Question

Please help without utilizing NPV. My calculator is TI-84. Having difficulty gathering the correct PV for these calculations

Fred and Barney need some investment advice and have asked you to evaluate their offers. Fred is looking at an investment that would pay him nothing until five years from today and then he would receive $40,000 every six months for ten years (20 payments) with the first payment coming five years from today. He then would receive $100,000 every year for ten years with the first of these coming six months after the last payment of $40,000. Finally he would receive two payments of $500,000 with the first coming six months after the last $100,000 and the second coming five years after the first payment of $500,000. The investment would cost him $725,000 today. Barney's investment would pay him $25,000 every year for thirty years with the first of these coming six months from today. He would also receive $120,000 every five years for the next fifty years with the first coming five years from today and the last coming fifty years from today. Finally he would receive $2,500,000 forty years from today and another $2,500,000 fifty years from today. His investment would cost him $690,000 today. Using present value and assuming they have an opportunity cost of 8% (semi-annual), should they invest?

Answer 1

Opportunity cost is 8% semi annual i.e. 4% for every period of 6 months.

FRED : Receipts are as follows:

Period Amount    PVAF@4% PV=amount*PVAF

1 - 10 Nil 8.111 Nil

11 - 30 40,000 9.181 367,240

31 - 50 100,000 4.190 419000

51 500,000 0.135 67500

61 500,000 .091 45500

Total receipts = $899,240

Initial investment at period 0 = $725,000

NPV = $899,240 - $725,000 = $174,240

Since NPV is positive , Fred should invest.

BARNEY : Receipts are as follows:

Period Amount    PVAF@4% PV=amount*PVAF

1 - 60 25000 22.624 565600

10    120,000 0.676 81120

20    120,000 0.456 54720

30 120,000 0.308 36960

40 120,000 0.208 24960

50 120,000 0.141 16920

60 120,000 0.096 11520

70 120,000 0.064 7680

80 120,000 0.043 5160

90 120,000 0.029 3480

100    120,000 0.0198 2376

110    120,000 0.013 1560

80 2,500,000 0.043 107500

100 2,500,000 0.0198 49500

Total receipts = $969,056

Initial investment at period 0 = $690,000

NPV = $969,056 - $690,000 = $279,056

Since NPV is positive , Barney should invest.