Question

Please solve using a BA II Plus calculator and not using NPV.

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? ***Hint - On Barney life is not always an annuity and remember you will never use 8% - you will use 8/2 or the Effective rate.

Answer 1

First, let us understand and calculate the effective interest rate for discounting

As the opportunity cost is 8% (semi-annual), effective annual interest rate would be (1.04*1.04) = 1.0816 = 8.16%

Fred's calculation:

NPV calculation is as done using the following formula

NPV = Amount/(1.0816)^Year

Year	Amounts	NPV @ 8.16%		Year	Amounts	NPV @ 8.16%
0	(725,000)	(725,000)		11.50	40,000	16,229
1.00				12.00	40,000	15,605
2.00				12.50	40,000	15,005
3.00				13.00	40,000	14,428
4.00				13.50	40,000	13,873
5.00	40,000	27,023		14.00	40,000	13,339
5.50	40,000	25,983		14.50	40,000	12,826
6.00	40,000	24,984		15.00	100,000	30,832
6.50	40,000	24,023		16.00	100,000	28,506
7.00	40,000	23,099		17.00	100,000	26,355
7.50	40,000	22,211		18.00	100,000	24,367
8.00	40,000	21,356		19.00	100,000	22,529
8.50	40,000	20,535		20.00	100,000	20,829
9.00	40,000	19,745		21.00	100,000	19,257
9.50	40,000	18,986		22.00	100,000	17,805
10.00	40,000	18,255		23.00	100,000	16,461
10.50	40,000	17,553		24.00	100,000	15,219
11.00	40,000	16,878		24.50	500,000	73,171
				29.50	500,000	49,431
					NPV	1,697

Fred's NPV is positive, can be invested

Barney's calculation

Year	Amounts	NPV @ 8.16%		Year	Amounts	NPV @ 8.16%
0.00	(690,000)	(690,000)		17.50	25,000	6,335
0.50	25,000	24,038		18.50	25,000	5,857
1.50	25,000	22,225		19.50	25,000	5,416
2.50	25,000	20,548		20.00	120,000	24,995
3.50	25,000	18,998		20.50	25,000	5,007
4.50	25,000	17,565		21.50	25,000	4,629
5.00	120,000	81,068		22.50	25,000	4,280
5.50	25,000	16,240		23.50	25,000	3,957
6.50	25,000	15,014		24.50	25,000	3,659
7.50	25,000	13,882		25.00	120,000	16,886
8.50	25,000	12,834		25.50	25,000	3,383
9.50	25,000	11,866		26.50	25,000	3,127
10.00	120,000	54,766		27.50	25,000	2,891
10.50	25,000	10,971		28.50	25,000	2,673
11.50	25,000	10,143		29.50	25,000	2,472
12.50	25,000	9,378		30.00	120,000	11,407
13.50	25,000	8,670		35.00	120,000	7,706
14.50	25,000	8,016		40.00	2,620,000	113,667
15.00	120,000	36,998		45.00	120,000	3,517
15.50	25,000	7,412		50.00	2,620,000	51,876
16.50	25,000	6,852			NPV	1,225

NPV is positive, hence, can be invested