Question

Crockin Corporation is considering a machine that will save $9,000 a year in cash operating costs each year for the next six years. At the end of six years it would have no salvage value. If this machine costs $33,165 now, the machine's internal rate of return is closest to (Ignore income taxes.):

Answer 1

Answer:

rate = 16%

Explanation:

We need to understand that IRR is the one which makes the NPV equal to zero

In this case we have an annuity of 9,000 for 6 year

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C  9,000.00

time  6.00

rate  IRR

$9000 \times \frac{1-(1+IRR)^{-6} }{tir} = PV$

At the Pv will equal the invesment so:

$9000 \times \frac{1-(1+IRR)^{-6} }{tir} = 33,165$

we can look for the annuity factor in hthe table to look for the closed one

33165 / 9000 = 3.685

we can look into the table for values of n = 6 which is the closed.

And then start doing trial and error until find it.

For this particular case, hit the IRR just by looking at the table.

for n = 9 and rate = 16% factor = 3.685

This value is the factor of our annuity, so this is the rate.

Answer 2

The Internal Rate of Return (IRR) of the company is 15.97%.

What is Internal Rate of Return (IRR)?

IRR is a technique that is used to calculate the rate of return of an investment. It is used to determine the profitability of proposed investments. IRR is a rate on which NPV is zero.

The calculation of IRR can be classified into 3 steps:

1. Assuming a rate of return and calculating NPV on that rate.

2. Assuming a second rate and calculating NPV.

3. Calculating IRR using the formula:

$\rm Lower \:rate + \dfrac{NPV\:at\:lower\:rate}{NPV\:at\:lower\:rate - NPV\:at\:higher\:rate} \times (Higher\: rate - Lower\: rate)$

NPV refers to the net present value calculated as the difference between present value of inflows and the initial outflows.

The rates assumed are 15% and 16%. The calculation of NPV is given in the attachment.

The IRR therefore will be:

$\rm IRR = 15+ \dfrac{95.35}{95.35 + 2.37 } \times (16 - 15)\\\\ IRR = 15+ \dfrac{95.35}{97.92 } \\\\ IRR = 15+ 0.975\\ \\ IRR = 15.975\%$

Learn more about IRR here:

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