Special Application of Time Value of Money Problems and Solutions

Problem 1:

A firm wants to open a new coal mine. The price of coal is very volatile and the projected profits over the next five years are : Rs. 100,000  ,  Rs. 250,000  ,  Rs. 10,000  ,  Rs. 200,000  and  Rs. 50,000 respectively. After that profits will be a constant Rs. 150,000 per year for next 20 years at which time the mine closes. If 7% is the appropriate discount rate for the first five years and is 8% after that, what is the present value of the mine?

Solution: 

time value of money

time value of money formula

present value formula

Total Present Value = 508,208.96 + 1,050,025.44

Answer: Rs. 1,558,234.4

 

Problem 2:

You are borrowing Rs. 80,000 for 25 years at 10% nominal annual interest.  How much must your annually payments be if you will completely retire the loan over the 25-year period by factor formula?

Solution: 

value of money over time

Answer: Rs. 8,813.48

 

Problem 3:

Perpetuity makes payments of Rs. 500 every year, with the first payment coming one year from today. If the discount rate is 5%, what is the present value of the perpetuity?

Solution: 

time value of money examples

Answer: Rs. 10,000

 

Problem 4:

Waleed just purchased a new house for Rs. 120,000. He was able to make a down payment equal to 25% of the value of the house; the balance was mortgaged. The rate by the bank is 10% compounded annually. The mortgage has a 20 year amortization period (this means that payments are calculated assuming it will take 20 years to pay off the loan).

(a) What will be the size of the payments by factor formula?

(b) What will be the balance remaining on the mortgage after 5 years?

Solution: 

Down Payment = 120,000* 25%   = Rs. 30,000

Loan Amount = 120,000 – 30,000   = Rs. 90,000

the concept time value of money indicates

CCF = Rs. 10,571.32

loan amortization schedule

Answer: (a) Rs. 10,571.32      (b) Rs. 80,409

 

Problem 5:

If you borrow Rs. 150,000 for a house at 8% compound annual interest rate for 30 years, what is your monthly payment by general formula?

Solution: 

loan amortization formula

Answer: Rs. 10,935.73

 

Problem 6:

An annual interest rate of 12% compounded monthly has an effective yield of?

Solution: 

effective annual return

Answer: 12.68%

 

Problem 7:

An annual interest rate of 12% compounded quarterly has an effective yield of?

Solution: 

effective annual rate of return

Answer: 12.55%

 

Problem 8:

A simple annual interest rate of 12% compounded semi-annually is an effective yield of?

Solution: 

how to calculate effective annual rate of return

Answer: 12.36%

 

Problem 9:

A real estate investor feels that the cash flow from a property will enable his to pay a lender Rs. 15,000 per year, at the end of every year, for 10 years.  How much should the lender be willing to loan her if he requires a 9% annual interest rate by general formula (annually discounting, assuming the first of the 10 equal payments arrives one year from the date the loan is disbursed)?

Solution: 

present value of annuity formula

Answer: Rs. 96,265.5

 

Problem 10:

Now that you are finished school, you also have to start paying back your student loans. You borrowed a total of Rs. 12,500. You plan to pay back the loan over 10 years at an interest rate of 9.4% interest, compounded monthly. How much will your monthly payments be?

Solution: 

monthly payments formula

Answer: Rs.161.06