Question 1

You received a $5,000 loan at the end of each of your four years of college. Aunt Rose agreed to pay off your loans at the end of your fourth year of school. How much will she have to pay? Assume a 4% interest rate compounded annually on student loans.

Accepted Answer

Aunt Rose will pay the future value of each loan compounded at 4% annually. The first loan compounds for 3 years, the second for 2 years, the third for 1 year, and the fourth is not compounded. The total is $5,000(1.04)^3 + $5,000(1.04)^2 + $5,000(1.04)^1 + $5,000 = $21,235.

Question 2

A series of equivalent cash flows is called the accumulation factor.

Accepted Answer

A series of equivalent cash flows is referred to as an annuity, not the accumulation factor. The accumulation factor is used to calculate the future value of a single cash flow or series of cash flows.

Question 3

You are a sports agent who is representing Jack Lofton, a star football player, in contract negotiations with the New York Landmarks. The Landmarks have offered Lofton a four-year contract, with annual raises and performance bonuses that will result in a growing cash-flow stream for Lofton each year. Which table factor(s) should you use to most efficiently determine the "value" of the contract?

Accepted Answer

C

Question 4

The sum of the discount factors applicable to individual cash flows in a series of equal cash flows is called the:

Accepted Answer

The annuity discount factor is used to calculate the present value of a series of equal cash flows, making it the correct term for the sum of the discount factors applicable to individual cash flows in such a series.

Question 5

Lawson Company invests $60,000 today and has $148,560 by the end of eight years. What is the firm's compound annual interest rate?

Accepted Answer

The compound annual interest rate can be calculated using the formula for compound interest: $ FV = PV \times (1 + r)^n $. Here, $ FV = 148,560 $, $ PV = 60,000 $, and $ n = 8 $. Solving for $ r $, we get $ r \approx 0.12 $ or 12.00%.

Question 6

The interest rate used when we discount a future cash flow to compute its present value is called the discount rate.

Accepted Answer

The discount rate is indeed the interest rate used to discount future cash flows to their present value, reflecting the time value of money and risk associated with the cash flows.

Question 7

Norton Company has a 12% compound annual interest rate. If the firm invests $60,000 today, how much will have accumulated by the end of eight years?

Accepted Answer

The future value of an investment can be calculated using the formula: FV = PV * (1 + r)^n, where PV is the present value ($60,000), r is the annual interest rate (0.12), and n is the number of years (8). Plugging in the values: FV = $60,000 * (1 + 0.12)^8 = $148,560.

Question 8

Uncle Roscoe, a wealthy relative, has given you a choice of receiving $10,000 today or $3,000 at the end of each year for the next four years. Which table factor(s) should be used to most efficiently determine the "value" of the $3,000 cash-flow stream?

Accepted Answer

To determine the value today of receiving $3,000 at the end of each year for the next four years, you would use the present value of a $1 annuity factor. This factor helps calculate the current worth of a series of future payments.

Question 9

The fundamental concept in a capital-budgeting decision analysis is inflation.

Accepted Answer

The fundamental concept in a capital-budgeting decision analysis is the time value of money, which considers how the value of money changes over time due to inflation, but also incorporates other factors such as interest rates and opportunity cost.

Question 10

Which of the following choices is closest to the amount of money that must be invested today in order to have $25,000 at the end of four years if the rate of return is 12% compounded annually?

Accepted Answer

The formula for the future value of an investment is:FV = PV * (1 + r)^nwhere:FV is the future valuePV is the present valuer is the annual interest raten is the number of yearsIn this case, we have:FV = $25,000r = 12% = 0.12n = 4Substituting these values into the formula, we get:$25,000 = PV * (1 + 0.12)^4$25,000 = PV * 1.5735PV = $25,000 / 1.5735PV = $15,900Therefore, the closest choice to the amount of money that must be invested today in order to have $25,000 at the end of four years if the rate of return is 12% compounded annually is A) $15,900.

Question 11

You desire to invest $3,000 at the end of each year for the next five years to accumulate the funds needed for a down payment on a home. Which table factor(s) should be used to most efficiently determine the amount accumulated by the end of the five-year period?

Accepted Answer

Since the investment involves making regular (annual) payments for a specific period (5 years) to accumulate a sum, the future value of a $1 annuity table factor is the most appropriate to use. This factor helps in calculating the future value of a series of equal, end-of-period payments.

Question 12

Compound interest is interest earned not only on the principal invested but also on the interest earned in previous periods.

Accepted Answer

Compound interest is calculated on the initial principal and also on the accumulated interest of previous periods, allowing the investment to grow at a faster rate compared to simple interest, where interest is calculated only on the principal amount.

Question 13

All other things being equal, which of the following would be most attractive to an investor?

Accepted Answer

A cash outflow of $60,000 in six years is most attractive because the present value of a future cash outflow is less than an immediate cash outflow, assuming a positive discount rate.

Question 14

The main idea behind the time value of money is that:

Accepted Answer

The main idea behind the time value of money is that a dollar today is worth more than a dollar in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. Therefore, cash flows received in the distant future are considered less valuable than cash flows received in the near-term future.

Question 15

The procedure used to compute the present value of a series of cash flows is known as:

Accepted Answer

Discounting is the process used to determine the present value of a series of future cash flows by applying a discount rate. This method is essential in finance for assessing the value of investments, loans, and other financial instruments that involve cash flows over time.

Question 16

The procedure used to compute the future value of a series of cash flows is known as:

Accepted Answer

Compounding is the process of calculating the future value of a series of cash flows by applying interest over time.

Question 17

A series of equal cash flows is called a (n):

Accepted Answer

An annuity is a series of equal cash flows occurring at regular intervals for a fixed period of time.

Question 18

Consider the following items of information:
I. The target recovery period.
II. The discount rate.
III. The timing (i.e., year) of a cash flow.
Which of the above items would be needed to calculate the present value of a cash flow?

Accepted Answer

To calculate the present value of a cash flow, you need the discount rate (to discount future cash flows back to their present value) and the timing of the cash flow (to know how far in the future the cash flow occurs, which affects how it's discounted). The target recovery period is not directly used in present value calculations.

Question 19

You estimate that it will take five years to complete your college education. Your parents want to invest enough money today at an interest rate of 8% compounded annually to allow you to withdraw $10,000 at the end of each year for the next five years, with nothing left at the end. The amount of money to invest today is:

Accepted Answer

The present value of an annuity formula is used to calculate the amount needed today: PV = PMT × [(1 - (1 + r)^-n) / r]. Here, PMT = $10,000, r = 0.08, n = 5. Plugging in these values gives PV = $39,929.98, which rounds to $39,930.

Question 20

All other things being equal, which of the following would be the most attractive to an investor?

Accepted Answer

The most attractive option for an investor, all other things being equal, is a cash inflow of $10,000 today (Option D). This is because of the time value of money principle, which states that a dollar today is worth more than a dollar in the future due to its potential earning capacity.

Quiz 19: Compound Interest and the Concept of Present Value