Question

1. Project L requires an initial outlay at t = 0 of $40,000, its expected cash inflows are $15,000 per year for 9 years, and its WACC is 10%. What is the project's NPV? Do not round intermediate calculations. Round your answer to the nearest cent.

2. Project L requires an initial outlay at t = 0 of $43,775, its expected cash inflows are $9,000 per year for 8 years, and its WACC is 13%. What is the project's IRR? Round your answer to two decimal places.

3. Project L requires an initial outlay at t = 0 of $55,000, its expected cash inflows are $11,000 per year for 9 years, and its WACC is 9%. What is the project's MIRR? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Part 1:

NPV = PV of Cash Inflows - PV of Cash Outflows

Year	CF	PVF @10%	Disc CF
0	$ -40,000.00	1.0000	$ -40,000.00
1	$ 15,000.00	0.9091	$ 13,636.36
2	$ 15,000.00	0.8264	$ 12,396.69
3	$ 15,000.00	0.7513	$ 11,269.72
4	$ 15,000.00	0.6830	$ 10,245.20
5	$ 15,000.00	0.6209	$    9,313.82
6	$ 15,000.00	0.5645	$    8,467.11
7	$ 15,000.00	0.5132	$    7,697.37
8	$ 15,000.00	0.4665	$    6,997.61
9	$ 15,000.00	0.4241	$    6,361.46
NPV			$ 46,385.36

Part 2:

IRR is the rate at which PV of cash inflows are equal to PV of cash Outflows.

Year	CF	PVF @12%	Disc CF	PVF @13%	Disc CF
0	$ -43,775.00	1.0000	$ -43,775.00	1.0000	$ -43,775.00
1	$    9,000.00	0.8929	$    8,035.71	0.8850	$    7,964.60
2	$    9,000.00	0.7972	$    7,174.74	0.7831	$    7,048.32
3	$    9,000.00	0.7118	$    6,406.02	0.6931	$    6,237.45
4	$    9,000.00	0.6355	$    5,719.66	0.6133	$    5,519.87
5	$    9,000.00	0.5674	$    5,106.84	0.5428	$    4,884.84
6	$    9,000.00	0.5066	$    4,559.68	0.4803	$    4,322.87
7	$    9,000.00	0.4523	$    4,071.14	0.4251	$    3,825.55
8	$    9,000.00	0.4039	$    3,634.95	0.3762	$    3,385.44
NPV			$        933.76		$      -586.07

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

= 12% + [ 933.76 / 1519.83 ] * 1%

= 12% + 0.61%

= 12.61%

Part 3:

MIRR is similar to IRR, In IRR it is assumed that intermediry Cfs are reinvested at IRR. In MIRR intermediary CFs are reinvested at Cost of Capital.

Year	Bal Years	CF	FVF @9%	FV of CF
1	8	$ 11,000.00	1.9926	$    21,918.19
2	7	$ 11,000.00	1.8280	$    20,108.43
3	6	$ 11,000.00	1.6771	$    18,448.10
4	5	$ 11,000.00	1.5386	$    16,924.86
5	4	$ 11,000.00	1.4116	$    15,527.40
6	3	$ 11,000.00	1.2950	$    14,245.32
7	2	$ 11,000.00	1.1881	$    13,069.10
8	1	$ 11,000.00	1.0900	$    11,990.00
9	0	$ 11,000.00	1.0000	$    11,000.00
FV of CFs				$1,43,231.40

Thus $ 55000 has become $ 143,231.40 over a period of 9 years

Fv = PV (1+r)^n

143231.40 = 55000(1+r)^9

(1+r)^9 = 143231.40 / 55000

= 2.6042

1+r = 2.6042^ ( 1 / 9)

= 1.1122

r = 1.1122 - 1

= 0.1122 i.e 11.22%