Question

The Blue Sky Ski Resort plans to install a new chair lift. Construction is estimated to require an immediate outlay of $210,000. The life of the lift is estimated to be fifteen years with a salvage value of $70,000. Cost of clearing and grooming the new area is expected to be $20,000 for each of the first three years of operation. Net cash inflows from the lift are expected to be $39,000 for each of the first five years and $60,000 for each of the following ten years. Calculate the internal rate of return​ (IRR).

Answer 1

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

Cash Inflows for Year 1 to 3:

= Net Cash Inflow - COst

= $39000 - $ 20000

= $ 19000

Cash Inflows for Year 4to 5:

Net CF = 39000

Cash Flows for Year 6 to 14 :

= 60000

Cash flow Year 15:

= Net cash Flow + Salvage Value

= $ 60000 + $ 70000

= $ 130,000

IRR:

Year	CF	PVF @17%	Disc CF	PVF @18%	Disc CF
0	$ -2,10,000.00	1.0000	$ -2,10,000.00	1.0000	$ -2,10,000.00
1	$      19,000.00	0.8547	$      16,239.32	0.8475	$      16,101.69
2	$      19,000.00	0.7305	$      13,879.76	0.7182	$      13,645.50
3	$      19,000.00	0.6244	$      11,863.04	0.6086	$      11,563.99
4	$      39,000.00	0.5337	$      20,812.35	0.5158	$      20,115.77
5	$      39,000.00	0.4561	$      17,788.33	0.4371	$      17,047.26
6	$      60,000.00	0.3898	$      23,390.32	0.3704	$      22,225.89
7	$      60,000.00	0.3332	$      19,991.72	0.3139	$      18,835.50
8	$      60,000.00	0.2848	$      17,086.94	0.2660	$      15,962.29
9	$      60,000.00	0.2434	$      14,604.22	0.2255	$      13,527.36
10	$      60,000.00	0.2080	$      12,482.24	0.1911	$      11,463.87
11	$      60,000.00	0.1778	$      10,668.58	0.1619	$        9,715.14
12	$      60,000.00	0.1520	$        9,118.45	0.1372	$        8,233.17
13	$      60,000.00	0.1299	$        7,793.55	0.1163	$        6,977.26
14	$      60,000.00	0.1110	$        6,661.15	0.0985	$        5,912.94
15	$ 1,30,000.00	0.0949	$      12,335.46	0.083516	$      10,857.09
NPV	$        4,715.44		$      -7,815.27

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

= 17% + [ 4715.44 / 12530.71 ] * 1%

= 17% + [ 0.38 * 1% ]

= 17.38%