Question

loan refinancing is a typical option if there are changes in interest rates in the market. your company has just completed its 4th year payment of 100,000,000 10 year loan. The existing loan has an interest rate of 8% compounded semi-annually and has a uniform semi-annual payment as well. now, the market interest rate is 6% and you have opportunity to expand further requiring another 50,000,000 loan payable for 10 years. you also want to refinance the remaining part of the existing loan with a 6% rate copmpounded quarterly, for another 10 years.

1.how much is the semi-annual payment of the existing loan?

2.how much is the remaining value of th existing loan at the end of 4th year?

3.how much is the combined monthly payment of the new loan and refinancing?

Answer 1

1)

Rate of interest=i=8%/2=4% semi annual

Number of periods=n=10*2=20

Loan amount=PV=$100,000,000

Semi annual payment=R=PV/(P/A,4%,20)

Semi annual payment of first loan=R=PV/(P/A,4%,20)=100000000/13.59032634=7,358,175.03

b)

No. of payments made=4*2=8

Rate of interest=i=4% semi annual

Semi annual payment=R=7358175.03

Remaining loan amount=Future value of loan-Future value of payments

Remaining loan amount=100000000(F/P,4%,8)-7358175.03*(F/A,4%,8)

(F/P,4%,8)=(1+4%)^8=1.36856905

Remaining loan amount=100000000*1.36856905-7358175.03*9.21422626=69,057,015.41

c)

New loan requirement=50000000+69057015.41=119,057,015.41

Rate of interest=6%/4=0.015 per quarter

Effective monthly interest rate=i=(1+0.015)^(1/3)=0.00497521

Loan period=n=10*12=120 months

Monthly payment=119057015.41/(P/A.0.00497521,120)

Monthly payment=119057015.41/90.19478861=1319998.83 or say 1,319,999