Question

Need help urgently; it's financial math! Will fan and medal anyone who can help!

Answer 1

DAY STOCK TICKER HIGH CLOSE
1 Ferber Inc FER 24.76 19.25
2 Ferber Inc FER 25.16 19.87
3 Ferber Inc FER 26.81 20.19
4 Ferber Inc FER 25.90 21.17
5 Ferber Inc FER 26.05 22.43

Suppose you purchased 87 shares of Ferber stock on Day 1 at the high price. What is the return on your investment, if you sold the stock on Day 5 at the high price?

4.95%
5.21%
16.52%
35.32%

Answer 2

@whpalmer4 So sorry to bother you but do you think you could help me with this one too? You were extremely helpful in the other question and I actually understood it

Answer 3

okay, what is your basis (cost) for the Ferber stock if you bought 87 shares at the Day 1 high?

Answer 4

there's a shortcut you can take in this problem, by the way, but I'll wait until we've done the whole thing the "long" way to tell you

Answer 5

24.76

Answer 6

Or do I multiply 24.76 by 87 ?

Answer 7

okay, that's the basis for 1 share, but you bought 87 of them, right?

Answer 8

you've stumbled across the shortcut: if we buy and sell the same quantity of shares, all we have to is figure out the percentage change of the share price. this does NOT work if we don't have the same number of shares bought and sold...

Answer 9

24.76 * 87 = 2,154.12

Answer 10

Right. And if she sells at the high price on Day 5, how much does she receive?

Answer 11

I'm not sure how to do that math, do I divide it or multiply and then subtract or something else?

Answer 12

what is the high price on day 5?

Answer 13

26.05

Answer 14

so, if she sells 87 shares at 26.05, how much does she receive?

Answer 15

She would receive $2,266.35

Answer 16

Okay. How much of a percentage increase is $2266.35 over 2154.12?

Answer 17

I know the monetary difference is $115.23 but I'm not sure how to see the percentage increase

Answer 18

okay, to find the percentage change between \(a\) and \(b\),

\[\text{% change} = \frac{b-a}{a} * 100\%\]

For example, if you go from 10 to 11:

\[\frac{11-10}{10}*100\% = 10\%\]

Answer 19

And to check, if you compute \(10\%\) of \(10\), that's \(1\), so increasing \(10\) by \(10\%\) gives you \(10+1 = 11\) just as we would expect from my example.

Answer 20

might be easier to remember as

\[\text{% change} = \frac{finish - start}{start} * 100\%\]

Answer 21

So B is 2,266.35

and A is 2,154.12 correct?

So 2,266.35-2,154.12 = 115.23 and that divided by 2,154.12 = 0.05349284 * 100% = 0.05349284

Answer 22

well, pretty close :-)

2266.35-2154.12 = 115.23

115.23/2154.12 = 0.0521

multiply that by 100% and you get 5.21%

Answer 23

So the answer is 5.21%?

Thank you so much once again for your patience and help!

Answer 24

sorry, 112.23, not 115.23

yes, the answer is 5.21%.

Notice that we could get there more quickly by simply computing the percentage change of the share price:

\[\frac{26.05-24.76}{24.76}*100\% = 5.21\% \]

Answer 25

but that works only if you have the same number of shares!

Answer 26

If you had a more complicated problem, say

Suzy buys 100 shares at $10, and sells 70 shares at $20, and the shares are now valued at $25, how much is the total return on her investment?

there you could not use the shortcut, because some of the shares are sold at a different price, and some of them aren't sold at all.

value of her investment at the end would be

70*20 + (100-70)*25 = 1400+750 = 2150
return is 2150-100*10 = 1150
which is \[\frac{2150-1000}{1000} *100\%= 11.5\%\]
(and 11.5% is not the amount the price went up!)