Question

Bruno Corporation is involved in the business of injection molding of plastics. It is considering the purchase of a new computer-aided design and manufacturing machine for $ 439,800. The company believes that with this new machine it will improve productivity and increase quality, resulting in an increase in net annual cash flows of $ 100,981 for the next 6 years. Management requires a 10% rate of return on all new investments. Click here to view PV table.

Calculate the internal rate of return on this new machine. (Round answer to 0 decimal places, e.g. 10. For calculation purposes, use 5 decimal places as displayed in the factor table provided.)

Internal rate of return

enter the internal rate of return in percentages rounded to 0 decimal places %

Answer 1

Cost of New Machine= $439800

Incremental Net Annual Cash Inflow= $ 100981

Life of the Machine= 6 years

Required Rate of Return = 10%

At Internal Rate of Return, Net Present Value = 0

Net Present Value = Present Value of all Cash Inflows - Present Value of all Cash Outflows

When Net Present Value = 0,

Present Value of all Cash Inflows = Present Value of all Cash Outflows

For computation of IRR, we have to compute the Present Value of Cash Inflows at two different levels, one at a level which gives Present Value at an amount lower than the Initial Investment and one at a level which gives Present Value at an amount higher than the Initial Investment.

We will first Compute Present Value of Cash Flow of all years at PVF @ 12%.

PV = Cash Flow / r (1- (1/(1+r)ⁿ))

where,

r = Present Value Factor

n = Number of Years

= $100981 / 0.12 (1- (1/(1+0.12)⁶))

=$ 841,508 ( 1- 0.50663)

= $ 415,173

Since at PVF 12% the amount is lower than the Initial Investment, now we have to compute the Present Value of all Cash Inflows at a rate which gives an amount higher than the initial investment. So now we will compute Present Value of Cash Flow of all years at PVF @ 9% (Lower the rate, higher the Present Value will be).

PV = Cash Flow / r (1- (1/(1+r)ⁿ))

= $100981 / 0.09 (1- (1/(1+0.09)⁶))

= $1,122,011 (1- (1/1.6771))

= $1,122,011 * 0.40373

= $ 452,993

We have computed PV at both 12% and 9% to get the Present Value at a level above the Initial Investment and at a level lower than Initial Investment.

Now we can compute the IRR using the following equation,

IRR = Lower Rate + [(Higher Rate - Lower Rate)/ (PV at Lower Rate - PV at Higher Rate)] * (PV at Lower Rate - Initial Investment)

= 9 + [(12 - 9) / (452,993 - 415,173)] * (452,993 -  439,800)

= 9 + [(3 / 37820)] * 13193

= 10.05

IRR = 10%

Conclusion: Since the new machinery has an IRR of 10%, the new machinery has met the management's required rate of return.

Note: The rate 12% and 9% is taken as an assumption to for lower rate and higher rate. The objective is to find a rate above and below the IRR rate. Student may take any rate above 10 for Higher Rate and any rate below 10 as lower rate, the answer would remain same.

Please give me a feedback for the answer. And I am happy to help you if you require any further clarification.

Thank you,