Question

6. Consider the two loan financing alternatives:

Home Value = $180,000

• Two Financing Alternatives
  23. #1: 70% Loan to Value (LTV), 7.5% Interest Rate, 30 Years
  24. #2: 80% Loan to Value (LTV), 8% Interest Rate, 30 Years

1. What are the monthly payments with alternatives 1 and 2?

2. What is the incremental borrowing cost for the additional amount borrowed through alternative 2 (i.e., the loan with the higher LTV)?

3. Suppose you expect to relocate after 11 years, but you do not have the option of a second mortgage. What is the incremental borrowing cost for loan 2?

Answer 1

Given:

Home Value = $180,000

• Two Financing Alternatives
  1. #1: 70% Loan to Value (LTV), 7.5% Interest Rate, 30 Years
  2. #2: 80% Loan to Value (LTV), 8% Interest Rate, 30 Years

a. Monthly Payments can be calculated using PMT formula in Excel:

PMT(rate, nper, pv)

where, rate is the Interest rate per month

nper is the number of months

pv is the PV of the Loan

Loan Amount = LTV ratio * House Value

Interest rate per month = Interest rate per annum / 12

Number of periods = No of years * 12

	Alternative 1	Alternative 2
House Value	180000	180000
LTV	70%	80%
Loan Amount	126000	144000
Interest rate	7.50%	8%
Interest rate per month	0.63%	0.67%
Number of Years	30	30
Number of months	360	360
Monthly Payments	PMT(0.63%,360,-126000)	PMT(0.67%,360,-144000)
Monthly Payments	$881.01	$1,056.62

b. Incremental borrowing cost for the additional amount borrowed through alternative 2 is given by:

Additional Borrowing = 144000-126000 = 18000

Additional Payment per month = 1056.62 - 881.01 = 175.61

The cost of additional amount brorrowed through alternative 2 is calculated using RATE function in Excel as shown below:

RATE(nper, pmt, pv)

where nper is the number of periods = 360

pmt is the Additional Payment per month = 175.61,

pv is the Additional Borrowing = 18000

Additional Borrowing	18000
Additional Payment	175.61
Number of months	360
Interest rate per month	RATE(360,175.61,-18000)
Interst rate per month	0.94%
Interest rate per year	11.31%

Hence, the Incremental borrowing cost for the additional amount borrowed through alternative 2 is 11.31%

c. Expect to relocate after 11 years:

Loan Balance in Alternative 1 & Alternative 2 are given by:

PV formula in Excel - PV(rate, nper, pmt)

where rate is the Interest rate per period

nper is the number of periods = 11 * 12 = 132 months

pmt is the Monthly installment values

	Alternative 1	Alternative 2
Monthly Installment	$881.01	$1,056.62
Interest rate per period	0.63%	0.67%
Number of periods	132	132
Value of the Loan Balance	PV(0.63%,132,-881.01)	PV(0.67%,132,-1056.62)
Value of the Loan Balance	$79,028.51	$92,560.63

Here, Additional Amount = 92560.63 - 79028.51 = 13532.12. This is the Future Value of teh additional amount after 11 years.

RATE function is used to find the cost of addtional borrowing as given below:

RATE(nper,pmt, pv,fv)

where nper is the number of periods premianing = 360-132 = 228 months

pmt is the additional payment per month = 175.61

pv is the Value of the additional payment at the beginning = -18000

fv is the Value of the Additional payment after 11 years = 13532.12

Additional Borrowing (PV)	$18,000.00
Additional Borrowing (FV)	$13,532.12
Additional Payment	175.61
Number of months	228
Interest rate per month	RATE(228,175.61,-18000,13532.12)
Interst rate per month	0.94%
Interest rate per year	11.33%

Expecting to relocate after 11 years, incremental borrowing cost for loan 2 is 11.33%