# Finance Essay

Time Value of Money

MINI CASE

Assume that you are nearing graduation and that you have applied for a job with a local bank. As part of the bank's evaluation process, you have been asked to take an examination which covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the following questions.

a. Draw time lines for (a) a $100 lump sum cash flow at the end of year 2, (b) an ordinary annuity of $100 per year for 3 years, and (c) an uneven cash flow stream of -$50, $100, $75, and $50 at the end of years 0 through 3.

Answer: (Begin by discussing basic discounted cash flow concepts, terminology, and solution methods.) A

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Answer: Show dollars corresponding to question mark, calculated as follows:

0 1 2 3 | | | | 100 FV = ?

After 1 year:

FV1 = PV + i1 = PV + PV(i) = PV(1 + i) = $100(1.10) = $110.00.

Similarly:

FV2 = FV1 + i2 = FV1 + FV1(i) = FV1(1 + i) = $110(1.10) = $121.00 = PV(1 + i)(1 + i) = PV(1 + i)2.

FV3 = FV2 + i3 = FV2 + FV2(i) = FV2(1 + i) = $121(1.10)=$133.10=PV(1 + i)2(1 + i)=PV(1 + i)3.

In general, we see that:

FVn = PV(1 + i)n, SO FV3 = $100(1.10)3 = $100(1.3310) = $133.10.

Note that this equation has 4 variables: FVn, PV, i, and n. Here we know all except FVn, so we solve for FVn. We will, however, often solve for one of the other three variables. By far, the easiest way to work all time value problems is with a financial calculator. Just plug in any 3 of the four values and find the 4th.

Finding future values (moving to the right along the time line) is called compounding. Note that there are 3 ways of finding FV3: using a regular calculator, financial calculator, or spreadsheets. For simple