Question

A project that will provde annual cash flows of $2,800 for nine years costs $9,200 today.
a.	At a required return of 11 percent, what is the NPV of the project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	At a required return of 27 percent, what is the NPV of the project? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.	At what discount rate would you be indifferent between accepting the project and rejecting it? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Part A:

NPV = PV of Cash Inflows - PV of cash outflows

Year	CF	PVF @11%	Disc CF
0	$ -9,200.00	1.0000	$ -9,200.00
1	$ 2,800.00	0.9009	$ 2,522.52
2	$ 2,800.00	0.8116	$ 2,272.54
3	$ 2,800.00	0.7312	$ 2,047.34
4	$ 2,800.00	0.6587	$ 1,844.45
5	$ 2,800.00	0.5935	$ 1,661.66
6	$ 2,800.00	0.5346	$ 1,496.99
7	$ 2,800.00	0.4817	$ 1,348.64
8	$ 2,800.00	0.4339	$ 1,214.99
9	$ 2,800.00	0.3909	$ 1,094.59
NPV			$ 6,303.73

Part B:

NPV = PV of Cash Inflows - PV of cash outflows

Year	CF	PVF @27%	Disc CF
0	$ -9,200.00	1.0000	$ -9,200.00
1	$ 2,800.00	0.7874	$ 2,204.72
2	$ 2,800.00	0.6200	$ 1,736.00
3	$ 2,800.00	0.4882	$ 1,366.93
4	$ 2,800.00	0.3844	$ 1,076.32
5	$ 2,800.00	0.3027	$     847.50
6	$ 2,800.00	0.2383	$     667.32
7	$ 2,800.00	0.1877	$     525.45
8	$ 2,800.00	0.1478	$     413.74
9	$ 2,800.00	0.1164	$     325.78
NPV			$      -36.22

Part C:

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

Year	CF	PVF @26%	Disc CF	PVF @27%	Disc CF
0	$ -9,200.00	1.0000	$ -9,200.00	1.0000	$ -9,200.00
1	$ 2,800.00	0.7937	$ 2,222.22	0.7874	$ 2,204.72
2	$ 2,800.00	0.6299	$ 1,763.67	0.6200	$ 1,736.00
3	$ 2,800.00	0.4999	$ 1,399.74	0.4882	$ 1,366.93
4	$ 2,800.00	0.3968	$ 1,110.90	0.3844	$ 1,076.32
5	$ 2,800.00	0.3149	$     881.67	0.3027	$     847.50
6	$ 2,800.00	0.2499	$     699.74	0.2383	$     667.32
7	$ 2,800.00	0.1983	$     555.35	0.1877	$     525.45
8	$ 2,800.00	0.1574	$     440.75	0.1478	$     413.74
9	$ 2,800.00	0.1249	$     349.80	0.1164	$     325.78
NPV			$     223.84		$      -36.22

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

= 26% + [ 223.84 / 260.06 ] * 1%

= 26% + 0.86%

= 26.86%