Practice problems in Time Value of Money

1. You are analyzing an investment decision, in which you will have to make an initial investment of $10 million and you will be generating initial cash flows to the firm of $2.5 million, growing at 5% a year for the next 5 years. Estimate the NPV of this project, if the cost of capital is 10%.

2. Mr. Rohit is interested in fixed annual income. He is offered 3 possible annuities. If he could earn 8 % on his money elsewhere, which of the following alternatives, if any, he would choose and explain?

1) Pay Rs 80,000 now in order to receive Rs 14,000 at the end of each year for the next 10 years

2) Pay Rs 1, 50,000 now in order to receive Rs 14,000 at the end of each year for the next 20 years.

3) Pay Rs 1, 20,000 now in order to receive Rs 14,000 at the end of each year for the next 15 years.

3. You buy a flat for Rs 50 lakh and immediately make cash payment for Rs 10 lakh. You finance the balance amount at 15 % for 5 years with equal annual installments. How much are the annual installments? Prepare a loan amortization schedule.

4. Mr. Robert has come to you for advice on his retirement planning. He is 45 years old, and has Rs 100,000 in his savings account. He also expects to receive an additional Rs 80,000, in ten years, when he sells his house. He plans to work for 20 years more, and expects to save Rs 10,000 a year for the next 10 years, and Rs 15,000 a year for the following 10 years.

a. Assuming that he earns 5% on both his current and future savings, how much should he expect to have in savings, when he retires in 20 years?

b. If Mr. Robert plans to withdraw the money in equal annual installments over the 15 years following his retirement, how much can each withdrawal be? (Assume that the interest rate continues to be 5% after the twentieth year.)

c. If the nominal rate of interest is 12 % per annum, calculate the effective rate of interest when a sum is compounded a) annually, b) semi annually, c) quarterly and d) monthly

5. How much amount should an investor invest now in order to receive Rs 10,000 every year for the next 5 years and Rs 15,000 every year for the following 5 years? Assume 10 % rate of interest.