Finance Ch. 5
What are the two factors to be considered in time value of money?
he factors that are critical in time value of money are the size of the cash flows and the timing of the cash flows.
Why is a dollar today worth more than a dollar one year from now?
A dollar is worth more today than one year from now, due to its potential earning capacity. If you have the money in your hand today, you have the opportunity to invest it and earn interest or you can purchase goods and services for your immediate consumption. Given that people have a positive preference for consumption, time value of money holds true.
What is a time line, and why is it important in financial analysis?
A time line is a horizontal line that starts at time zero (today) and shows cash flows as they occur over time. It is an important tool used to analyze cash flows over certain time periods, as the timing of each cash flow has a big impact on the final figure, and therefore on the resulting investment decision.
What is compounding, and how does it affect the future value (FV) of an investment?
Compounding is the process that refers to converting the initial (principal) amount into a future value. In order to obtain the future value of the principal amount, you calculate what the value of that amount will be at the end of the time period, assuming the initial investment will earn interest and that interest is invested and earns additional interest in future periods.
You are planning to take a spring break trip to Cancun your senior year. The trip is exactly two years away, but you want to be prepared and have enough money when the time comes. Explain how you would determine the amount of money you will have to save in order to pay for the trip.
First, determine how much money you will need for the trip. Second, check how much you already have and how it translates into future value cash—how much it will be worth in two years. Next, determine how much you will have to deposit today, given the bank's offered interest rate, to ensure that you will have saved up the difference when the time for your senior spring break comes.
Explain the difference between future value and present value.
Future value measures what one or more cash flows will be worth at the end of a specified period, while present value measures what one or more future cash flows are worth today (at time = 0).
Compound growth is exponential over time. Explain.
Growth rates, as well as interest rates, are not linear, but rather exponential over time. In other words, the growth rate of the invested funds is accelerated by the compounding of interest. Over time, the principal amount gets larger as interest is added due to the compounding effect.
What is the present value (PV), and when is it used?
Present value is the amount a future sum is worth today, given a certain rate of return. The present value concept should be used when calculating how much money you need today in order to reach your financial goal sometime in the future.
Explain how compound interest differs from simple interest.
Suppose I invest $100 for three years at a rate of 10 percent. Simple interest would imply that I will earn $10 for each of the three years for a total of $30 interest. At the end of three years I would have $130. Compound interest recognizes that the interest earned in years 1 and 2 will also earn interest over the remaining period. Thus, the $10 earned in the first year would earn interest at 10 percent for the next two years, and the $10 earned in the second year would earn interest for the third year. Thus the total amount that I would have at the end of three years would be: $100(1.10)^3 = $133.10. By compounding, I have earned additional interest of $3.10. The total compound interest is the $33.10 earned on the $100 invested, while the simple interest earned is equal to $30.00.
Explain why you would expect the discount factor to become smaller when based on the longer the time to payment.
The discount factor will become smaller the longer the time to payment due to time value of money. The longer you have to wait to obtain the money, the less value it will have to you. Mathematically, the discount factor is calculated as 1/(1 + i)^n. The longer the time to payment, the larger "n" gets, which will make the discount factor smaller.
What is the discount rate? How does the discount rate differ from the interest rate in the future value equation?
The discount rate is the rate of return used in a discounted cash flow analysis to determine the present value of future cash flows. Both discount and interest rates essentially represent the same concept. The only difference is the context in which they are used.
What is the difference between simple interest and compound interest?
The effect of compounding, where interest is earned on interest, makes an investment grow to a larger value than it would if it only paid simple interest. Simple interest is interest earned only on the original principal.
If you were given a choice between investing in a savings account that paid quarterly interest and one that paid monthly interest, which one should you choose if they both offered the same stated interest rate and why?
The impact of compounding dictates that one should pick the account that pays interest more frequently (as long as the interest rates are the same). This allows for the interest earned in the earlier periods to earn interest and the investment to grow more.
Explain the phrase "a dollar today is worth more than a dollar tomorrow."
The implication is that if one was to receive a dollar today instead of in the future, the dollar could be invested and will be worth more than a dollar tomorrow because of the interest earned during that one day. This makes it more valuable than receiving a dollar tomorrow.
What is the difference between the interest rate (i) and the growth rate (g) in the future value equation?
The interest rate and the growth rate in the future value equation essentially represent the same concept. The growth rate is used when we deal with numerical values such as sales or change over time. When referring to money being invested, we use the term interest rate.
How does changing the compounding period affect the amount of interest earned on an investment?
The more frequent the compounding schedule, the higher the interest earned. For example, $100 invested for one year at 10 percent compounded annually will earn you $10 of interest at the end of the year, but if your bank compounded interest quarterly, your earnings from interest would increase to $10.38.
What is the relation between the present value factor and the future value factor?
The present value factor is the reciprocal of the future value factor. To obtain the present value factor, you divide 1 by the future value factor (1 + i)^n.
Explain the difference between compounding and discounting.
The process of converting an amount given at the present time into a future value is called compounding. It is the process of earning interest over time. Discounting is the process of converting future cash flows to their current or present value. In other words, present value is the current value of future cash flows that are discounted at an appropriate interest rate.
What is the Rule of 72?
This is a rule of thumb to determine how fast an investment can double. It is a rule that allows you to closely approximate the time that it would take to double your money. It works well with interest rates between 5 and 20 percent, but varies more with higher rates. The Rule of 72 says that the time to double your money (TDM) approximately equals 72/i, where i is the rate of return expressed as a percentage. For example, if a bank paid 10% interest it would take 7.2 (72/10 = 7.2) years to double your money.
Explain the importance of a time line.
Time lines are important tools used to analyze investments that involve cash flow streams over a period of time. They are horizontal lines that start at time zero (today) and show cash flows as they occur over time. Because of time value of money, it is crucial to keep track of not only the size, but also the timing of the cash flows.