Question

Problem 1:

To examine the implications of selecting various discount rates, consider the installation of an air filtration system that would generate $20,000 of annual benefits over a 20-year period starting in Year 3 (relative to now, which is Year 0).

1. Find the present value of the system using first a discount factor of 10% and then 5%. (Hint: using EXCEL is a much faster way to perform these calculations). Upload your completed Excel spreadsheet in HuskyCT.

2. After you complete the Excel spreadsheet for A: Explain the difference between the present value calculated under the assumption of a 10 percent rate and the one calculated under the assumption of a 5 percent rate.

Answer 1

A) sum of present value of 20 year cash flow from year 3 to 20 ={a(r^18-1)}/(r-1), where a is present value of 3 year cash flow and r is 1/(1+i), i is discount rate.

Third year cash flow present value=20,000/(1+0.1)=15,026.2=a

r=1/(1.1)=0.9

Sum of 20 year cash flow starting from 3rd year and end in 20th year={15,026.2(0.9^18-1)}/(0.9-1)=127,708.4

If i=5%=0.05

Third year benefit present value =20,000/(1.05)=17,276.7

r=1/(1.05)=0.95

Sum of 20 year cash flow starting from 3rd year and end in 20th year={17,267.7(0.95^18-1)}/(0.95-1)=208,174.4

B) the difference is the present value at 10% discount rate is lower than present value discounted at 5% .the higher the discount ,lower will be present value.

answered by: anonymous