Question

Thom Corporation is considering an investment opportunity with the following expected net cash​ inflows:

Year​ 1, $ 230,000​; Year​ 2, $ 370,000​; Year​ 3, $ 360,000.

The company uses a discount rate of 13​%, and the initial cost of the investment is $ 720,000.

Present Value of​ $1: ​
| 10% | ​ 11% | ​12% | ​13% | ​14% | ​15%
1 | 0.909 | 0.901 | 0.893 | 0.885 | 0.877 | 0.870
2 | 0.826 | 0.812 | 0.797 | 0.783 | 0.769 | 0.756
3 | 0.751 | 0.731 | 0.712 | 0.693 | 0.675 | 0.658
4 | 0.683 | 0.659 | 0.636 | 0.613 | 0.592 | 0.572
5 | 0.621 | 0.593 | 0.567 | 0.543 | 0.519 | 0.497

The IRR of the project will be​ ________.
A. between 13​% and 14​%
B. less than 13​%
C. between 14​% and 15​%
D. more than 13​%

Answer 1

C. between 14​% and 15​%

Step-by-step explanation:

IRR (internal rate of return) is the rate whereas the net present value (NPV) of project is zero.

We can easily calculate IRR in excel by the formula = IRR(-720000,230000,370000,360000) = 14.73%

However, this exercise want you to do the calculation manually, so we have to do as followings:

- calculate NPV of each year cash inflow with every present value of $1 according to every discount rate

- The sum up of all NPV of 3 years cash inflow with the initial investment

- Any sum up nearest to zero, then the applied rate is the IRR

For example 1: we do for rate 14%

NPV of Cash inflow Year 1 = 230,000*0.877= 201.710

NPV of Cash inflow Year 2 = 370,000*0.769= 284,530

NPV of Cash inflow Year 3 = 360,000*0.675= 243,000

So NPV of investment = 201.710 + 284,530 +243,000 – 720,000= 9,240

For example 2: we do for rate 15%

NPV of Cash inflow Year 1 = 230,000*0.870= 200,100

NPV of Cash inflow Year 2 = 370,000*0.756= 279,720

NPV of Cash inflow Year 3 = 360,000*0.658= 238,880

So NPV of investment = 200,100+ 279,720 + 238,880 – 720,000= (3,300)

The NPV of investment turn from $9,240 to (3,300) when rate change from 14% to 15%; thus IRR is between 14% and 15%