Question

Fred and Barney Need some investment advice and you have been asked to evaluate their offers. Fred is looking at a 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 of $40,000 coming five years from today. He then would receive $100,000 every year for ten years with first of these coming six months after his last payment of $40,000. Finally he would receive two payments of $500,000 with the first of these coming six months after the last payment of $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 will pay him $25,000 every year for thirty years with the first of these payments coming six months from today. He also would receive @120,000 every five years for the next fifty years with the first of these 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 method and assuming that they have an opportunity cost of 8%(semi-annual), should they invest? SHOW ALL WORK USING FORMULAS AND USE FINANCIAL CALCULATOR!

Answer 1

As per the net gain/loss calculated as of today, Fred should invest (positIve NPV) but Barney should not (negative NPV).

NPV for Fred's investment schedule:

Time period (years)	Number of payments (N)	Payment type	Interest rate used 8% p.a.	Periodic payments	PV (at the start of the payment period)		PV at t = 0
5				0	0		0
5-10	20	Annuity due; semi-annual	4%	40,000	5,65,357.58	Discount at 4% (semi-annual) for 10 periods	3,81,935.32
10.5-20.5	10	Annuity due; annual	8%	1,00,000	7,24,688.79	Discount at 4% for 21 periods	3,18,017.79
21	1	Single payment	4%	5,00,000	5,00,000	Discount at 4% for 42 periods	96,287.47
26	1	Single payment	4%	5,00,000	5,00,000	Discount at 4% for 52 periods	65,048.36
						Total PV	8,61,288.94
						Present cost	7,50,000
						Net gain	1,11,288.94

NPV for Barney's investment schedule:

Time period (years)	Number of payments (N)	Payment type	Interest rate used 8% p.a.	Periodic payments	PV (at the start of the payment period)		PV at t = 0
0-0.5					0
0.5-30.5	30	Annuity due; annual	8%	25,000	3,03,960.15	Discount ar 4% (semi-annual) for 1 period	2,92,269.38
5-50	10	Annuity due; 5-yearly	147%	1,20,000	2,01,646.06	Discount at 4% for 10 periods	1,36,224.85
40	1	Single payment	4%	25,00,000	25,00,000	Discount at 4% for 80 periods	1,08,460.82
50	1	Single payment	4%	25,00,000	25,00,000	Discount at 4% for 100 periods	49,500.10
						Total PV	5,86,455.14
						Present cost	6,90,000
						Net loss	-1,03,544.86