**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: **

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

**Answer: Rs. 1,558,234.4**

**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: **

**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: **

**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: **

**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

**CCF = Rs. 10,571.32**

**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: **

**Answer: Rs. 10,935.73**

**Problem 6:**

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

**Solution: **

**Answer: 12.68%**

**Problem 7:**

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

**Solution: **

**Answer: ****12.55****%**

**Problem 8:**

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

**Solution: **

**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: **

**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: **

**Answer: Rs.161.06**

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