Question

An investment has an installed cost of $521,800. The cash flows over the four-year life of the investment are projected to be $227,850, $244,450, $211,110, and $159,820.

At what discount rate is the NPV just equal to zero? (Round the final answer to 2 decimal places.)

Answer 1

We know that at IRR, NPV is 0

Computation of IRR.

Let us assume few discount rate to find out at which rate NPV is 0.

Year	Cash flows	Disc @ 10%	Discounted Cash flows	Disc @ 15%	Discounted Cash flows	Disc @ 25%	Discounted Cash flows	Disc @ 26%	Discounted Cash flows
0	($521,800)	1	($521,800)	1	($521,800)	1	($521,800)	1.0000	($521,800)
1	$227,850	0.909091	$207,136.36	0.869565	$198,130	0.833333	$189,875	0.7937	$180,833
2	$244,450	0.826446	$202,024.79	0.756144	$184,839	0.694444	$169,757	0.6299	$153,975
3	$211,110	0.751315	$158,610.07	0.657516	$138,808	0.578704	$122,170	0.4999	$105,535
4	$159,820	0.683013	$109,159.21	0.571753	$91,378	0.482253	$77,074	0.3968	$63,409
		Total	$155,130		$91,356		$37,076		($18,048)

We know that at IRR, NPV is 0.

Given in the Question NPV should be 0.

From the Table we can observe that IRR lies between 25% and 26%

We can find the exact rate by using interpolation method

L.R +[ { NPV at L.R * ( H.R - L.R)}/ ( NPV at L.R - NPV at H.R) ]

Here L.R = Lower rate and H.R = Higher ratee

= 25% +[{ $ 37076*( 26% - 25%) }/ ( $ 37076-( - $ 18048) ]

= 25% + [ $ 37076/ ( $ 55124)]

= 25% + 0.6725%

=25.6725%

Hence at 25.6725% discount rate NPV is equal to 0.

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