Question

Use the following information for the Quick Study below.

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A company is considering investing in a new machine that requires a cash payment of $41,597 today. The machine will generate annual cash flows of $17,319 for the next three years.

QS 11-13 Internal rate of return LO P4

What is the internal rate of return if the company buys this machine? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Answer 1

Internal rate of return is that rate at which all the Present values of Future cash flows will be equal to Present outflow i.e., NPV will be 0

There is no Particular formula for calculation of IRR, This can be calculated by trial and error method i.e., by using interpolation concept.

Given cash inflows for three years is $17319

Initial cash outflow is $41597

We have to assume two rates at which NPV will be calculated

Lets suppose the two rates are 10% and 15%

We have to calculate NPV at 10% and 15% for the investment

Year	Cash inflows     (A)	Present value factors @10% (B)	Present value factors @15% (C)	Present value @10%       (A*B)	Present value @15%      (A*C)
1	17319	0.909	0.869	15581	14904
2	17319	0.826	0.756	14165	12960
3	17319	0.751	0.657	12877	11270
Total				42623	39134

NPV = PV of cash inflows - Initial Cash outflow [$41597 is initial cash outflow here)

So if the rate is 10% then NPV is =42623-41597=$1026 [this is NPV at lower rate]

Similarly if rate is 15% NPV is= 39134-41597= -$2463[this is NPV at higher rate]

What should be the rate if NPV is =0?

Interpolation formula would be = Lower rate + NPV at lower rate (Higher rate- Lower rate)/(NPV at lower rate – NPV at higher rate)

By substituting the figures in above formula we get

                                        = 10% +     1026(15%-10%)/(1026-(-2463))

                                          =10%+ 1026(5%)/3489

                                         =10%+51.3/3489

                                           =10%+0.0147

                                        =11.47%

Therefore IRR is approximately equal to 11.4% in this case i.e., at 11.4% NPV will become zero.