Question

Daryl Kearns saved $240,000 during the 25 years that he worked for a major corporation. Now he has retired at the age of 50 and has begun to draw a comfortable pension check every month. He wants to ensure the financial security of his retirement by investing his savings wisely and is currently considering two investment opportunities. Both investments require an initial payment of $189,000. The following table presents the estimated cash inflows for the two alternatives:

PV Table 1 Year 1-4

Year 1	0.892857
Yr 2	0.797194
Yr 3	0.711780
Yr 4	0.63518

PVA

Yr 1	0.892857
Yr 2	1.690051
Yr 3	2.401831
Yr 4	3.037349

  

	Year 1			Year 2			Year 3			Year 4
Opportunity #1	$	55,675		$	58,810		$	78,840		$	101,440
Opportunity #2		104,400			109,300			16,900			14,000

  

Mr. Kearns decides to use his past average return on mutual fund investments as the discount rate; it is 12 percent. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.)

  

Required

1. Compute the net present value of each opportunity. Which should Mr. Kearns adopt based on the net present value approach?

2. Compute the payback period for each opportunity. Which should Mr. Kearns adopt based on the payback approach?

Answer 1

NPV
	a	b	c = (1/1.12)^year	a*c	b*c
Year	Opportunity 1	Opportunity 2	Discount rate @ 12%	PV of cash flows Opportunity 1	PV of cash flows Opportunity 1
0	(189,000)	(189,000)	1	(189,000)	(189,000)
1	55,675	104,400	0.893	49,710	93,214
2	58,810	109,300	0.797	46,883	87,133
3	78,840	16,900	0.712	56,117	12,029
4	101,440	14,000	0.636	64,467	8,897
			NPV	28,177	12,274
Payback period
Year	Opportunity 1	Cumulative cashflow Opportunity 1	Year	Opportunity 2	Cumulative cashflows Opportunity 2
0	(189,000)	(189,000)	0	(189,000)	(189,000)
1	55,675	(133,325)	1	104,400	(84,600)
2	58,810	(74,515)	2	109,300	24,700
3	78,840	4,325	3	16,900	41,600
4	101,440	105,765	4	14,000	55,600
Payback period	=A+(B/C)
A is the last period number with a negative cumulative cash flow;
B is the absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of the period A;
C is the total cash inflow during the period following period A
Payback period	=2+(74515/78840)
(opportunity 1)	2.95	years
Payback period	=1+(84600/109300)
(opportunity 2)	1.77	years

Update

NPV calculations (2 digits rounding off)

NPV
	a	b	c = (1/1.12)^year	a*c	b*c
Year	Opportunity 1	Opportunity 2	Discount rate @ 12%	PV of cash flows Opportunity 1	PV of cash flows Opportunity 1
0	(189,000)	(189,000)	1	(189,000.00)	(189,000.00)
1	55,675	104,400	0.892857	49,709.81	93,214.27
2	58,810	109,300	0.797194	46,882.98	87,133.30
3	78,840	16,900	0.711780	56,116.74	12,029.08
4	101,440	14,000	0.635518	64,466.95	8,897.25
			NPV	28,176.47	12,273.91