Question

Internal Rate of Return

Manzer Enterprises is considering two independent investments:

    A new automated materials handling system that costs $900,000 and will produce net cash inflows of $300,000 at the end of each year for the next four years.

    A computer-aided manufacturing system that costs $775,000 and will produce labor savings of $400,000 and $500,000 at the end of the first year and second year, respectively.

Manzer has a cost of capital of 8 percent.

The present value tables provided in Exhibit 19B.1 and Exhibit 19B.2 must be used to solve the following problems.

Required:

1. Calculate the IRR for the first investment. Enter your answers as whole percentage values (for example, 16% should be entered as "16" in the answer box).
Between  % and  %.

Determine if it is acceptable or not.

2. Calculate the IRR of the second investment. Use 12 percent as the first guess. Enter your answers as whole percentage values (for example, 16% should be entered as "16" in the answer box).
Between  % and  %.

Comment on its acceptability.

3. What if the cash flows for the first investment are $250,000 instead of $300,000? Give your answer to the nearest whole percent.
The IRR would be about  %  

Answer 1

Ans.1. First investment:

Cost = $900,000

Annual cash flows = $300,000

Tenure = 4 years

Initial cost of investment = Sum of all cash flows discounted at a discount rate (IRR)

To compute Internal Rate of return using present value tables,

Internal Rate of Return factor = Initial investment / Annual cash flow

= $900,000 / $300,000 = 3.00

Now, looking up a Present value of an ordinary annuity (end of year cash flows) for interest rate corresponding to interest factor of 3.00 in the 4 years row, we find that 3.00 lies between 3.037 and 2.974,i.e., 12% and 13%.

So, Internal Rate of Return lies between 12% and 13%.

Ans.2. Second investment:

Cost = $775,000

1st year cash flows = $400,000

2nd year cash flows = $500,000

Tenure = 2 years

Now, using 12% as 1st guess

Present value of cash flows using PVIF table at 12% :

Present value of 1st year cash flow = $400,000 * 0.893 = $357,200

Present value of 2nd year cash flow = $500,000 * 0.797 = $398,500

Total present value = $755,700, which is less than Present value (or cost) of $775,000. So let’s try for a lower discount rate, say 11%, to increase present value of cash flows

Present value of cash flows using PVIF table at 11% :

Present value of 1st year cash flow = $400,000 * 0.901 = $360,400

Present value of 2nd year cash flow = $500,000 * 0.812 = $406,000

Total present value = $766,400

It is still lower than present value of $775,000. So, let’s try for a still lower discount rate, 10%, to increase present value of cash flows

Present value of cash flows using PVIF table at 10% :

Present value of 1st year cash flow = $400,000 * 0.909 = $363,600

Present value of 2nd year cash flow = $500,000 * 0.826 = $413,000

Total present value = $776,600

It is above the cost,i.e,$755,700

So, it means that the IRR lies between 10% and 11%.

Ans.3. First investment:

Cost = $900,000

Annual cash flows = $250,000

Tenure = 4 years

Internal Rate of Return factor = Initial investment / Annual cash flow

= $900,000 / $250,000 = 3.60

Now, looking up a Present value of an ordinary annuity (end of year cash flows) for interest rate corresponding to interest factor of 3.60 in the 4 years row, we find that 3.60 lies 3.630 and 3.546 (between 4% and 5%), more closer to 4% approx.