Three different plans were presented to the GAO (General Accounting Office) by a high-tech facili­ties manager for operating a portable cyber-secu­rity facility.

Question

Plan A: Renewable 1-year contracts with payments of $1 million at the beginning of each year.
Plan B: A 2-year contract that requires three pay­ments of $600,000 each, with the first one to be made immediately and the second and third payment made at the beginning of the following two 6?month intervals; no payments required during the second year of the contract.
Plan C: A 3-year contract that entails a payment of $1.5 million now and another payment of $0.5 million 2 years from now.

Assuming the GAO can renew any of the plans under the same conditions, if it decides to do so, which plan is best on the basis of a present worth analysis at an interest rate of 6% per year, com­pounded semiannually? Solve using (a) factors and (b) a spreadsheet. (Hint: Construct a cash flow dia­gram before working this problem.)

Answer 1

(a) Factor solution. Must use a 6-year evaluation period for equal-service analysis.

Plan A: effective i/year = (1 + 0.03)2 – 1 = 6.09%
PWA = -1,000,000 - 1,000,000(P/A,6.09%,5)
= -1,000,000 - 1,000,000(4.2021)
= $-5,202,100

PWB = -600,000[1 + (P/A,3%,2) + (P/A,3%,3)(P/F,3%,3) + (P/A,3%,3)(P/F,3%,7)]
= -600,000[1 + 1.9135 + (2.8286)(0.9151) + (2.8286)(0.8131)]
= -600,000(7.8019)
= $-4,681,132

PWC = -1,500,000 – 500,000(P/F,3%,4) – 1,500,000(P/F,3%,6)
- 500,000(P/F,3%,10)
= -1,500,000 – 500,000(0.8885) – 1,500,000(0.8375) – 500,000(0.7441)
= $-3,572,550

Select plan C

b) Spreadsheet: Cash flow details not included. PW functions and displays are:
Plan A: = NPV($B2,B6:B10)+B5 displays $-5,202,070
Plan B: = NPV($D2,D6:D15)+D5 displays $-4,681,182
Plan C: = NPV($D2,E6:E15)+E5 displays $-3,572,517

Select plan C