Question

3. (25) Suppose you were offered to invest X Dollars now and receive Y Dollars a year from now. The annual interest rate is 10% and the following three investment alternatives were presented to you. Alternative X $50 $85 $100 Y $75 $145 $165 Your utility function for this situation is exponential and represented by -NPV U(NPV)=1-e R . Yotardi indifferent between alternatives A and B. How would you rank order the alternative C with respect to alternatives A and B? ASSUME R=100

Answer 1

Utility function equation -

U (NPV) = 1- e^ (-NPV/R)

Where, R = 100

For alternative A, NPV = $75/ (1+10%) - $50 = $68.18 - $50 = $18.18

Therefore utility for A

U (NPV) = 1- e^ (-18.18/100)

= 1- 1.1994

= 0.1994

For alternative A, NPV = $75/ (1+10%) - $50 = $68.18 - $50 = $18.18

Therefore utility for A

U (NPV) = 1- e^ (-18.18/100)

= 1- 0.8338

= 0.1662

For alternative B, NPV = $145/ (1+10%) - $85 = $131.82 - $85 = $46.82

Therefore utility for B

U (NPV) = 1- e^ (-46.82/100)

= 1- 0.6261

= 0.3739

For alternative C, NPV = $165/ (1+10%) - $100 = $150 - $100 = $50

Therefore utility for C

U (NPV) = 1- e^ (-50/100)

= 1- 0.6065

= 0.3935

Base on utility function alternative C is ranked one with respect to alternative A & B