Question

The cash flow diagram below has an internal rate of return of 30%. What is the value of Y if perpetual service is assumed?

Year 0 is $1000000

Year 1 is $500000

Year 2 is $500000

Year 3 is $Y

Year 4 is $Y

Year 5 is $Y

Year 6 is $Y

Year ∞ is $Y

Answer 1

	cash flow	PV @ IRR 30%	PV
yr0	1000000	1
yr1	500000	0.769230769	384615.3846
yr2	500000	0.591715976	295857.9882
yr3	Y	0.455166136	0.4551661 Y
yr4	Y	0.350127797	0.3501278 y
yr5	Y	0.269329074	0.269329 y
yr6	Y	0.207176211	0.207176 y
yr ∞	Y	0.69058737	0.690587 y
		1.972386588	680473.373+1.9723865 y
total Known amount =		680473.3728
		1000000 = 680473.373+1.9724Y
		1.9724Y =	319526.6272
	Y = 319526.63/1.9724		161998.8998
			y = 161998.9 SAY 162000

Cash flow in year 0 = 1000000 is out flow and at IRR the PV of inflow will be equal to PV of outflow. the PV factor at year 6 =0.207176211. but the cash flow is perpetual after year 6, then the PV of perpetuity at 6th year end = cash flow / discount rate = y/.3 = 3.333 is discounted by using 6th year discound rate =3.33333 x 0.207176211 = 0.69058737