I'm trying to figure out what rate of return I would need on an investment in order to compare to paying down a mortgage.
I have calculated the change in the mortgage - I know how much money I'd save by the end of the loan term and how much money I'd need to put in. I'm trying to compare that to an equivalent investment - treat any lump sum payment as the principal of an investment, treat any monthly overpayment as a monthly contribution to an investment, plug in the final value, and solve for the effective rate of return.
I've looked at the RATE and the IRR commands. IRR seems close to what I want, but it wants a series of values for the input flows, but I have it as a periodic regular investment.
For an example with numbers - if I pay an extra $100 a month on the mortgage for 120 months, I can save $10000 in total cost. What command can I use to calculate this in terms of an investment? If I invest $100 a month for ten years and end up with $10000, what was my annualized rate of return?
If I start with principal PV invested at rate R, I contribute monthly payment M for N months, and I end up with final value FV at the end of those N months, I'd like to solve for R given the other variables.
I know there's another factor regarding the mortgage interesting being tax deductible - I'll look at worrying about that after I figure this part out.
:)
Your monthly return is given by this RATE formula
number of periods = 120 (10*12)
contributions of $100 per period
future value of 10,0000
=RATE(10*12,-100,0,10000)
=-0.32% per month
Note as a check =RATE(10*12,-100,0,12000) = 0
which is equivalent to an annual rate of
=1-(1-0.32%)^12
=-3.73%
Related
When using XIRR to calculate the performance of a stock trading account, do you need to have a beginning cash flow equal to the starting balance of the account (seed money) ?
When I do that, it throws the formula completely for a loop and I either get errors because it can't calculate the return, or the return is very, very negative despite the account actually increasing in value over the year.
$7,000 starting balance/seed money, entered as a negative, January 1st
$6,800 invested in a trade, January 2nd
$8,000 deposited from closing the trade, December 22nd.
The ROIC on the trade would be 17.6%, and the MWRR should be about 17.1%, +/- 1% since the investment period was slightly less than a full year.
But XIRR is returning -43%?! If I tell XIRR to ignore the seed money, and only look at the amount invested in the trade and the amount received when closing the trade, I get just over 18%, which seems right.
What am I not understanding about XIRR? I thought all IRR needed to include the seed money?
I took a loan from the bank in the amount of 200,000 USD. The loan is for 17 years.
I repay the loan through regular payments every month. The monthly interest rate on the loan is 0.4%.
At the end of the loan period, in addition to the last payment, I pay an additional 10,000 USD.
What is the regular monthly payment I will make each month?
Can you explain me please how to use this formula?
As you are paying the last 10k at the end, that is effectively the Future Value of the loan when it terminates. So you can enter that as the fv in the PMT function:
=PMT(0.004,17*12,-200000,10000)
or 1404.25
Note that the signs of the Pv and Fv must be opposite in this case. So
if you want to show your PMT as a negative value, you must use +200000
and -10000.
I am able to use the PMT function in Excel for periods of 12, 24 and 36 months. But I am falling short of understanding how to use the function for 6 months periods.
Let's suppose I have a debt of 10 000$ and the annual interest from the bank is 10%.
If I pay monthly and I want to pay within the first year, I will do the following formula :
=PMT(10%/12;12;10000)
But what if I need to pay in 6 months?
At first I thought of doing
=PMT(10%/6;6;10000)
But this gives me more interest than paying over a year!
I searched various websites without luck.
My last resort was the official Excel website : they actually have an example of a payment over 10 months. Following their code, I would write :
=NPM(10%/12;6;10000)
The result is smaller than 12 months' interest (yay!), but why!?
Why do we calculate the interest over 12 months, and not 6? I can't seem to understand that part.
The issue is that you're adjusting an interest rate which is independent of the time you pay it off in. Technically PMT takes an interest rate equal to the period of time you are considering.
So if you're talking about paying over 6 months with an annual interest rate the correct formula is:
=PMT(10%/12;6;10000)
10%/12 is the 10% annual interest converted to a monthly period. 6 is the number of months, and 10000 is the value of the loan. 10%/6 is actually a bi-monthly interest rate.
Technically if you're compounding annually and pay off $10,000 in 5 years, at 10% p.a. the formula would be:
=PMT(10%;5;10000)
I'm trying to calculate a lifetime value of a customer. Let's assume a new customer pays $100K per year and stays for 5 years. Let's discount any future years' payments with 10% rate.
This is manual calculation:
Year 1 $100,000.00
Year 2 $90,000.00
Year 3 $81,000.00
Year 4 $72,900.00
Year 5 $65,610.00
---------------------
Total $409,510.00
I can get the same value by using FV with negative rate.
FV(-0.1,5,-100000,0,0) = $409,510.00
What I'm trying to do is to get the same value using PV. And it's not exactly the same:
PV(0.1,5,-100000,0,1) = $416,986.54
I'm not sure what am I missing here. Does MS Office Excel 2010 PV understand discounting differently?
If you calculate out what PV is doing manually, the formula is actually this, for each individual year:
=Base Amount / (1 + Discount Rate) ^ Periods
Vs what FV is doing manually, the formula is this (which you seem to know based on coming to the same answer in your data):
=Base Amount * (1 - Discount Rate) ^ Periods
The reason for the difference in calculation is the mathematical difference between the two items - for background see here: http://www.investopedia.com/walkthrough/corporate-finance/3/time-value-money/future-value.aspx and here: http://www.investopedia.com/walkthrough/corporate-finance/3/time-value-money/present-value-discounting.aspx.
In short, if you have $100k today, and invest it in something which gives you 10% each year, then each year you add 10% of the current balance to get the new balance. ie: in year 1 you add 100k * 10% = 10k, giving a new total of 110k; in year 2 you add 110k * 10% = 11k, giving a new total of 121k, etc. - Mathematically, each year's amount is given by the formula listed above for the FV calculation.
Where this gets tricky is that you are giving yourself a negative interest rate - meaning every year, the value is decreasing each year by 10%. You have attempted to use the FV calculation with a negative interest rate, but that's not quite correct. What you should be using is the PV formula.
For the PV formula, if you know that you will receive 100k each year, you need to determine how much cash you would have needed originally, in order to earn the same amount - that is the present value of the cash flow stream. Now, you need to 'gross-up' the value of each year's income stream. The formula for this gross-up is derived mathematically and results in what I have above there for PV. Think about it like this - if there's a shirt that normally costs $100 and is now 30% off, you can see that you simply multiply it by 30%, to get $70. But if you see of shirt on sale for $70, and it's 30% off, then to determine the original base price you need to take $70 & divide by .3 - which gives us $100.
To prove to yourself that the PV formula is appropriate, take the income stream of, say, year 4 [3 periods of interest later, assuming first payment is received in day 0]: 100k / (1 + 10%)^3 = $75,131. Now, work backwards - if you want to know the future value of a $75k investment held for 3 periods of interest compounded annually with a 10% annual rate, you go: 75,131 * (1 + 10%) ^ 3 = 100k.
This is an important financial distinction, and you should read over the sources I've linked to ensure you understand it.
There is a difference in the calculation. FV takes 100,000 and discounts it by 10% to the number X so that X is 90% of the original value (i.e. X=90,000). PV by contrast discounts it to the number X such that 100,000 is 10% more than X. Quick math says X will be 10/11 of 100,000, i.e. 90909.09.
Indeed, if we apply this calculation 5 times:
Year 1 $100,000.00
Year 2 $90,909.09
Year 3 $82,644.63
Year 4 $75,131.48
Year 5 $68,301.35
---------------------
Total $416,986.5
I don't know if there is a way to make them behave the same way (I don't think there is, as they're calculating different things), but since FV solves your problem why not just use that?
I had tried to run some example from my calculator on excel. I cannot get the correct answer of 203.13. Can someone try to pinpoint the error in my formula?
You plan to open a savings account and deposit the same amount of money at the beginning of each month. In 10 years, you want to have $25,000 in the account.
How much should you deposit if the annual interest rate is 0.5% with quarterly compounding?
FV 25000
NPER 10
RATE 0.50%
PMT ($193.23)
=PMT(RATE/4, NPER*12,,FV)
You must observe consistency in the periodicity. If you use monthly payments, you must have an NPER in months as well, and a monthly RATE. THe difficulty here is that the quarterly compound with a monthly deposit.
If you calculate everything on a quarterly basis, you will also have dfferences, but I think they will be minor.
To calculate a precise answer you would need to know when you made the first payment relative to the bank's quarterly interest cycle. If your first deposit was immediately before the interest compound date, interest would start accruing immediately. If your first deposit was immediately after the interest compound date, interest would not accrue immediately.
Also the bank may calculate interest based on the ending balance or on the average balance for that quarter.
After a long time, I found the answer. However, I cannot understand the formula. isnt RATE/4 as it is quarterly compounded?
=PMT(RATE/12, NPER*12,,FV,1)