To cut right to the chase I’ll dive right into the question, and if you think this is a homework problem or want the situation behind the question you can read my P.S. below.
Starting with $0 on July 1st if deposit $208.33 on the 15th and 30th of July, August and September. I will have contributed a total of $1249.98. On October 1st the balance in my account is $1437.48.
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My question is what is the annual yield have I earned in these 90 days?**
I’m fairly good with numbers, but this has me stumped because of the biweekly contributions. This isn’t life or death, but if anyone could help me out I’d appreciate it. Thanks.
P.S. The story behind the math…
I work at a bank where we have the option of having money automatically deducted from our paychecks (up to $5,000 per year) and this money is used quarterly to purchase shares of our company at a 15% discount. Now after following the whole Enron fiasco I have no desire to use company stock as a savings vehicle.
The kicker is that there is no required holding period for these shares so the day they grant them to me I am able to cash them out penalty free. So I can’t turn down a guaranteed 15% return. (I am aware of the tax issues regarding selling the share immediately)
I’m trying to convince my co-workers that this is a much better investment idea than putting the money into a CD or Savings account not just because its a risk free savings at a great rate, but also because the money that you contribute just before the period ends earns the same 15% as the money that you immediately invested. I’d like to show them just how MUCH better a savings vehicle it is. The people I work with would rather have a 5.5% yield that they don’t have to do any tax papers for than a 15% return that they do. I want to show them that it actually earns a helluva lot more than the flat 15% when you look at the whole picture.
The semimonthly interest rate j satisfies 1437.48j = 208.33((1 + j)[sup]6[/sup] - 1), but I don’t have my financial calculator with me, so I can’t give you a numerical value. Once you do have it, the annual interest rate can be calculated as i = (1 + j/24)[sup]24[/sup] - 1.
I screwed this up–the interest rate j is already per half-month, so there’s no need to divide by 24. Sticking this into Excel as (1 + RATE(6,-208.33,0,1437.48,0))^24 - 1, I get that you’re earning about 267% interest per year. Either these numbers are fake, or I want in on this scheme.
Nope its not a mistake, I figured it would be roughly 300%. The catch is that you can only contribute $5000 over the course of the year. They used to purchase the shares once a year and you got to buy the shares at either 85% of the ending price or 85% of the beginning price, whichever price is lower!!!
It was a pretty good arrangement and in previous years you’d make 30-40% profit without risk. Then the whole backdating stock options mess hit so they changed it to 85% of the ending price every quarter. I prefer the latter option because I need the quarterly “bonus” checks for ~$1500.00.
Since this is the first year they’ve done it I’m taking advantage of it and I don’t know if my good fortune will last very long.
using round numbers and i am sure someone wll correct my error it seems as if you are saving $1250 per quarter and have on the average $625 invested at any point in time, since you sell the stock immediately after buying it you starty fresh every quarter. since you made $187.50 for 1 quarter you can expect to make $750 for the year, more or less on your $625 investment which works out to 120% on your money with very little risk, virtually none after that first year.
The average amount invested isn’t a particularly meaningful measure, and you can’t combine the per quarter returns and treat them as per quarter interest like that.
I am just wondering why, frankly when you give me a formula like the one you gave it means nothing to me. I always compute interest this way and it seems to be reasonably accurate.
The 300 or 267 % number that you arrived at would cause me to expect a $15,000 profit at the end of a year given the $5000 investment or if you take my average investment of $625 an $1875 profit. (While I still arrive at an average expected profit of $750.)
Which numbers are more accurate or relevant when compared to putting your $5000 in the bank at 5% for the year?
It probably does work for a single deposit, but when you have a series of deposits like in the OP (known as an annuity), you have to use the right formulas. If you have deposits of $R at times 1, 2, …, n, and j is the effective interest rate per period, the accumulated value at time n is $R((1 + j)[sup]n[/sup] - 1)/j (see here for a short overview). If your computation doesn’t agree with that formula, it’s not right.
The big issue here (and the reason I needed help calculating it) is because the 208.33 I deposit at the beginning of the quarter gives me the same return of 15% as the money that I invest literally the day before I cash out. So while the first quarter deposit makes 15% in 3 months, the last deposit earns 15% in 24 hours.
I think you might be able to take an average, but the rate on the last deposit would be so astronomically huge that it would bring the overall rate up significantly.
I don’t think it’s a mistake. 15% ESPP discount is fairly common. It’s a benefit that’s part of your compensation. The trick is that unless you hold it 2 years after the grant you’re paying short-term capital gains on any profits you get.
Well, you’re going to pay income tax on any savings account, as well. I’d rather have to pay income tax on a 300% rate of return than on a 5% rate of return.
The 15% discount is the maximum allowed on an Employee Stock Purchase Plan (ESPP) by the IRS (or perhaps the SEC) without nasty tax implications. I’m surprised that they don’t require some sort of holding period; allowing you to immediately cash out seems like a somewhat silly lack of forethought on the part of the people who designed the plan.
Yes, by cashing it out immediately it becomes taxable as ordinary income, which isn’t as nice as if I were to hold it for two years. Honestly though, I don’t have the money to invest $5,000 a year and leave it sit, and even if I did I wouldn’t leave it in company stock. I look at it as giving myself a $750.00 a year raise. I thought that it was odd also that there was no holding period, but I’m not complaining.
Well, the answer is just a number and not coin of the realm, as they say, but you just alluded to your $750/yr. raise. And you are getting that by investing how much? If you are cashing out immediately I say your investment is basiclally $625, half of the max $1250 (the most you will ever have in there) but even if you ignore the last deposit, since it is only there for 24 hours, and take half of $833 your effective rate of return would be less than 200%. I just don’t understand why my number is so different.
Using the Excel **rate ** function =RATE(6, -208.33, ,1437.48,0) I get an effective rate of 5.57% which is about 133% per annum allowing for 24 periods.
It’s called an ESPP (Employee Stock Purchase Plan). There’s no holding period because once the shares are purchased on your behalf, they’re yours to do with as you please.
Also, INA tax professional, but I think it’s one year for long term capital gains, not two.
The actual number is somewhere between one and two depending on what price is used for the grant, I believe. If I’m not mistaken it’s two years from the date of the price used, which can be effectively a year from the date of the purchase. Tax professionals, correct me if I’m wrong.
Yes thats why my HR department led me to believe, If I cash it out after 1 year I get to claim it as a capital gain based on the amount it was purchased at, but if I hold if for 2 years my earnings are based on what the stock price actually was (without the discount) as my cost basis.
Yes, the effective semi-monthly rate is 5.57%. But you can’t just multiply that by 24 to get the effective annual rate, because doing so would ignore the effects of compounding. The effective annual rate is 100 x ((1.0557)[sup]24[/sup]-1), or about 267%