This example question was found in schwesser book in the alternative investment (real estate) section. I am a little confused about the concept of sinking fund annuity. The question asks you to calculate the market capitalization rate of this property. It is financed by 60% 15-year 7% mortgage and 40% cash. The cash on cash return on equity is 14%. Normally I would have thought it would be a simple: 7%*60 + 14%*40 type of question however to get the “effective mortgage rate”, they added a sinking fund annuity factor. My question is why is that necessary. According to the solution, to calculate it, it is with the calculator: FV = -1, PV = 0, N=12*15, I/Y=7/12 calculate PMT Add 12 * PMT to the 7% which gets 10.79 (7% + 3.79%) Then you take 10.79%*60 + 14%*40 to reach ~12% for the market capitalization rate. Can someone explain the logic of adding that extra 3.79% to the 7% mortgage rate? Thanks

I would just think of it as the “total required payment to the lender” (interest + return of principal) is what goes into the debt portion of the “overall capitalization rate” for the property. The sinking fund pays off the principal at the end of the loan. In your calc. above, you need to set aside 3.79 cents / yr. per dollar of principal to pay off the principal balance at the end of 15 yrs. I know this doesn’t fully answer the “logic” question but if you just remember that the debt side for Band of Investment Cap Rate has two components (i) interest and (2) return of capital at the end, you will answer the question correctly.

solution from schweser book 6/7, there’s one q it says return of capital and instead of using FV and I/Y to get PMT=0.0219, it writes as 0.08/[exp(1.08, 20)-1]=2.19% Can anyone help me on what does this equation mean?

think of morgage payment -> combination of interest and sinking factor

still struggling how 0.08/[exp(1.08, 20)-1]=2.19% comes out…

anybody can help me on this?

First of all… keep in mind that this calculation is done to get the market capitalization rate for the band of investments method only. The sinking fund factor is really introducing (unnecessarily) a new term. Basically the idea is that because your mortgage (just like any homeowner’s mtg) includes required principal payments, we should include those on top of the interest rate in the imputed cost of debt to finance the property. I don’t really understand the equation either. But what I do to calculate the market cap rate for band of investments method is I figure out the first month’s mortgage payment and multiply that by twelve (for the first year’s payment). Then I simply divide that by the amount of the mortgage. This gives you the total cost of the debt, including sinking fund. If you needed to calculate the cost of the sinking fund separately, you could then subtract the amount of interest for one year at the stated interest rate on the beginning mortgage balance, and divide the remainder by the original balance of the mortgage. I believe that is essentially what they are doing here.

Let me expand a bit, because I see the example you are referring to in the book. In this case, I would solve the problem differently. Let’s assume that the 60% you are financing with debt in the example is represented by a $100 mortgage (we could use $1 or $60 too, but the calculations are easy with $100). Use your calculator to figure out the monthly payment on that mortgage, given the terms in the problem. You should be able to do this (if not, just ask). The monthly payment is $0.90. Therefore the annual payment will be $0.90 x 12 = $10.79 (some rounding). We can usually stop here – the $10.79 means that the mortgage cost (all in) is 10.79%. We could also state this as the interest cost of the mortgage being 7% and the sinking fund factor being 3.79% (10.79% - 7%). I hope this helps. I do not like the way the CFAI books or Schweser explains this calculation. I have used my method for every problem and it always returns the correct result. It is much more intuitive, especially for anyone who has ever had a mortgage.

Wow. That is much easier and more intuitive.

hi plyon, your solution is amazing. maybe I just ignore the solution from practice exams by schweser: the 0.08/[exp(1.08, 20)-1]=2.19% stuff the solution on notes is OK, it more or less provides some reasoning