Question

. Your firm recently sold an asset and financed the sale of the asset. The firm took back a $170,000 loan on the equipment sale with monthly payments and 8% interest. The loan was a 5-year loan. Your firm now needs cash and desires to sell the loan. If investors require 12% rate of return to invest in this type of loan and 6 payments have been made on the loan, how much will your firm loose from the sale of this financial asset?

Answer 1

First step:

Existing monthly payments:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          170,000
Rate of interest per period:
Annual rate of interest		8.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.08 /12 =	0.6667%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	5
Total number of payments	N	5 × 12 =	60
Period payment using the formula	=	[ 170000 × 0.00667 × (1+0.00667)^60] / [(1+0.00667 ^60 -1]
Monthly payment	=	$                                                         3,446.99

Second step:

Balance in loan principal after six payments:

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	170,000.00
Rate of interest	r=	0.6667%
nth payment	n=	6
Payment	P=	3,446.99
Loan balance	=	170000*(1+0.00667)^6 - 3446.99*[(1+0.00667)^6-1]/0.00667
Loan balance	=	155,884.63

Existing loan balance is $155,884.63

Third step:

Sale value of loan with existing monthly payments for 54 months is:

a	Present value of annuity=	P* [ [1- (1+r)-n ]/r ]
P=	Periodic payment	$                  3,446.99
r=	Rate of interest per period
	Annual interest	12.00%
	Number of interest payments per year	12
	Interest rate per period	0.12/12=
	Interest rate per period	1.000%
n=	number of periods:
	Number of years	4.5
	Periods per year	12
	number of payments	54
	Present value of annuity=	3446.99* [ (1- (1+0.01)^-54)/0.01 ]
	Present value of annuity=	143,286.77

Loss on sale of loan = $155,884.63 - $143,286.77 = $12,597.86

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