Question

1. The cash flows for four projects are shown below, along with the cost of capital for these projects. If these projects are mutually exclusive, which one should be taken?

   	A.	Year:                         0                1            2              3            4                  5 Cash flow:                     -$12,000    $4000    $4000      $4000    $4000          $4000 Cost of Capital: 5.0%
   	B.	Year:                              0                1            2              3            4                  5 Cash flow:                     -$15,000    $4000    $4000      $4000    $4000          $4000 Cost of Capital: 7.0%
   	C.	Year:                              0                1            2              3            4                  5 Cash flow:                     -$20,000    $6000    $6000      $6000    $6000          $6000 Cost of Capital: 8.2%
   	D.	Year:                              0                1            2              3            4                  5 Cash flow:                     -$18,000    $5000    $5000      $5000    $5000          $5000 Cost of Capital: 7.6%

Answer 1

Answer: (A) As NPV is higher for Project A, it should be accepted.

	Computation of NPV					Computation of NPV					Computation of NPV					Computation of NPV
	A					B					C					D
	Year	Cashflows	PVF@ 5 %	PV		Year	Cashflows	PVF@ 7 %	PV		Year	Cashflows	PVF@ 8.2 %	PV		Year	Cashflows	PVF@ 7.6 %	PV
A	0	$ (12,000)	1.0000	$        (12,000)		0	$       (15,000)	1.0000	$        (15,000)		0	$             (20,000)	1.0000	$           (20,000)		0	$ (18,000)	1.0000	$(18,000)
		PV of Cash Outflows		$        (12,000)			PV of Cash Outflows		$        (15,000)			PV of Cash Outflows		$           (20,000)			PV of Cash Outflows		$(18,000)
B	1	$     4,000	0.9524	$             3,810		1	$            4,000	0.9346	$            3,738		1	$                 6,000	0.9242	$                5,545		1	$      5,000	0.9294	$    4,647
	2	$     4,000	0.9070	$             3,628		2	$            4,000	0.8734	$            3,494		2	$                 6,000	0.8542	$                5,125		2	$      5,000	0.8637	$    4,319
	3	$     4,000	0.8638	$             3,455		3	$            4,000	0.8163	$            3,265		3	$                 6,000	0.7894	$                4,737		3	$      5,000	0.8027	$    4,014
	4	$     4,000	0.8227	$             3,291		4	$            4,000	0.7629	$            3,052		4	$                 6,000	0.7296	$                4,378		4	$      5,000	0.7460	$    3,730
	5	$     4,000	0.7835	$             3,134		5	$            4,000	0.7130	$            2,852		5	$                 6,000	0.6743	$                4,046		5	$      5,000	0.6933	$    3,467
		PV of Cash Inflows		$          17,318			PV of Cash Inflows		$          16,401			PV of Cash Inflows		$              23,831			PV of Cash Inflows		$ 20,176
	NPV	= B-A		$          5,318		NPV	= B-A		$ 1,401		NPV	= B-A		$ 3,831		NPV	= B-A		$ 2,176

All the Projects have Positive NPV, So all the projects can be accepted if they are independent.

However, as the projects are mutually exclusive, i.e., selection of one project, excludes other projects. So, Project with higher NPV should be NPV should be Selected, So, Project A

Computation of NPV Computation of NPV Year Cashflows PVF@ 5% PV Year Cashflows PVF@ 7% PV 0 $(12,000) 1.0000 $ (12,000) 0 $ (15,000)| 1.0000 $ (15,000) PV of Cash Outflows $ (12,000) PV of Cash Outflows $ (15,000) 1 $ 4,000 0.9524 $ 21 $ 4,000 0.9070$ 3 $ 4,000 0.8638 $ 4 $ 4,000 0.8227 $ 5 $ 4,000 0.7835 $ PV of Cash Inflows $ 3,810 3,628 3,455 3,291 3,134 17,318 1 $ 4,000 0.9346 $ 21 $ 4,000 0.8734 $ 31 $ 4,000 0.8163 $ 4 $ 4,000 0.7629 $ 5 $ 4,000 0.7130 $ PV of Cash Inflows $ 3,738 3,494 3,265 3,052 2,852 16,401 NPV =B-A $ 29,318 NPV =B-A $ 31,401

Computation of NPV Computation of NPV Year Cashflows PVF@ 8.2% PV Year Cashflows PVF@ 7.6% PV AL0 $ (20,000) 1.0000 $ (20,000) 0 $(18,000) 1.0000 $ (18,000) PV of Cash Outflows $ (20,000) PV of Cash Outflows $ (18,000) 1 $ 6,000 2 $ 6,000 3 $ 6,000 4 $ 6,000 5 $ 6,000 PV of Cash Inflows 0.9242 $ 0.8542 $ 0.7894 $ 0.7296 $ 0.6743 $ 5,545 5,125 4,737 4,378 4,046 23,831 1 $ 5,000 0.9294 $ 4,647 2 $ 5,000 0.86371 $ 4,319 3 $ 5,000 0.8027 $ 4,014 4 $ 5,000 0.7460 $ 3,730 5 $ 5,000 0.6933 $ 3,467 PV of Cash Inflows $ 20,176 NPV =B-A $ 43,831 NPV =B-A $ 38,176