Question

Builtrite has estimated their cost of capital is 14% and they are considering the purchase of a machine with the following capital budget:

Initial Investment	$62,000
RATFCF Year 1	$38,000
RATFCF Year 2	$30,000
RATFCF Year 3	$24,000

What is the machine’s IRR?    
           
         

		20.98%
		20.80%
		20.16%
		24.90%

Answer 1

Solution:
	Answer is the 4th option 24.90%
Working Notes:
	a	b	c = a x b	d	e = a x d
Year	Cash flow	PVF @ 25%	Present value @25%	PVF @ 14%	Present value @14%
0	-62,000	1	-62,000.00	1	-62,000.00000000
1	38,000	0.80000	30,400.00	0.87719	33,333.33333333
2	30,000	0.64000	19,200.00	0.76947	23,084.02585411
3	24,000	0.51200	12,288.00	0.67497	16,199.31638885
		NPV	-112.0000	NPV	10,616.67557629
Here	Low rate =14%
	High rate =25%
	NPV at low rate @14% = 10,616.67558
	NPV at high rate @25% = -112
	Since the above cash flow is unequal the IRR will be calculated by
	IRR = low rate +( NPV at low rate / (NPV at low rate - NPV at high rate)) x (Difference in rates)
	IRR = 14% +( 10616.6755762907/ (10616.6755762907 -( -112))) x (25%-14%)
	IRR=0.248851676
	IRR = 0.2489
	IRR = 24.89%
	IRR = 24.9 %
	IRR = 24.90%	closet answer
Notes: PVF is calculated @ 14% = 1/(1+0.14)^n     where n is the period for which PVF is calculated.
Please feel free to ask if anything about above solution in comment section of the question.