PResent Worth and Annual Worth

Tallulah

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Jun 21, 2011
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Hello! Here is the problem...

Allied Electrons must purchase a new automatic soldering machine to meet increased demand for its electronic goods. Of all the machines considered, management has narrowed the choices to the following three mutually exclusive machines. Allied uses a planning horizon of four years (all three can last this long) and a MARR of 10%. The initial cost is at (year 0) and the payments are in years 1-4. Determine the present worth, future worth, and annual worth for when the salvage value is in year 4.

Initial Cost (in Year 0) $800,000
Annual Operating Cost $50,000
Salvage value (in year 4) $40,000
MARR 10%
Period 4 years


I only showed calculations for 1 machine since I figure the calculation methods would be the same for each machine. I first created a table to show cash flow for each year and then calculated the PW of this cash flow, which is below. Then using the PW answer I calculated my FW. To calculate annual worth, I used the salvage value as my future value. I am just wondering if I calculated these correctly? I wasnt exactly sure whether to use my own Calculated FV ($1.3M) or use the salvage value ($40K) in order to calculate my annual worth. Any assistance/explanation would be appreciated. Thanks.

Year Cash Flow
0 (800,000.00)
1 (50,000.00)
2 (50,000.00)
3 (50,000.00)
4 (10,000.00)

PW (931,172.73) I also calculated this using our interest tables (in the book) and calculated the PW to be (931,173.10).
FV ($1,363,330.00)
AW ($310,995.48)
 
Okay, is that how you are supposed to calculate these values? What errors did you make on purpose?

Please define "Annual Worth".
 
Tallulah said:
Hello! Here is the problem...

Allied Electrons must purchase a new automatic soldering machine to meet increased demand for its electronic goods. Of all the machines considered, management has narrowed the choices to the following three mutually exclusive machines. Allied uses a planning horizon of four years (all three can last this long) and a MARR of 10%. We are not mind readers. I am guessing that MARR stands for Marginal Annual Rate of Return on the machine. If so, what is the denominator in the definition of MARR? The initial cost is at (year 0) and the payments are in years 1-4. Determine the present worth (present value ?), future worth (future value ?), and annual worth (no idea what this is, do you have a definition?) for when the salvage value is in year 4.

Initial Cost (in Year 0) $800,000
Annual Operating Cost $50,000 Presumably incurred at year end?
Salvage value (in year 4) $40,000 Presumably realized at year end?
MARR 10%
Period 4 years


I only showed calculations for 1 machine since I figure the calculation methods would be the same for each machine. Yes good thought. I first created a table to show cash flow for each year and then calculated the PW of this cash flow, which is below. I do not understand what you are trying to do. All your cash flows are negative so it looks on the surface like a really bad investment. That is OK, however, if you are just comparing the costs of the machines. In that case, I guess MARR is the discount rate. If, on the other hand, you are supposed to be calculating the economic value of the investment, you need to incorporate information about the revenue that the machine will produce. Then using the PW answer I calculated my FW. To calculate annual worth, I used the salvage value as my future value. I am just wondering if I calculated these correctly? I wasnt exactly sure whether to use my own Calculated FV ($1.3M) or use the salvage value ($40K) in order to calculate my annual worth. Well the salvage value is not a cost so my guess that this was about cost comparisons may look shaky. Of course you can treat salvage value as an offset to cost. It looks in fact as though that is what you did in year 4, 50K in operating offset by 40K in salvage value. If that is what you did, you cannot count the salvage value again. Any assistance/explanation would be appreciated. Thanks.

I think you need to be much more clear about your terminology and what the problem is asking for before we can provide much help.

Year Cash Flow
0 (800,000.00)
1 (50,000.00)
2 (50,000.00)
3 (50,000.00)
4 (10,000.00)

PW (931,172.73) I also calculated this using our interest tables (in the book) and calculated the PW to be (931,173.10).
FV ($1,363,330.00)
AW ($310,995.48)
 
MARR means minimum attractive rate of return. It also can be referred to as the hurdle rate.
Future Worth is future value
Annual Worth is the value of an equivalent uniform annual series of cash flow
Present Worth is Present Value. When using MARR, PW

All costs were incurred at the end of the year.

I created the table and made the cash flows negative based on how the question read. I am figuring that annual operating costs are negative since it's cash paid by the organization. However, the salvage value would be a positive cash flow since you are selling the machine. So, yes I offset the annual operating costs ($50K) in year 4 by the salvage value. Should I not do this?

Do you need any more information?
 
Tallulah said:
OK I agree with you on present value of 931,172.73
MARR means minimum attractive rate of return. It also can be referred to as the hurdle rate. Ahh hurdle rate. Thanks
Future Worth is future value
Annual Worth is the value of an equivalent uniform annual series of cash flow Why would that not be identical to present or future value? Or is it the annual cash flow that would have an equal present (future ?) value to the actual present (future ?) value at the same discount rate over the same term?
Present Worth is Present Value. When using MARR, PW

All costs were incurred at the end of the year.

I created the table and made the cash flows negative based on how the question read. That is typical to make costs negative and benefits positive. I am figuring that annual operating costs are negative since it's cash paid by the organization. Right you are. However, the salvage value would be a positive cash flow since you are selling the machine. Again, you are quite right. So, yes I offset the annual operating costs ($50K) in year 4 by the salvage value. Should I not do this? That is a perfectly sensible thing to do. I was just saying that you could not do this and then count salvage value again somewhere.

Do you need any more information? Just make sure that I really understand this concept of annual worth See question above
 
Hi JeffM:

I believe annual worth is a preferable terminology that is used when comparing investments alternatives for their economic worth. Think of it this way, if you use PW to compare alternative investments, then you have a preference to use a single sum of money at the "present" as a basis of comparison. The same goes for using a future value. So, instead of expressing an investment alternative as a single sum as with PW or FW, you are thinking in terms of an annualized figure. Does that make sense?
 
Tallulah said:
Hi JeffM:

I believe annual worth is a preferable terminology that is used when comparing investments alternatives for their economic worth. Think of it this way, if you use PW to compare alternative investments, then you have a preference to use a single sum of money at the "present" as a basis of comparison. The same goes for using a future value. So, instead of expressing an investment alternative as a single sum as with PW or FW, you are thinking in terms of an annualized figure. Does that make sense?
Well you need to learn what you are being taught and will be examined on. As a practical matter, present value is already a theoretical abstraction. For example, in your problem, do you already have or can you acquire 800K to make the initial investment? If not, the problem is moot. Are interest rates likely to be constant over a four-year time horizon? If not, what are the probabilities of different interest rate forecasts. Obviously, real-world analysis quickly becomes very complicated. So calculating the present value of a theoretically equivalent annuity rather than the present value of the estimated cash flows seems to me to introduce a known fiction into what is already an analysis subject to considerable uncertainty. But that is my personal opinion, and you should absolutely ignore it until after you have completed your course successfully. Maybe you should ignore it even then because most bosses tend to like simple answers.

By the way, if you are looking for the annuity in arrears over four years at a rate of 10% annually that has a present value equal to 931,172.73, I think the correct answer is 293,757.81. Check my work; it's been a long day for me.
 
This is what it "looks like" (using Jeff's annual equivalent):
Code:
0          800,000             800,000
1 -293,758  50,000   80,000    636,242
2 -293,758  50,000   63,624    456,108
3 -293,758  50,000   45,611    257,961
4 -293,758  10,000   25,797          0
 
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