[pres2112]

Pole Cp. is investing in a machine with a 3 year life. The machine is expected to reduce annual cash operating costs by $30,000 in each of the first 2 years and in year 3 by $20,000. Present Values of an annuity of $1 at 14% are:

Period 1 -.88

Period 2 -1.65

Period 3 -2.32

Using a 14% cost of capital, what is the present value of these future savings?

Per the Becker explanation, the answer is $62,900.

PV of year 1: 30,000 x 0.88 = 26400

PV of year 2: 30000 x [1.65-.88] = 23100

PV of year 3: 20000 x [2.32-1.65]= 13400

Total= 62900

My question about this solution:

I don’t understand why they are subtracting the PV factors against the previous period PV factors in years 2 and 3. From my understanding you should multiply each uneven cash flows by the respective pv factor for that year. Can anyone clear this up for me please.

Any help is greatly appreciated.

[2BORNOT2B]

I remember this Question…You need to look at each year individually if the respective cash flows are different. Remember, you are DISCOUNTING the total cash flow back to PV. If all of the future cash flows are the same you could multiply the cumulative rate by the 1 cash flow number. For example the cash flow for year 1 & 2 is 30,000 each…30,000 x 1.65 = 49,500 + 20,000 x .67 = 13,400. 49,500+13,400 = 62,900. Does this help??? I looked at it a couple time my first shot also…

[pres2112]

I agree that since the cash flows are different that we need to look at each year individually and discount them back accordingly. I guess my issue is that when looking at the PV factors, I assumed that they were for individual years versus a cumulative point of time. With this question, you have to extrapolate the individual periods PV factors to calculate the answer.

[pres2112]

I guess my next question is how are you suppose to tell if the PV factors are for one period or a cumulative period (ie per above) when the question doesn't indicate it?

[michelle119]

@pres2112 – If it is for a cumulative period it is labeled “PV of $1 annuity factor” or something to that extent. Additionally you can see that after Year 1 they are greater than 1 which usually helps me recognize that these are for annuities.

FAR 7/2 - 88
BEC 7/30 - 87
AUD 8/27 - 80
REG 11/12 - 96

[2BORNOT2B]

It is confusing, I guess my best answer is that if the future cash flows are constant every year, you do not have to extrapolate the rate and just use the given rate. If the cash flow changes in any year, you need to extrapolate the rate for that year. i.e 2.32-1.65=.67……….. yr1 30,000, yr2 30,000, you could use 1.65 x 30,000, for the last year 20,000 you have to use the individual rate for that year. I hope I am helping and not confusing you even more, I may not be explaing it very well.

[2BORNOT2B]

Again, remember that the annuity table will work if the cash flows are constant year to year, it will not work if the cash flows change from year to year.

[Trevor]

Not sure if this will confuse more or help, but this is what I see:

You must find the PV of the annual cash flows. For an annuity the payment MUST be eqaul. In this case you can take The PV of annuity for 2 years and mulitply it by the constant cash flow of 30,000. (1.65*30,000=49,500).

Now because the 3rd year it not an eqaul payment you simply find the PV of that. In order to get the PV of $1 from the information given you must subtract the PV of annuity of $1 for 2 years form the third (2.32-1.65=.67) then multiply that by the 20,000 cash inflow and that would give you 13,400.

The total is then 62,900 (49,500+13400).

BEC: 73,81(7/6/2010); AUD: 75(5/24/2010); FAR: 76(8/31/2010); REG: 77 (10/18/2010) - DONE!!!!

[pres2112]

I understand it now. Thank you everyone for your help.

[Anonymous]

Sounds like you already have it figured out but I thought I'd add in my .02. The present value factor should get progressively smaller the further out in the future it is if it is the PV of $1 (not the PV of an annuity). You probably noticed that on all of the other “PV of $1” questions you had. An easy way to see if you need to extrapolate the PV factors for each year is see if the factor grows or shrinks. In the question you posted up, the factor grows so you know it must be cumulative and thus require extrapolation to get each individual year's factor.

Hope that helps.

[Author]

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