Question

Internal Rate of Return Method for a Service Company

The Riverton Company, announced a $620,761 million expansion of lodging properties, ski lifts, and terrain in Park City, Utah. Assume that this investment is estimated to produce $151,000 million in equal annual cash flows for each of the first six years of the project life.

Present Value of an Annuity of $1 at Compound Interest
Year	6%	10%	12%	15%	20%
1	0.943	0.909	0.893	0.870	0.833
2	1.833	1.736	1.690	1.626	1.528
3	2.673	2.487	2.402	2.283	2.106
4	3.465	3.170	3.037	2.855	2.589
5	4.212	3.791	3.605	3.353	2.991
6	4.917	4.355	4.111	3.785	3.326
7	5.582	4.868	4.564	4.160	3.605
8	6.210	5.335	4.968	4.487	3.837
9	6.802	5.759	5.328	4.772	4.031
10	7.360	6.145	5.650	5.019	4.192

a. Determine the expected internal rate of return of this project for six years, using the present value of an annuity of $1 table above.
%

b. Identify the uncertainties that could reduce the internal rate of return of this project?
All of these

Answer 1

1)	IRR = 12%
	IRR: IRR stands for Internal rate of return, it is a rate where Net present value is zero.
	Steps: To Calculate IRR, we took two random discount rate where at one present value is in negative while in other in positive. Here we took 20% and 28%.
	Year	Cash Flows	PVF	PVF	Present Value at	Present Value at
			10%	15%	10%	15%
	0	(620,761)	1.00000	1.000	(620,761)	(620,761)
	1	151,000	0.90909	0.86957	137,273	131,304
	2	151,000	0.82645	0.75614	124,793	114,178
	3	151,000	0.75131	0.65752	113,449	99,285
	4	151,000	0.68301	0.57175	103,135	86,335
	5	151,000	0.62092	0.49718	93,759	75,074
	6	151,000	0.56447	0.43233	85,236	65,281
		Net Present Value			36,883	(49,304)
	IRR = Lower Discount Rate + [Lower Rate NPV / (Lower Rate NPV - Higher Rate NPV)] * (Higher Discount Rate - Lower Discount Rate)
	By putting above values in the give formula we get IRR = 12%
2)	Following are the uncertainicities
	a) Fluctuation is cash flow
	b) Change in market rate of interest during the project
	c) Fluctuations in amount of initial investment