Computing PV according to the discounted cash flow criterion

[Sue0113]

Replacing old equipment at an immediate cost of $75000 and an additional outlay of $10000 six years from now will result
in savings of $3120 per quarter for 11years. The required rate of return is 11.4% compounded annually.
Compute the Present Value of each alternative and determine the perferred alternative according to the discounted cash flow criterion.
75000(1-1.114^-6/.114)(1.114^-3)
75000(3.589696875)(.723343241) = 194743.7145

10000(1-1.114^-6/.114)-3120(1.114)^-11
10000((3.589696875)(.304974060)=10947.64430
194743.7145 - 10947.64430 =183796.0702

Does this seam right?

 

[tkhunny]

Sue0113 - You can't just throw numbers at your calculator. You must first see and believe what it is you are supposed to be doing.

1) You provided only one scenario. That makes it difficult to compare alternatives.

2) Why do you have five occurrences of the $75,000? There should be only one.

3) Why do you have five occurrences of the $10,000? There should be only one.

4) Why do you have only one occurrences of the $3,120? There should be 44.

Give it another go.

 

[Sue0113]

Having difficulty!

I'm really struggling with this math, I've been trying......and sometimes I just don't get it.
The question is copied exactly as printed in assignment, so i'm not to sure what you mean by one scenario.
75000(1-1.114^-1/.114)(1.114)
75000(-6.874263756)(1.114)
574344.74
10000(1-1.114/.114)-3120(1.114)-44
10000(-68742.63756)-3120(.008650707)
-6.8742.63756 - 26.990020584
=68739.62758
574344.74 - 68769.62758 =505575.1124
If this is wrong I guess I just don't get it. It's been 35years since I did any math.
So please understand why I seem stupid.

 

[tkhunny]

No one said anything about "stupid". You seem just to be guessing, rather than having a plan. You are trying to use formulas when they don't exist. It certainly doesn't help anyone when the problem statement makes no sense.

immediate cost of $75000

-75,000.00 -- That's all there is to this piece. It happens at the beginning and there is no discounting and there is not repetition. Notice how it is negative. This is a cost.

and an additional outlay of $10000 six years from now

-10,000.00*(1+i)^(-6) -- That's all there is to this piece. There is only discounting, not any repetition. Negative again. More costs.

will result in savings of $3120 per quarter for 11 years.

This is a little unclear. Exactly when during the quarter will this savings occur? Since the problem statement didn't tell us, let's just make an assumption and go with it.
I'll assume the benefit is at the END of the quarter.

v = (1.114)^(1/4) -- Since we have quarterly cash flows but annual compounding.

11*4 = 44 quarters.

$3,120.00*[(v - v^(45))/(1-v)] -- This one is positive.

Add up the three pieces and you have the Net Present Value of this option.

Don't try to cram the whole thing in your head at once. Tackle it one piece at a time.