Risk and Uncertainty
Crystal Rugg
BUS 640: Managerial Economics
Professor Sidney Okolo
May 17, 2016
Question 1
In order to find out the better deal between the second alternative at an 8% interest rate versus a 12% interest rate, we will need to calculate the present value as well as the given interest rates. To do this we use the following calculation formula:
Present Value (PV) Formula: FVn = PV (1+r)
The FVn = Future Value with n being number of years
Discount Factor formulation: 1/(1+r) n
The following graph has been made to show these calculations:
Year
Option 1
Int. Rate (8%)
PV
Option 2
Int. Rate (12%)
PV
0
0
0
1
7 mil.
0.9259
$6,481,481
7 mil.
0.8929
$6,250,000
2
7 mil.
0.8573
$6,001,372
7 mil.
0.7972
$5,580,357
Total
14 mil.
$12,482,853
14 mil.
$11,830,357
Show Work:
7000000(n=1) = (1+.08) 1 = discount factor = 0.9259 Present Value = $6,481,481
7000000(n=2) = (1+.08) 2 = discount factor = 0.8573 Present Value = $6,001,372
7000000(n=1) = (1+.12) 1 = discount factor = 0.8929 Present Value = $6,250,000
7000000(n=2) = (1+.12) 2 = discount factor = 0.7972 Present Value = $5,580,357
Option 1 PV minus Option 2 PV Total = $652,496
Based on the above calculations, the present value for the second alternative at an 8% interest rate is a total of $12,482,853. The present value for the second alternative at a 12% interest rate is a total of $11,830,357. In summing up these present values we find that option 2 at a 12% interest rate, being $652,496 cheaper in present value terms, offers the better deal.
There are many real life scenarios in which these calculations would be necessary. To provide an example, a business man wants to provide funding for a community development and offers 2 ways in which he will do this. Option 1 would be a lump sum payment up front of 50 million dollars with no interest or...