Velma and Keota (V&K;) is a partnership that owns a small company. It is conside

Question

Velma and Keota (V&K;) is a partnership that owns a small company. It is considering two alternative investment opportunities. The first investment opportunity will have a four-year useful life, will cost $12,310.94, and will generate expected cash inflows of $3,800 per year. The second investment is expected to have a useful life of five years, will cost $8,513.16, and will generate expected cash inflows of $2,600 per year. Assume that V&K; has the funds available to accept only one of the opportunities. (PV of $1 and PVA of S1) (Use appropriate factor(s) from the tables provided.) Required a. Calculate the internal rate of return of each investment opportunity. (Do not round intermediate calculations.) b. Based on the internal rates of return, which opportunity should V&K; select? Internal Rate of Return a. First investment Second investment V&K; should select the b.

Explanation / Answer

Solution:

Internal Rate of Return (IRR) is the discounting rate at which initial cash outflow of an proposed investment is equals to the present value of Cash Inflows.

In other words, at IRR Present Value of Cash Outflow is equals to Present Value of Cash Inflows.

Part a -

First Investment - Internal Rate of Return

We know, at IRR

Present Value of Cash Outflow = Present Value of Cash Inflow

$12,310.94 = Annual Cash Inflow $3,800 x Present Value of Annuity at IRR for 4 times

Present Value of Annuity at IRR for 4 period = $12,310.94 / $3,800 = 3.23972

Looking to the Table 2 Present Value of An Annuity of $1 at 9% for 4 period comes 3.23972

It means 9% is the Internal Rate of Return for First Investment

Similarly,

Second Investment - Internal Rate of Return

We know, at IRR

Present Value of Cash Outflow = Present Value of Cash Inflow

$8,513.16 = Annual Cash Inflow $2,600 x Present Value of Annuity at IRR for 5 period

Present Value of Annuity at IRR for 4 period = $8,513.16 / 2,600 = 3.274294

Looking to the Table 2 Present Value of An Annuity of $1 at 16% for 5 periods comes 3.274294

It means 16% is the Internal Rate of Return for Second Investment

IRR for First Investment = 9%

IRR for Second Investment = 16%

Part b --- The investment having higher IRR should be selected. It means the Second Investment should be selected.

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