Question

You have been asked to consult on the Rio Salado 2.0 Project, which is an effort to restore the Salt River as it flows through Phoenix. The project will cost $29,000,000 in the first year and an additional $600,000 each year for another 11 years. The increased amenities, recreational opportunities, and local business activity are expected to yield $4,000,000 in benefits each year, beginning in the second year of the project. The benefit yield will last 12 years total, starting the 1st year.

Find the breakeven discount rate such that the net present value of this development opportunity is zero (i.e. find the internal rate of return)

Please provide steps to explain how you found the answer. I am really confused.

Answer 1

Computation of Internal rate of return:

Year	Amount	Disc @ 1%	Discounted value	Disc @ 3%	Discounted value	Disc @ 4%	Discounted value	Disc @ 5%	Discounted value
1	($29,000,000)	0.99009901	($28,712,871.29)	0.970874	($28,155,339.81)	0.961538	($27,884,615.38)	0.952381	($27,619,047.62)
2	$3,400,000	0.980296049	$3,333,006.57	0.942596	$3,204,826.09	0.924556	$3,143,491.12	0.907029	$3,083,900.23
3	$3,400,000	0.970590148	$3,300,006.50	0.915142	$3,111,481.64	0.888996	$3,022,587.62	0.863838	$2,937,047.84
4	$3,400,000	0.960980344	$3,267,333.17	0.888487	$3,020,855.96	0.854804	$2,906,334.25	0.822702	$2,797,188.41
5	$3,400,000	0.951465688	$3,234,983.34	0.862609	$2,932,869.87	0.821927	$2,794,552.16	0.783526	$2,663,988.97
6	$3,400,000	0.942045235	$3,202,953.80	0.837484	$2,847,446.47	0.790315	$2,687,069.39	0.746215	$2,537,132.35
7	$3,400,000	0.932718055	$3,171,241.39	0.813092	$2,764,511.14	0.759918	$2,583,720.56	0.710681	$2,416,316.52
8	$3,400,000	0.923483222	$3,139,842.96	0.789409	$2,683,991.40	0.73069	$2,484,346.70	0.676839	$2,301,253.83
9	$3,400,000	0.914339824	$3,108,755.40	0.766417	$2,605,816.89	0.702587	$2,388,794.90	0.644609	$2,191,670.32
10	$3,400,000	0.905286955	$3,077,975.65	0.744094	$2,529,919.31	0.675564	$2,296,918.17	0.613913	$2,087,305.06
11	$3,400,000	0.896323718	$3,047,500.64	0.722421	$2,456,232.34	0.649581	$2,208,575.17	0.584679	$1,987,909.58
12	$3,400,000	0.887449225	$3,017,327.37	0.70138	$2,384,691.59	0.624597	$2,123,629.97	0.556837	$1,893,247.22
		Total	$6,188,055.49		$2,387,302.90		$755,404.63		($722,087.29)

Annual Cash flow = $ 40,00000-$ 600000= $ 34,00000

We know that

At IRR, Present value of cash inflows is equal to the Present value of cash outflows

So NPV should be 0.

From the table we can say that IRR lies between 4% and 5%

By using interpolation technique we can find the IRR.

Disc rate	NPV
4%	$755,404.63
5%	($722,087.29)

For 1% Change in Discount rate, Change in NPV is $ 755404.63-( -$ 722087.29) is $ 1477491.92

Change in Disc	Change In NPV
1%	$1,477,491.92
X	$755,404.63

X = $ 755404.63/$ 1477491.92

X = 0.5112

Hence the IRR is 4% + 0.5112% = 4.5112%

Hence Break Even Discount rate is 4.5112%.

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