Question

Suppose, an asset worth $ 1.8 million was financed using a debt ratio of 0.75, 10-year, annually amortizing loan @10% contract rate.

What is the loan amount?
What is the annual loan amount?
The loan will be pre-paid at the end of the 5th year, when the asset is sold. What will be the outstanding loan payment to the lender at the time of sale (including the loan balance and the fifth year's annual payment)? Consider no pre-payment penalty.

Answer 1

Debt Ratio = Debt/Total Assets

Debt Ratio = 0.75

Total Assets = $1,800,000

Debt = 0.75*1,800,000 = $1,350,000.00

Hence loan amount is $1,350,000.00

Interest Rate = 10%

Term = 10 years

Annual amortizing

Amount of annual payment = P*r/(1-(1+r)^-n), P is Loan Principal, r is interest rate per period, n is number of time periods.

Amount of Annual payment = 1350000*10%/(1-(1+10%)^-10) = $219,706.28

Hence, annual loan amount = $219,706.28

Loan outstanding after 4 years = PV of Future payments = $219,706.28*((1-(1+10%)^-6)/10%) = $956,878.13

Loan Outstanding after 4 years = $956,878.13

Loan outstanding after 5 years = $956,878.13 * (1+10%) = $1,052,565.94

Hence, loan payment at the end of 5^th year is full payment is made = $1,052,565.94

ALTERNATE METHOD:

Loan outstanding after 5 years = $219,706.28*((1-(1+10%)^-5)/10%) = $832,859.66

Since, this amount is after paying the annual payment,

Total payment = Loan outstanding after 5 years + annual payment amount = $832,859.66 + $219,706.28 = $1,052,565.94