Question

Daryl Kearns saved $270,000 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 $186,000. The following table presents the estimated cash inflows for the two alternatives:

  

	Year 1			Year 2			Year 3			Year 4
Opportunity #1	$	55,705		$	58,800		$	78,860		$	101,270
Opportunity #2		103,800			109,050			18,000			15,700

  

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

Ans 1	NPV
		Outflow	Inflow Oppurtunity 1	Formula for NPV using Discount Rate (12%)	Discount Rate (12%)	Net Inflow
	Year 0	$            180,000.00	0	1	1.0000	$ (180,000.00)
	Year 1		$                     55,705.00	1/1.12	0.8929	$      49,736.61
	Year 2		$                     58,800.00	1/(1.12)^2	0.7972	$      46,875.00
	Year 3		$                     78,860.00	1/(1.12)^3	0.7118	$      56,130.99
	Year 4		$                  101,270.00	1/(1.12)^4	0.6355	$      64,358.92
	Total Inflow		294,635.00			$      37,101.51
		Outflow	Inflow Oppurtunity 2	Formula for NPV using Discount Rate (12%)	Discount Rate (12%)	Net Inflow
	Year 0	$            180,000.00	0	1	1.0000	$ (180,000.00)
	Year 1		$                  103,800.00	1/1.12	0.8929	$      92,678.57
	Year 2		$                  109,050.00	1/(1.12)^2	0.7972	$      86,933.99
	Year 3		$                     18,000.00	1/(1.12)^3	0.7118	$      12,812.04
	Year 4		$                     15,700.00	1/(1.12)^4	0.6355	$        9,977.63
	Total Inflow		246,550.00			$      22,402.24
	Hence Mr Daryl Kearns, should go with Oppurtunity 1 as NPV is more than the NPV of Oppurtunity 2
Ans 2	Pay Back period
	Where the cashflow is uneven the Payback period is calculated as follows
	Payback Period =	X*Y/Z
	Where X is the priord with last negative cumulative cash flow;
	Y is the absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of the period X; and
	Z is the total cash inflow during the period following period X
	Oppurtunity 1
	Year	Annual Cash Inflow	Culumutive Cash Flow
	0	$         (180,000.00)	$                (180,000.00)
	1	$              55,705.00	$                (124,295.00)
	2	$              58,800.00	$                  (65,495.00)
	3	$              78,860.00	$                     13,365.00
	4	$            101,270.00	$                  114,635.00
	Payback Period		2+65495/78860
			2.83	years
	Oppurtunity 1
	Year	Annual Cash Inflow	Culumutive Cash Flow
	0	$         (180,000.00)	$                (180,000.00)
	1	$            103,800.00	$                  (76,200.00)
	2	$            109,050.00	$                     32,850.00
	3	$              18,000.00	$                     50,850.00
	4	$              15,700.00	$                     66,550.00
	Payback Period		1+76200/109050
			1.70	years