Question

TIME VALUE OF MONEY

Jeff Warren after consulting with some PhD students and his Financial Advisor decided to register his server building company as S corporation, which 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. Jeff is satisfied with this choice because he is aware that one of the disadvantages of a corporation is the double taxation of corporate earnings.

Jeff is determined to make sure his business succeeds and has a long-term plan of expanding his business to some emerging countries. He has been reading some articles in finance journals about time value of money and how he can apply the concept to manage his 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 tomorrow. On his google search he came across this article:

Schmidt, C. E. (2016). A journey through time: From the present value to the future value and back or: retirement planning: A comprehensible application of time value of money concept. American Journal of Business Education, 9(3), 137 – 143.

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. Schmidt (2016) explains with practical examples the applications of the concept of time value of money to retirement planning, valuing stocks and bonds, setting up loan amortization schedules, and making capital budgeting decisions. Jeff does not fully understand some of the finance terms such as future value of compounding, present value and discounting, perpetuity and annuities etc. that the article discussed. He believes that once he grasps these time value of money concepts, he will be able to make sound financial and investment decisions. His major concern is that these concepts require application of some basic quantitative techniques which he tried to avoid at the graduate school two years ago.

Jeff has approached you for help in answering the following questions:

a. Suppose Jeff has $85,000 to invest in an IRA at an interest rate of 10% per year for his retirement in 10 years. How much money can he accumulate at the end of the time period?

b. Jeff wants to send his daughter to college in 18 years. He has assumed that he would need $100,000 at the time in order to pay for her tuition, room and board, school supplies etc. If he can earn an average of 8% per year, how much money does he need to invest today as a lump sum to achieve that goal?

c. Jeff wants to move $50,000 from his checking accounts and invests it in money market securities for 3 years. The money market earns 7% interest compounded annually. How much can this investment grow at the end of the investment period?

d. Jeff wants to find the present value of the following uneven cash flows he expects to receive in the next 3 years from his business.

Year	Cash Flows
2020	$25,000
2021	$20,000
2022	$15,000

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

e. Jeff wants to invest in preferred stocks issued by Camden Company. The company pays $3 dividend per share on its stock. The dividend is expected to grow at a constant rate of 10% per year indefinitely. If Jeff requires a rate of return of 15% on the stock, what is the (estimated) current price of Camden stock?

Answer 1

a]

future value = present value * (1 + rate of return)^{number of years}

future value = $85,000 * (1 + 10%)¹⁰

future value = $220,468.11

b]

present value = future value / (1 + rate of return)^{number of years}

present value = $100,000 / (1 + 8%)¹⁸

present value = $25,024.90

c]

future value = present value * (1 + rate of return)^{number of years}

future value = $50,000 * (1 + 7%)³

future value = $61,252.15

d]

present value of each cash flow = future value / (1 + discount rate)ⁿ

where n = number of years after which the cash flow occurs.

Present value of cash flows = $53,077.73

Cash Flows flows PV of Cash Number of years after Year which cash flow occurs 2020 2021 2022 2 $25,000 $20,000 $15,000 Total $23,364 $17,469 $12,244 $53,077.73

A Year Number of years after which cash flow occurs Cash Flows PV of Cash flows 2 2020 3 2021 4 2022 25000 20000 15000 Total =C2/(1+7%)^B2 =C3/(1+7%)^B3 =C4/(1+7%)^B4 =SUM(D2:04)