Finance, chapter 4, analyzing single cash flows
Five years ago, Lewis Equipment purchased equipment costing $212,000. Two years ago, the firm paid 32,000 for updates to that equipment. This year, the firm sold the equipment for 189,000. Which of those cash flows are cash inflows for the company?
$189,000, sale price
You expect to receive a gift of 1000 three years from today. What is the value of this gift today if the discount rates are 6%, 6.5%, and 7% over the next three years?
1000/1.06x1.065x1.07 = 1000/1.207923 = 827.87
If you want to double your money in five years, what is the approximate annual rate of return you must earn?
72/5 = 14.4%
Time line
A graphical representation showing the size and timing of cash flows through time
Rule of 72
An approximation for the number of years needed for an investment to double in value
Outflow
Cash payment
Inflow
Cash received
This morning, Kurt invested 500 for five years. He will earn 3 % interest for the first 2 years and 5 % interest for the last three years. How much will his investment be worth 5 years from now?
FV = 500 x (1+0.03)^2 x (1+0.05)^3 = 614.06
10 years ago, Alicia invested 9000 at 5% interest. How much more money would she have had today if she had invested the money at 6% instead of 5%? Interest is compounded annually
FV = 9000 x ( 1 + 0.05)^10 = 14,660.05 FV = 9000 x (1 + 0.06)^6 = 16,117.63 Difference = 1457.58
T/F: Several years ago, your grandmother invested 500 for you at 2.5% interest. Today, that investment is worth 1,864. When computing the number of years, the 1,864 should be used as the present value
False, the present value is 500
How long will it take to increase a 2,200 investment to 10,000 if the interest rate is 6.5%?
I = 6.5, PV = -2,200, PMT = 0, FV = 10,000, 24,04 years
Simple interest
Interest earned only on the original deposit
Charity House has been promised a 25,000 donation five years from today. How much would that gift be worth next year? Assume an interest rate of 8%
PV = 25,000 / (1+0.08)^4
You expect to receive a gift of 5,000 six years from today. Which formula provides the value of this gift two years from today if the discount rate is 15%?
PV = 5000/(1+0.09)^4
A project has these cash flows: -2000 two years ago, 800 one year ago, and 1,200 one year from now. Which is the correct formula for computing today's value of these cash flows given a 6% rate of interest?
TV=-2000 x (1+0.06)^2 + 800 (1+0.06) x 1,200 / (1+0.06)
Present value
The amount a future cash flow is worth today
Interest rate
The cost of borrowing money, denoted as a percent
Discount rate
The interest rate used to discount future cash flows to the present
Compounding
The process of adding interest earned every period on both the original investment and the reinvested earnings
Discounting
The process of finding present value by reducing future values using the discount, or interest, rate
Future value
The value of an investment after one or more periods
T/F: If you invest 1,000 and earn compound interest, the dollar amount of your annual interest payment will increase each year
True
Which of the following best illustrates simple interest? a. Ann has a 1,000 savings account that will pay her 40 of interest each year for five years b. Rita has a savings account that paid her 40, 41, 42 and 43 in interest over the past four years on a 1,000 investment c. Ivan invested 1,000 and receives an increasing amount of interest each year even though the interest rate is constant d. Alex invested 1,000 and has received 35, 42, 46, and 49 in annual earnings over the past four years?
a. Ann has a 1,000 savings account that will pay her 40 of interest each year for five years
4 years ago, AB tools had an extra $500 it did not currently need so the firm deposited the 500 in a new savings account. 3 years ago, the firm withdrew 200. Last year, the firm deposited 800 into the account. Today, the account is worth 1,180 and the firm is withdrawing the entire balance. Which statement correctly defines a portion of the timeline for AB tools if the 500 deposit is shown at time zero? a. At year one, there is a cash inflow of 200 b. At year four, there is a cash outflow of 1,180 c. At time zero, there is a cash inflow of 500 d. At year 2, there is a cash outflow of 800
a. At year one, there is a cash inflow of 200
Which one of these cash flows best illustrates a cash outflow? a. Better Bakery purchased a new oven for 28,600 b. Ernst withdrew 900 from his savings account c. Paulette received a 100 dividend payment on her stock investment d. Carlton Mills collected 1,200 from the sale of a product
a. Better Bakery purchased a new oven for 28,600
Which formula illustrates the value of $100 invested for one year at 5% interest? a. FV = 100 x (1 + 0.05) b. FV = 100 x 1 ^0.05 c. FV = 100 / (1 + 0.05) d. FV = 100 x (0.05)^1
a. FV = 100 x (1+0.05)
Which one of these statements is correct concerning the relationship of i to PV, FV, and N? a. If you increase the interest rate, all else held constant, the future value will increase b. If you increase the interest rate, all else held constant, the time period will remain constant c. If you increase the interest rate, all things held constant, the present value will increase d. If you increase the interest rate, all else held constant, the time period will increase
a. If you increase the interest rate, all else held constant, the future value will increase
Which of these statements are correct? a. The longer the time period, the greater the future value of a stated sum b. The shorter the time period, the lower the present value of a stated future value c. The shorter the time period, the higher the present value of a stated future value d. The longer the time period, the higher the present value given a stated future value
a. The longer the time period, the greater the future value of a stated sum c. The shorter the time period, the higher the present value of a stated future value
Which one of these correctly defines the future value of a 1,000 investment? a. The future value is the value obtained by discounting the 1,000 for a stated period of time b. Future value is the value of the investment at any date after the initial investment date c. The initial 1,000 investment is the future value d. Future value is the value of the 1,000 investment at any point in time prior to the date of investment
b. Future value is the value of the investment at any date after the initial investment date
Which one of these formulas illustrates the compounding of interest? a. 100 / (1+0.06) b. 100 x (1+0.06) c. 100 x (1+0.06) x (1+0.06) d. 100 + 6 + 6 +6 +6
c. 100 x (1+0.06) x (1+0.06)
Which one of these statements is correct concerning the relationship of PV, FV, i, and N? Assume the interest rate is constant and positive a. All else held constant, the longer the time period, the lower the future value b. All else held constant, the longer the time period, the higher the interest rate c. All else held constant, the longer the time period, the lower the current value d. All else held constant, the shorter the time period, the lower the present value
c. All else held constant, the longer the time period, the lower the current value
Which of these statements correctly defines the rule of 72 a. The theory that money has a 72% probability of doubling in value within a ten year period b. Provides an exact number of years needed to double your money if the interest rate is 7.2 percent c. Provides an approximation of the number of years needed to double your money given a particular rate of investment d. States that you can double your money in one year if you can earn a rate of return of 72% for the year
c. Provides an approximation of the number of years needed to double your money given a particular rate of investment
Alicia invested 1,000 three years ago at a fixed rate of 5% interest. Which one of these illustrates the compounding of interest over time? a. Alicia spends 50 of her interest each year as soon as she receives it b. Alicia withdrew 1,050 two years ago c. Alicia received 50 in interest in years 1, 2, and 3 d. Alicia's investment was worth 1,050 after one year and 1,102.50 after 2 years
d. Alicia's investment was worth 1,050 after one year and 1,102.50 after 2 years
Which formula moves a cash flow ahead 6 years in time at an interest rate of 5%? a. PV = 800/(1+0.06)^5 b. PV = 800/(1+0.05)^6 c. FV = 800 (1+0.06)^5 d. FV = 800 (1+0.05)^6
d. FV = 800 (1+0.05)^6
Which of these is the correct formula for computing the interest rate on an investment a. i = (FVn / PV)^1/N b. i= (FVn/PV)^N c. i = (FVn/PV)^N-1 d. i = (FVn / PV) ^1/N -1
d. i = (FVn / PV) ^1/N -1
Two years ago, your investments were worth 11,000. Today, those same investments are only worth 9,800 for an annual loss of 5.61%. How do you compute the return needed to increase your investments to 11,000 in the next two years?
i = (11,000/9,800)^1/2 -1
You invested 1,000 and lost 21% of that value during the first year. Which formula computes the rate needed to increase your investment back to 1,000 by the end of the second year?
i = 1,000/[1,000 x (1-0.21)]^1/1 - 1
