Question

Problem 8-15 Comparing Investment Criteria [LO 1, 3, 4, 6]

Consider the following two mutually exclusive projects:

Year A	Year B
-417000	-36000
48000	19600
58000	14100
75000	14600

532000

11400

The required return on these investments is 13 percent.

Required: (a) What is the payback period for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Payback period Project A 3.44 years Project B 2.16 years

(b) What is the NPV for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).) Net present value Project A $ Project B $

(c) What is the IRR for each project? (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).) Internal rate of return Project A % Project B %

(d) What is the profitability index for each project? (Do not round intermediate calculations. Round your answers to 3 decimal places (e.g., 32.161).)

Answer 1

Payback period is the period in which initial investment is recovered.

Project A:

Year	Opening Bal	CF	Closing Bal
1	$ 4,17,000.00	$    48,000.00	$ 3,69,000.00
2	$ 3,69,000.00	$    58,000.00	$ 3,11,000.00
3	$ 3,11,000.00	$    75,000.00	$ 2,36,000.00
4	$ 2,36,000.00	$ 5,32,000.00	$ -2,96,000.00

PBP = Year in which least CB + [ CB in that Year / CF in Next year ]

= 3 + [ 236000 / 532000 ]

= 3+0.44

= 3.44 Years

Project B:

Year	Opening Bal	CF	Closing Bal
1	$    36,000.00	$    19,600.00	$      16,400.00
2	$    16,400.00	$    14,100.00	$        2,300.00
3	$      2,300.00	$    14,600.00	$    -12,300.00
4	$ -12,300.00	$    11,400.00	$    -23,700.00

PBP = Year in which least CB + [ CB in that Year / CF in Next year ]

= 2 + [ 2300 / 14600 ]

= 2 + 0.16

= 2.16 Years

NPV = PV of Cash Inflows - PV of Cash Outflows

Project A:

Year	CF	PVF @13%	Disc CF
0	$ -4,17,000.00	1.0000	$ -4,17,000.00
1	$      48,000.00	0.8850	$      42,477.88
2	$      58,000.00	0.7831	$      45,422.51
3	$      75,000.00	0.6931	$      51,978.76
4	$ 5,32,000.00	0.6133	$ 3,26,285.56
NPV			$     49,164.71

Project B:

Year	CF	PVF @13%	Disc CF
0	$    -36,000.00	1.0000	$    -36,000.00
1	$      19,600.00	0.8850	$      17,345.13
2	$      14,100.00	0.7831	$      11,042.37
3	$      14,600.00	0.6931	$      10,118.53
4	$      11,400.00	0.6133	$        6,991.83
NPV			$        9,497.87

IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows

Project A:

Year	CF	PVF @16%	Disc CF	PVF @17%	Disc CF
0	$ -4,17,000.00	1.0000	$ -4,17,000.00	1.0000	###########
1	$      48,000.00	0.8621	$      41,379.31	0.8547	$ 41,025.64
2	$      58,000.00	0.7432	$      43,103.45	0.7305	$ 42,369.79
3	$      75,000.00	0.6407	$      48,049.33	0.6244	$ 46,827.79
4	$ 5,32,000.00	0.5523	$ 2,93,818.86	0.5337	###########
NPV			$        9,350.95		$   -2,874.96

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to 1% inc in disc Rate ] * 1%

= 16% + [ 9350.95 / 12225.90] * 1%

= 16% + 0.76%

= 16.76%

Project B:

Year	CF	PVF @26%	Disc CF	PVF @27%	Disc CF
0	$    -36,000.00	1.0000	$    -36,000.00	1.0000	$ -36,000.00
1	$      19,600.00	0.7937	$      15,555.56	0.7874	$ 15,433.07
2	$      14,100.00	0.6299	$        8,881.33	0.6200	$    8,742.02
3	$      14,600.00	0.4999	$        7,298.63	0.4882	$    7,127.57
4	$      11,400.00	0.3968	$        4,522.96	0.3844	$    4,382.18
NPV			$           258.47		$      -315.16

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to 1% inc in disc Rate ] * 1%

= 26% + [ 258.47 / 573.63 ] * 1%

= 26% + 0.45%

= 26.45%

PI = PV of Cash Inflows / PV of Cash Outflows

Project A:

Year	CF	PVF @13%	Disc CF
1	$      48,000.00	0.8850	$      42,477.88
2	$      58,000.00	0.7831	$      45,422.51
3	$      75,000.00	0.6931	$      51,978.76
4	$ 5,32,000.00	0.6133	$ 3,26,285.56
PV of Cash Inflows			$ 4,66,164.71
PV of Cash Outflows			$ 4,17,000.00
PI			1.12

Project B:

Year	CF	PVF @13%	Disc CF
1	$      19,600.00	0.8850	$      17,345.13
2	$      14,100.00	0.7831	$      11,042.37
3	$      14,600.00	0.6931	$      10,118.53
4	$      11,400.00	0.6133	$        6,991.83
PV of Cash Inflows			$     45,497.87
PV of Cash Outflows			$      36,000.00
PI			1.26

Project B: