Interest Annually Question

I’m working on a management case study and need an explanation and answer to help me learn.

Sara Gandhi is a 50-year-old entrepreneur with a great idea of developing a new computer software product that will help users communicate using the next-generation magnet. Sara owns a software company registered as S corporation. S Corp is a special designation that allows small businesses to be taxed as if they were a sole proprietorship or a partnership rather than as a corporation whilst at the same time enjoying limited liability of a corporation. Sara is satisfied with this choice because she is aware that one of the disadvantages of a corporation is the double taxation of corporate earnings. Sara is determined to make sure her business succeeds. She has a long-term plan of expanding the business to some emerging countries. She has been reading some articles in finance journals about time value of money and how she can apply the concept to manage her finances and expansion plans. The time value of money holds that it is better to receive money sooner than later. Money that is available today is worth more than money to be received in the future. This is so because money in hand today can be invested to earn a positive rate of return, thereby producing more money in the future. On her google search she came across this article:

Rahman, M. (2018). Time value of money: A case study on its concepts and its applications in real life problems. International Journal of Research in Finance and Management, 1(1), 18 – 23.

The article discusses a contemporary financial planning problem of correctly solving time value of money problems and identifying the cash flows and timing necessary for financial and investment decisions. Rahman (2018) explains with practical examples the applications of the concept of time value of money to retirement planning, valuing of stocks and bonds, setting up loan amortization schedules, and making capital budgeting decisions. Sara does not fully understand some of the finance terms such as future value and compounding, present value and discounting, perpetuity, annuities etc. that the article discussed. She believes that once she grasps these time value of money concepts, she will be able to make sound financial and investment decisions. Her major concern is that these concepts require application of some basic quantitative techniques which she tried to avoid at the graduate school twenty years ago.

Sara has approached you for help in answering the following personal and business-related questions:

1. Suppose Sara has $150,000 to invest in an individual retirement account (IRA) at an interest rate of 8% per year for her retirement in 15 years. How much money can she accumulate at the end of the time period?

2. Sara wants to send her two-year old daughter to college in 16 years. She has assumed that she would need $120,000 at the time in order to pay for her tuition, room and board, school supplies etc. If she can earn an average of 8% per year, how much money does she need to invest today as a lump sum to achieve that goal?

3. Sara wants to move $60,000 from her checking accounts and invests it in money market securities for 5 years. The money market earns 8% interest compounded annually. How much can this investment grow at the end of the investment period?

4. Sara wants to find the present value of the following uneven cash flows she expects to receive in the next 3 years from her business.

What is the present value of the cash flows assuming the discount rate is 7%?

5. Sara is considering a perpetuity that pays $100 a year. If the interest rate is 6%, what is the value of the perpetuity?

6. Sara also wants to invest in preferred stocks issued by Camden Company. The company is about to pay $3 dividend per share on its stock. Investors anticipate that the annual dividend will rise by 6% a year forever. If Sara requires a rate of return of 11% on the stock, what is the current price of Camden stock?

7. Sara’s software company is thinking of buying a real estate property for $400,000 with the intention of selling it at the end of the year. The company expects that the property will be worth $480,000 in one year. If the interest rate is 10%, should the company buy the property?

8. Should the company purchase the property if the interest rate is 25%?

9. Sara’s company wants to calculate the end-of-the year wealth if the company receives an annual rate of 24% compounded monthly. Calculate the effective annual rate.

10. If an annual percentage rate of 24% is compounded quarterly, what is the effective annual rate for Sara software company?