# Problem-5 (Internal rate of return and net present value methods)

## Net present value method:

Sunlight company needs a machine for its manufacturing process. The cost of the new machine is $80,700. The expected useful life of the machine is 8 years. At the end of 8-year period, the machine would have no salvage value. After installation, the machine would increase cash inflows by $30,000 per year. Sunlight is interested to know the net preset value of the machine to accept or reject this investment. The minimum required rate of return of the company is 16% on all capital investments.

**Required:**

- Compute net present value of the machine.
- Is it acceptable to purchase the machine?

### Solution:

#### (1) Net present value computation:

* Value from “present value of annuity of $1 in arrears table“.

**(2) Purchase decision:**

The positive net present value (computed above) indicates that the investment is profitable, therefore the machine should be purchased.

## Internal rate of return method:

A machine can reduce annual cost by $40,000. The cost of the machine is 223,000 and the useful life is 15 years with zero residual value.

**Required:**

- Compute internal rate of return of the machine.
- Is it an acceptable investment if cost of capital is 16%?

### Solution:

**(1) Internal rate of return (IRR) computation:**

Internal rate of return factor = Net annual cash inflow/Investment required

= $223,000/$40,000

= 5.575

Now see internal rate of return factor (5.575) in 15 year line of the present value of an annuity if $1 table. After finding this factor, see the corresponding interest rate written at the top of the column. It is 16%. Internal rate of return is, therefore, 16%.

**(2) Conclusion:**

The investment is acceptable because internal rate of return promised by the machine is equal to the cost of capital of the company.

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## 15 Comments on Problem-5 (Internal rate of return and net present value methods)

Nicely explained the two methods by the above problem but which on is the best for managerial use.

Different companies would prefer different methods. Usually a combination of capital budgeting methods is used.

is there any method of calculating IRR using NPV?

Yes, when IRR equals the rate then NPV equals 0, if IRR more then its NPV is positive, if IRR lower then NPV is in minus.

even explain what is the problem for multiple cash inflows

Both NPV and IRR are truly based time value of money. Of course these two economic analysis tools result in conflicts based on project size and timing of cash flows….

how many formulas for calculating IRR and NPV?

kindly help solve this question

A company is trying to decide whether to buy a machine for $ 80,000 which will save a cost of $20,000 pa for 5 years and which will have a resale value of $ 10,000 at the end of year 5. The company’s policy is to undertake a project that yields a return of 10% or more.

Assume the cost savings are inflows.

should this project be undertaken?

NPC – 4220

NPV – 4220

Calculate IRR from the following details

The original Investment is Rs 100000

Year Cash Inflow Discount factor @ 20% Discount factor @ 29

1 20000 0.833 0.775

2 30000 0.694 0.601

3 40000 0.579 0.466

4 50000 0.483 0.361

5 60000 0.402 0.280

IRR – 23.66

Net cash inflow Rs 2 Lakh for 6 years…cash outflow Rs.75lakh cost of capital at 11%.calculate IRR

Net cash inflow Rs 140000 for 6 years…cash outflow Rs.50 lakh cost of capital at 11%.calculate IRR

How do I solve the question below ???

Year. Cashflow

1. 900,000,000

2. 810,000,000

3-4. 960,000,000

5. 480,000,000

6. 960,000,000

7. 510,000,000

8-9. 1,350,000,000

Calculate the internal rate of return (IRR) and show that the use of IRR will generate a zero NPV