I get confused as far as when do I use present value of 1 table B1 or present va
ID: 2561117 • Letter: I
Question
I get confused as far as when do I use present value of 1 table B1 or present value of an annuity of 1? Do I use B1 if there is a salvage value and the cash flows are not even? Do I use annuity table B3 if the cash flows are even for example for 5 years?During an exam when do I know if it's asking the cumulative years and when it's only asking for the year end? What tables do I use? I get confused as far as when do I use present value of 1 table B1 or present value of an annuity of 1? Do I use B1 if there is a salvage value and the cash flows are not even? Do I use annuity table B3 if the cash flows are even for example for 5 years?
During an exam when do I know if it's asking the cumulative years and when it's only asking for the year end? What tables do I use?
During an exam when do I know if it's asking the cumulative years and when it's only asking for the year end? What tables do I use?
Explanation / Answer
An example could be taken for clear your doubts.
Example: Suppose a project has equal cash flow of $5,000 in each year. It has life of 5 years, and the salvage value after the end of 5 year is $2,000. The discounting rate is 10%. Calculate present value (PV).
Solution: In this case there is equal cash flow in each year; therefore, the annuity table should be used here for calculating PV of each year; but the salvage value is one-time receiving (at the end of 5th year only) therefore B1 table should be used.
PV = PV of annuity + PV of B1 table
= [$5,000 × Factor as per annuity table at 10% rate for 5 year] + [$2,000 × Factor as per B1 table at 10% rate for 5 year]
= [$5,000 × 3.7908] + [$2,000 × 0.6209]
= $18,954 + $1,241.80
= $20,195.80
Therefore, in case of regular and equal cash flows the annuity table should be used; in case of irregular and/or one-time cash flow B1 table should be used.
But we must know the relation between “annuity table” and “B1 table”. This is very important.
Annuity factor is the sum total of B1 factors.
Suppose the above annuity factor 3.7908 could be tested. In this case (at 10% rate for 5 years), B1 factors of each year are 0.9091, 0.8264, 0.7513, 0.6830, and 0.6209. If these are added (0.9091 + 0.8264 + 0.7513 + 0.6831 + 0.6209 =) 3.7908. Therefore, using the annuity table is not compulsory; we will get the same PV if “B1 table” is used; the only reason of using the annuity table is it gives quick calculation.
If the cash flows are not equal; like year1 is $5,000, year2 is $6,000, year3 is $6,000, year4 is $6,500, and year5 is $5,000; there would be no scope of using the annuity table; only the B1 table should be used here.
Cumulative years should be asked if there are equal and regular cash flows. If it is one-time or irregular cash flows (like salvage value, working capital, etc) it means it is asking for the year-end.
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