<p>The table appears to have a bunch of errors in it.  In particular, the cash flow column seems wrong in every instance.  I don't blame you for having problems understanding.  </p>

<p>For your first question, the cash flow in time 0 is wrong.  $1.1^0=1$ as we know.  The "end of year 0" means "right now," so there should be no discounting at all.  The cash flow should be -100,000, as indicated by the correct value in the present value column.  </p>

<p>For your second question, cash flow is discounted at the required rate of return to get the present value.  In this case, presumably</p>

<p>$$
\frac{25,454.55}{(1+0.1)^1} = 23,140.50
$$</p>

<p>Why does that not equal the present value column?  Because the table was set up by someone who was confused.  The quantity they put in the present value is simply the discounted value of \$30,000 - \$5,000. </p>

<p>$$
\frac{30,000-5,000}{(1+0.1)^1} = 22,727.27
$$</p>

<p>To me that seems like a reasonable solution to the problem text.  The next period's cash flow should again be (\$30,000-\$5,000) and its present value should be </p>

<p>$$
\frac{30,000-5,000}{(1+0.1)^2} = 20,661.16
$$</p>

<p>Anyway, the present value column seems right given the text of the problem.  The "cash flow" column was done by someone who was as confused as you are, if not more so.</p>

<p>Probably you got this already, but to solve the problem you simply take the sum of everything in the present value column.</p>

<p>-------------- EDIT -------------</p>

<p>Now that I look at it again, I bet they just forgot to put parentheses around the (30000-5000) in each entry.  And left off a few zeros in the first.  Shabby, but not as bad as I was originally thinking.</p>

CC BY-SA 3.0
2017-04-09T22:18:42.140Z
2017-04-09T22:42:10.510Z
2017-04-09T22:42:10.510Z
farnsy
<p>​First: for year 0, I do not know why the cash flow = $- 1000 / ( 1 + 0.10)^0 = 909.01$</p>

<p>Second: for year 1, if cash flow = $30,000-5000/(1+0.10)^1 = 25 454 $</p>

<p>How is "Cash Flow" column useful in getting the "Present Value" column? </p>

<p><a href="https://i.sstatic.net/Lc6Kj.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Lc6Kj.png" alt="enter image description here"></a></p>

<macroeconomics><microeconomics>
Cash Flow and present value Question
Hossam EL-Shahaby
# Cash Flow and present value Question

(Asked by: username_0 on 2017-04-09)

​First: for year 0, I do not know why the cash flow = $- 1000 / ( 1 + 0.10)^0 = 909.01$

Second: for year 1, if cash flow = $30,000-5000/(1+0.10)^1 = 25 454 $

How is "Cash Flow" column useful in getting the "Present Value" column?

[![enter image description here](https://i.sstatic.net/Lc6Kj.png)](https://i.sstatic.net/Lc6Kj.png)

**Tags:** macroeconomics, microeconomics

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## 1 answers

### Answer by username_1 on 2017-04-09. Score: 2

The table appears to have a bunch of errors in it. In particular, the cash flow column seems wrong in every instance. I don't blame you for having problems understanding.

For your first question, the cash flow in time 0 is wrong. $1.1^0=1$ as we know. The "end of year 0" means "right now," so there should be no discounting at all. The cash flow should be -100,000, as indicated by the correct value in the present value column.

For your second question, cash flow is discounted at the required rate of return to get the present value. In this case, presumably

$$
\frac{25,454.55}{(1+0.1)^1} = 23,140.50
$$

Why does that not equal the present value column? Because the table was set up by someone who was confused. The quantity they put in the present value is simply the discounted value of \$30,000 - \$5,000.

$$
\frac{30,000-5,000}{(1+0.1)^1} = 22,727.27
$$

To me that seems like a reasonable solution to the problem text. The next period's cash flow should again be (\$30,000-\$5,000) and its present value should be

$$
\frac{30,000-5,000}{(1+0.1)^2} = 20,661.16
$$

Anyway, the present value column seems right given the text of the problem. The "cash flow" column was done by someone who was as confused as you are, if not more so.

Probably you got this already, but to solve the problem you simply take the sum of everything in the present value column.

-------------- EDIT -------------

Now that I look at it again, I bet they just forgot to put parentheses around the (30000-5000) in each entry. And left off a few zeros in the first. Shabby, but not as bad as I was originally thinking.


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