Question

Internal Rate of Return Method for a Service Company

The Riverton Company, a ski resort, recently announced a $596,771 expansion to lodging properties, lifts, and terrain. Assume that this investment is estimated to produce $133,000 in equal annual cash flows for each of the first eight 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 eight years, using the present value of an annuity of $1 table above. If required, round your final answer to the nearest whole percent.
%

Answer 1

Let irr be x%
At irr,present value of inflows=present value of outflows.

596,771=133,000/1.0x+133,000/1.0x^2+................+133,000/1.0x^8

596,771=133,000[1/1.0x+1/1.0x^2+................+1/1.0x^8]

596,771/133,000=[1/1.0x+1/1.0x^2+................+1/1.0x^8]

[1/1.0x+1/1.0x^2+................+1/1.0x^8]=4.487

Hence looking at present value of annuity factor(15%,8 years);we get irr=15%