Question

Chestnut Tree Farms has identified the following two mutually exclusive projects: Year Cash Flow (A) -$40,000 11,300 14,800 13,700 7,900 Cash Flow (B) -$40,000 17,400 14,100 12,900 2,200 Over what range of discount rates would you choose Project A?

Answer 1

Computation of incremental cash flow:

Year	Cash Flow (A)	Cash Flow (B)	Incremental Cash Flow (A-B)
0	($40,000)	($40,000)	$0
1	$11,300	$17,400	($6,100)
2	$14,800	$14,200	$600
3	$13,700	$12,900	$800
4	$7,900	$2,200	$5,700

Computation of incremental IRR:

Let’s compute IRR using trial and error method.

Let’s compute NPV using discount rate of 5 %.

Year	Incremental Cash Flow (C)	Computation of PV Factor	PV Factor @ 5 % (F)	PV (=C x F)
0	0	1/ (1+0.05) 0	1	0
1	($6,100)	1/ (1+0.05) 1	0.952380952	-$ 5809.52381
2	$600	1/ (1+0.05)2	0.907029478	$ 544.2176871
3	$800	1/ (1+0.05) 3	0.863837599	$ 691.0700788
4	$5,700	1/ (1+0.05) 4	0.822702475	$ 4689.404106
			NPV	$ 115.1680627

As the NPV is positive let’s compute NPV at discount rate of 6 %.

Year	Incremental Cash Flow (C)	Computation of PV Factor	PV Factor @ 6 % (F)	PV (=C x F)
0	0	1/ (1+0.06) 0	1	0
1	($6,100)	1/ (1+0.06) 1	0.943396226	- $ 5754.716981
2	$600	1/ (1+0.06)2	0.88999644	$ 533.997864
3	$800	1/ (1+0.06) 3	0.839619283	$ 671.6954264
4	$5,700	1/ (1+0.06) 4	0.792093663	$ 4514.93388
			NPV	-$ 34.08981024

IRR = R1 + [NPV1 x (R2 -R1) %/ (NPV1 – NPV2)

       = 5 % + [$ 115.1680627 x (6 % - 5 %)/ [$ 115.1680627 – (-$ 34.08981024)]

       = 5 % + ($ 115.1680627 x 0.01)/ ($ 115.1680627 + $ 34.08981024)

       = 5 % + ($ 1.15.1680627/ $ 149.2578729)

       = 5 % + 0.007716046

       = 5 % + 0.7716046 %

       = 5.77 %

Incremental IRR is 5.77 %

At discount rate of 5.77 %, both projects have equal NPV.

Below 5.77 % Project A is preferable as it has higher NPV in that discount region.