What Is A Sinking Funds Factor?

[Dman33]

Hi everyone,

Newbie here, so sorry if this is a stupid question, but I was wondering if you guys could help me out. I'm looking through a couple appraisals at how they calculate a cap rate, specifically the mortgage-equity procedure, and I see that they are using a sinking funds factor to help calculate the equity build up credit. I understand the calculation of the sinking funds factor, but what is it exactly? Is it used to account for capital reserves? I can't seem to find a simple or direct definition. Any help would be great. Thanks!

 

[Gobears81]

How much would need to be added each year to achieve a certain level at a specified rate? If you are attaining $1 in five years, at a 5% interest rate, you would not need to add $0.20 per year, you would need to add slightly more than $0.18. Yes, I use it for calculating reserves.

 

[Terrel L. Shields]

It is to replace a wasting asset, like short term items such as stoves, dishwashers, fridge's etc. or for a longer term "thing" - the whole building.

In resources like rock quarries, oil wells, or any mining property, it sets aside an amount of money as the product is removed so that at the end of the life of the mine or field, you have money to replace the asset (i.e.- buy a new mine, drill a new well, etc.) Inwood and Hoskold's were the old standby formulations to calculate sinking funds. Your HP 12C can do it as well.

 

[Elliott]

And to add to Terrel, there is an interest rate that is associated with the concept which is different than other rates used in capitalization. The "sinking fund" is used with a rate which is a typically "safer" or lower rate.

 

[Terrel L. Shields]

Rule of thumb was that the "safe rate" is equal to T bills of the same typical life (5 yr, 10yr, 30 yr bond) , but with those so low, if you use a multiple of the safe rate as the "risk" rate, it is a very low number. I eschew that method for the most part under the assumption that todays FED controlled "zero" interest rate is too contrived and not a reflection of the "real" interest rate. I might substitute a muni bond rate at the safe rate.

 

[Dman33]

Rule of thumb was that the "safe rate" is equal to T bills of the same typical life (5 yr, 10yr, 30 yr bond) , but with those so low, if you use a multiple of the safe rate as the "risk" rate, it is a very low number. I eschew that method for the most part under the assumption that todays FED controlled "zero" interest rate is too contrived and not a reflection of the "real" interest rate. I might substitute a muni bond rate at the safe rate.

Ok, thanks for the quick responses everyone! It's make sense, but I guess I'm still having a bit of difficulty conceptualizing this one example I've been looking at. The appraiser states that the formula for the sinking funds rate is:

S = Y / ((1+Y)^N - 1)

Where:
S = sinking funds rate
Y = Equity yield rate, which is 18% in this case
N = Projection period, which is 10 yrs in this case

When plugging in 18% and 10 yrs, you end up with 4.25%. Where I'm stuck is, what exactly does this 4.25% represent?

Thanks again for all your help!

 

[Howard Klahr]

Basically the sinking fund factor is a mathematical representation of how much needs to be allocated on a periodic basis (monthly, quarterly, annually) over a period of time that will accumulate to a desired amount at a specific rate during the time period.

the combination of principal and earned compound interest total the future amount desired.

In terms of analysis of a cap rate, the sinking fund factor is utilized to account for the equity build-up component of the analysis

The Mortgage Equity Technique, sometimes referred to as the Ellwood Method (also "Ellwood without algebra as developed by Charles Akerson), addresses the Equity Buildup and Holding Period, but not the other factors that are mentioned in the list above. The technique implicitly relies upon the Time Value of Money concept. It builds (develops) a multiplier, referred to as the Capitalization Rate that mathematically represents the series of cash flows produced by an investment over the holding period of the investment. The first year (stabilized) income of the investment is then capitalized to determine the value of the investment's cash flows. The Mortgage Equity Technique is superior to the Band of Investment because it better reflects the circumstances of a real property transaction by recognizing three important factors that are excluded from the Band of Investment.

• The investment is typically not held forever - there is a "holding period".
• There is an "equity buildup" as the mortgage loan is paid down.
• The investor receives the proceeds of the sale at the end of the holding period.

Source: http://www.commercialappraisalsoftware.dcfsoftware.com/mtgequity.htm

The sinking fund factor is one of the the six functions of a dollar generally covered in finance classes.

Hope this helps.

 

[Gobears81]

Ok, thanks for the quick responses everyone! It's make sense, but I guess I'm still having a bit of difficulty conceptualizing this one example I've been looking at. The appraiser states that the formula for the sinking funds rate is:

S = Y / ((1+Y)^N - 1)

Where:
S = sinking funds rate
Y = Equity yield rate, which is 18% in this case
N = Projection period, which is 10 yrs in this case

When plugging in 18% and 10 yrs, you end up with 4.25%. Where I'm stuck is, what exactly does this 4.25% represent?

Thanks again for all your help!

It is the percentage that you would need to deposit each year to attain a certain level. At an 18% rate, you would need to deposit $0.0425 each year to have $1 in 10-years

 

[Pittsburgh Pete]

Ok, thanks for the quick responses everyone! It's make sense, but I guess I'm still having a bit of difficulty conceptualizing this one example I've been looking at. The appraiser states that the formula for the sinking funds rate is:

S = Y / ((1+Y)^N - 1)

Where:
S = sinking funds rate
Y = Equity yield rate, which is 18% in this case
N = Projection period, which is 10 yrs in this case

When plugging in 18% and 10 yrs, you end up with 4.25%. Where I'm stuck is, what exactly does this 4.25% represent?

Thanks again for all your help!

As Mr. Klahr pointed out it is adjusting the cap rate for equity build-up and return on that increasing equity.

 

[Dman33]

Ok. So in this example, if I would like my equity contribution to earn 18% over 10 years I would need to contribute 4.25% each year...

So in the CRE context, does this mean that in order for the equity that I put up in this transaction to make 18%, I would need to contribute 4.25% back into the property for things like capex, maintenance, repairs, etc. in order to keep the property in shape? Or am I completely missing the boat here?