Time Value of money

[Pandora]

Shawn is considering the purchase of a new piece of equipment which will cost $100,000 in cash. The
old piece of equipment it will replace originally cost $84,000 and can now be sold
for $16,000. Annual cash savings of $15,000 are expected for (10) ten years.

a) Compute the NPV (net present value) of the replacement alternative,
assuming that the desired rate of return is 10%.
b) What will be the IRR (internal rate of return)?
c) How long is the payback period on the incremental investment?
d) Would you recommend they proceed or not? Why?

I have answered all the questions, can anyone please tell me if I have done them right? Thank you

a) CF0 (100,000) + 16,000 = (84,000)
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
= 15,000[(1 - (1 / 1.10^10)) / 0.10]
= 15,000[(1 - 0.38554) / 0.10]
= 15,000[6.14457]
= $92,168.51 (rounded)

NPV = (84,000) + 92,168.51 = $8,168.51

b) IRR = 12.21869%

c) Payback period: 84,000 / 15,000 = 5.6 years
d) Yes, they should proceed because the NPV is positive and IRR of 12.2% is greater than the required rate of return of 10%.

 

[Ishuda]

92,168.51 is correct; but shouldn't you add 16,000 INSTEAD of deducting 84,000?

Don't think so. You are doing the computations under the assumption that you will buy the the 100K piece of equipment minus the 16K 'trade in value' which would be a total outlay of 84K cash.

 

[Ishuda]

...I have answered all the questions, can anyone please tell me if I have done them right? Thank you
...

Yes, I believe you have.

 

[jonah2.0]

WARNING: Beer soaked rambling/opinion/observation ahead. Read at your own risk. Not to be taken seriously. In no event shall Sir jonah in his inebriated state be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his beer (and tequila) powered views.

Shawn is considering the purchase of a new piece of equipment which will cost $100,000 in cash. The
old piece of equipment it will replace originally cost $84,000 and can now be sold
for $16,000. Annual cash savings of $15,000 are expected for (10) ten years.

a) Compute the NPV (net present value) of the replacement alternative,
assuming that the desired rate of return is 10%.
b) What will be the IRR (internal rate of return)?
c) How long is the payback period on the incremental investment?
d) Would you recommend they proceed or not? Why?

I have answered all the questions, can anyone please tell me if I have done them right? Thank you

a) CF0 (100,000) + 16,000 = (84,000)
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
= 15,000[(1 - (1 / 1.10^10)) / 0.10]
= 15,000[(1 - 0.38554) / 0.10]
= 15,000[6.14457]
= $92,168.51 (rounded)

NPV = (84,000) + 92,168.51 = $8,168.51

b) IRR = 12.21869%

c) Payback period: 84,000 / 15,000 = 5.6 years
d) Yes, they should proceed because the NPV is positive and IRR of 12.2% is greater than the required rate of return of 10%.

I wish all students (if you are one) are as competent as you are.