Sinking Fund Factor understand, exactly, someone, please

ba736

Could someone please help with this. I need to understand what exactly this is and how it is calculated and incorporated into the calculations.

I find that people's explanation here are much better than Shwaesers. Thanks in advance.

kickthatcfa

Sorry, talking about Property Investments. The Mortgage Constant.

smuggycfa

Vaguely intuitively, I think it is essentially "weighting" the interest rate.

To calculate it, assume:

$1 as PV
Payment Number (year x 12) as N
Mortgage rate divided by 12 as I/Y
0 as FV
and CPT for PMT

Now this PMT is monthly, so you multiply by 12 to get you the annual. This number is then the weighted rate you would use to calculate band of investment rate.

spreads

I see. Thanks I kind know how to calculate it, but was trying to build some intution aroud what it actually is, and why we put it instead of Cost of Debt.

I guess the best I can do at this hour is to understand that becasue you're paying part of the principal as well as interest back, the 'effective' cost of debt is more than just the interest rate, as your cash flows are going out quicker, and thats esentially what we care about.

Does that sound reasonable ?

Houjichasan

And the difference between mfbar's calculated interest rate and the original rate given in the problem is the sinking fund factor (usually 1-3%).

I think of it as a reserve, an extra spread on the debt yield.

neil1234

I think you are referring to Band of Investments method in Alternate Investments somewhere in there.
Let us say the property investor borrowed $1 at 5% interest to be repaid over 180 months in equal installments. According to an amortization schedule, she must repay the principal of $1 in addition to the monthly interest.
Every month she will pay the interest plus a very small amount as the repayment of the principal so that the principal is completely paid off in 180 months.
So, if the interest rate is 5%, that is not the complete cost for the borrower.
The complete cost should also include a proportionate repayment of the principal every month.
Sinking fund factor equals this small repayment of principal every month for every $1 borrowed.
You can calculate it using FV = -1, i = 5/12 %, N=number of months.
Calculate PMT. Say PMT = 0.005.
This 0.005 is what you will be paying back the lender every month in addition to the interest rate.
Each of these 0.005 will grow with time to repay the 1$ by the end of the mortgage.
So, if your mortgage is for 180 months, you pay back 0.005 in the first month towards principal repayment in addition to 5/12% interest in each month.
The first repayment of principal of 0.005 will grow for 179 months to become a larger amount.
The second payment of principla of 0.005 will grow for 178 months to become a larger amount.
All of these amounts put together will equal $1 by the end of 180 months and you would have completely paid off the principal in exactly 180 months.

Best of luck to you all in your forthcoming exams.

MiniMe7

If I recall correctly, a sinking fund is one that allows prepayment. You can see the sinking fund factor as an extra spread, like phrenchy mentioned, to compensate for the fact mortgages are by definition negatively convex, or callable. (this is precisely why we treat prepayment risk with such seriousness in MBS).

random_walker47

per my notes:

Band of Investment
- Basically just WACC with no taxes, and possibly need to calculate SFF

Mortgage constant = rD = SFF + INT

To solve for SFF:
? N = number of mortgage compounding periods
? i = periodic interest rate (int/m)
? PV = 0
? FV = -1
? Solve for PMT, PMT

ryanlb

May I add to above. Great explanations overall.

By adding sinking fund provision we can compare cost of amortizing debt such as mortgage
to non-amortizing debt such as coupon paying corporate bond.

Think about this extra interest payment as a payment to reserve which will pay at the end the full amount of outstanding principal.

In other words by adding SFP to mortgage rate you calculated the coupon of the equivalent non-amortizing bond. So, you can use it in WACC formular.

ayaz_mahmud369

My two cents:

SFF = periodic interest (e.g. monthly) / [(1+periodic interest)^n* - 1]

This is the monthly rate, so multiply times 12 for the yearly amount. This will be the amount you add to the nominal rate for calculating WACC in the alternativce investment section.

Example: What is the pre-tax cost of debt on an amortizing loan with a rate of 6.0% requiring monthly payments with a term of 20 years?

0.005/[(1.005)^240 -1] = 0.002164 (this is monthly) x 12 = 0.025972 so the pre-tax cost of debt is actually 6.0% + 2.6% = 8.6%