a seems to be riskier

c) Coefficient of variation for a = standard deviation of a / ES = 32682.60501/19890 = 1.643167

Coefficient of variation for b = standard deviation of b / ES = 19065.12678/19890 = 0.958528

Coefficient of variation is greater for a , which means that project a is riskier which is the same result we got from part b)

d)

probability of negative NPV for project a = no. of negative NPVs / total no. of NPVs = 2/5 = 0.4 = 40%

probability of negative NPV for project b = no. of negative NPVs / total no. of NPVs = 1/5 = 0.2 = 20%

e) from the above calculations since project b is less riskier , we should select project b