Question

A borrower is purchasing a property for $180,000 and can choose between two possible loan alternatives. The first is a 80% loan for 25 years at 8% interest and 1 point and the second is a 95% loan for 25 years at 9.25% interest and 2 points. Assuming the loan will be held to maturity, what is the incremental cost of borrowing the extra money?

Answer 1

Please see the table below. Please be guided by the second column titled “Linkage” to understand the mathematics. The last row highlighted in yellow is your answer. Figures in parenthesis, if any, mean negative values. All financials are in $.

Parameter	Linkage	Option 1	Option 2
Property value	A	180,000	180,000
Loan proportion	d	80%	95%
Loan amount	B = A x d	144,000	171,000
Points	C	1%	2%
Net borrowing	D = B x (1 - C)	142,560	167,580
APR	E	8%	9.25%
Rate	F = E /12	0.006666667	0.0077083
Term	G	25	25
Nper	H = G x 12	300	300
PMT	I = PMT(F,H,-B)	$1,111.42	$1,464.41
Incremental Analysis
Net Borrowing	J = 167,580 - 142,560	25,020
PMT	K = 1,464.41 - 1,111.42	$353.00
Incremental rate	L = RATE(300,K,-J)	1.3883%
the incremental cost of borrowing the extra money	12 x L	16.66%