ECONOMICS OF RISK AND UNCERTAINTY APPLIED PROBLEM 7

Economicsof Risk and Uncertainty Applied Problem

Problem1

Parta

Presentvalue = A / (1 + r)^n where A = annuity amount, r is the opportunityrate of interest and n the amount of years when the amount will bereceived

Presentvalue of the second alternative = $ 7000000 / (1+0.08) ^1

=6,481,481.48

7000000/ (1+0.08) ^2

=$6,001,371.74

$6,481,481.48 + $ 6,001,371.74 = $ 12,482,853.22

Becausethe donation received from the first alternative is $ 12 million,while that of the second alternative is $ 12.48 million, the secondalternative should be chosen because it provides 480,000 morecompared to the first alternative.

Partb

Incase the opportunity interest rate is 12%, the present value would asfollows

$7000000/ (1+0.12) ^ 1

=$6,250,000

$7000000/ (1+0.12) ^2

=$5,580,357.14

$6,250,000+ $5,580,357.14

=$ 11,830,357.14

Whenthe opportunity interest rate is 12%, the second alternative onlyprovides $11.83 million, while the first alternative provides $12million. Thus, the first alternative should be chosen when theopportunity interest rate is 12%.

Partc

Inthe real world, the two types of payment streams can be applied byfinancial managers in accounting for the time value of money. Ascenario is where services are provided in one year and paymentreceived later with an interest. For instance, an entity may offerservices in 2014 and receive payment in 2015 financial managers cancalculate the future value in order to determine whether to receivethe payment at the future date is profitable or not.

Problem2

Parta

ProjectA’s expected net present value

Cashfor year 1 cash flow = 0.2*50 + 0.3*40 + 0.4*30 + 0.1*20

=$36 million

Cashfor year 2 cash flow = 0.1*60 + 0.2*50 + 0.3*40 + 0.4*30

=$40million

Cashfor year 3 cash flow = 0.3*70 + 0.4*60 + 0.1*50 + 0.2*40

=$54 million

Scenario1: Expected net present value

-80+ 36/ (1.08) + 40/ (1.08) ^2 + 54/ (1.08) ^ 3

=$30.5 million

SanDiego LLC should make a decision of accepting this venture riskbecause the expected net present value is positive

Standarddeviation

Year 1 |
Year 2 |
Year 3 |
||||||

probability |
Deviations (d) |
d^2 |
Probability |
Deviations (d) |
d^2 |
Probability |
Deviations (d) |
d^2 |

0.2 |
50 – 30.5 = 19.5 |
380.25 |
0.1 |
60 – 30.5 = 29.5 |
870.25 |
0.3 |
70 -30.5 = 39.5 |
1560.25 |

0.3 |
40 – 30.5 = 9.5 |
90.25 |
0.2 |
50 – 30.5 = 19.5 |
380.25 |
0.4 |
60 – 30.5 = 29.5 |
870.25 |

0.4 |
30 – 30.5 = -4.5 |
20.25 |
0.3 |
40 – 30.5 = 9.5 |
90.25 |
0.1 |
50 – 30.5 = 19.5 |
380.25 |

0.1 |
20 – 30.5 =-9.5 |
90.25 |
0.4 |
30 – 30.5 = -0.5 |
0.25 |
0.2 |
40 – 30.5 = 9.5 |
90.25 |

Variationfor year 1 = 0.2*380.25 + 0.3*90.25 + 0.4*20.25 + 0.1*90.25

=76.05 + 27.075 + 8.1 + 9.025

=120.25

Standarddeviation for year 1= 10.97 (square root of 120.25)

Variationfor year 2 = 0.1*870.25 + 0.2*380.25 + 0.3*90.25 + 0.4*0.25

=87.025 + 76.05 + 27.075 + 0.1

=190.25

Standarddeviation for year 2 = 13.79 (square root of 190.25)

Variationfor year 3 = 0.3*1560.25 + 0.4*870.25 + 0.1*380.25 + 0.2 *90.25

=468.075 + 348.10 + 38.025 + 18.05

=872.25

Standarddeviation for year 3 = 29.53

Partb

Withoutconsidering risk factor in undertaking project A and project B, Iwould consider expected net present value. For the two projects, Iwould consider choosing the project with more expected net presentvalue. Since project A has more expected net present value comparedto project B, I would choose project A.

Partc

Incase a decision maker for San Diego LLC is considered risk averse,the decision maker would find the coefficient of variance thatrepresents standard deviation for project B, which would help inchoosing the project to undertake. The deviation for B is $10.5 M,while that of A is $30. In this case, as a risk averse decisionmaker, one would choose project B as compared to project A. As theCEO of the organization, I would also choose project B since it hasless risk compared to A.

References

Hirschey,M. (2009). *Fundamentalsof managerial economics*.Mason, OH: South-Western/Cengage Learning.