Can someone who understands this explain the rationale behind it? The book explains it as the following: If you purchase a house with 40% funded by equity (cost of cash = 6%) and 60% funded with a 15 year mortgage with 7% interest rate (monthly payments), what is your capitalization rate? The cost of cash is essentially to cost of equity so that’s simply 6% * 40. To solve for cost of debt, you use the sinking fund factor. N = 15*12 PV = 0 FV = -1 I = 7/12 Computer PMT = 0.0031549 since it’s monthly 0.0031549 * 12 = 0.037859 = 3.7859%. I like to understand the rationale why the cost of debt is 7% + 3.7859%.
confused
In sinking funds, you dont just pay the interest, you pay back the principal too, gradually until maturity (this is an opposed to a bullet payment of principal at maturity). Think about when you have a mortgage, you payl interest each month and part of the principal each month, so that when your mortgage ends, you’ve paid it all off. Therefore your cost is the interest each month plus the principal each month. the sinking fund factor, is the proportion on the principal that gets paid in percentage terms each month. 0.0031549 x nominal is paid back each month.
Your link helped a little. I guess my question is two fold. 1. How come the calculation does not work when I put PV = 1 and FV = 0. So the payments offset the PV. (essentially opposite of PV = 0 FV = -1) 2. Why do I need to add a sinking fund factor to mortgages when I don’t need to add it to anything else like corporate debt? If corporate debt has 8% interest then my cost of debt is simply 8% even though they have to pay back principle at the end too; just the timing is different. I don’t have to go through the sinking fund calculation unlike for mortgages. I think I have an answer to my second question and I like to confirm it. The corporate debt interest is given to me as a yield to maturity. And solving for Sinking Fund Factor essentially solves for the principle payments in the YTM calculations. I am still puzzled about my first question though.
- SFF is calculated by putting PV=0 and FV=-1 because you want to calculate how many payments you will need to save, per period, to have $1 (starting from noting - $0) at the end of the period. 2. chedges explained it pretty well that since it’s at Mortgage Debt, the loan is amortizing, in the sense, each payment consist of Interest payment and principal repayment. The interest payment part is taken care by the interest payment rate and the SFF will take care of the monthly principal repayment.
Thanks a lot. Your explanations helped a lot. Something so small in the exam but the concept was just bothering me for a while.