Question 1

If a few intermediate cash flows in valuing a stream of cash flows are zero can we delete those points on the timeline and squeeze the timeline to show only nonzero cash flows?

Accepted Answer

Every cash flow contains two pieces of information-the nominal value and the time stamp.If we decide to eliminate the zero cash flows from the timeline and concentrate only on the nonzero ones,we will be distorting the time stamp of some nonzero cash flows.Hence,we need to show the timeline in full,including all cash flows zero as well as nonzero.

Question 2

A perpetuity will pay $1000 per year,starting five years after the perpetuity is purchased.What is the present value (PV)of this perpetuity on the date that it is purchased,given that the interest rate is 4%?

Accepted Answer

Using the perpetuity formula,
PV = CF / r
Where PV is the present value, CF is the cash flow, and r is the interest rate.

In this case, CF = $1000 and r = 4%. However, since the cash flows start five years after the perpetuity is purchased, we need to discount the cash flows by five years using the present value formula:
PV = CF / (1+r)^n

where n = number of years (in this case, 5)

Therefore, PV = 1000 / (0.04) * [1 - (1/ (1+0.04)^5)]
PV = $21,369.83

Rounding off the final answer gives us choice C, $21,370

Question 3

A lottery winner will receive $1 million at the end of each of the next ten years.What is the future value (FV)of her winnings at the time of her final payment,given that the interest rate is 8.5% per year?

Accepted Answer

B

Question 4

Ally wishes to leave a provision in her will that $2000 will be paid annually in perpetuity to a local charity.How much must she provide in her will for this perpetuity if the interest rate is 6%?

Accepted Answer

We can use the formula for perpetuity:

PV = PMT / r

where PV is the present value, PMT is the annual payment, and r is the interest rate.

Substituting the given values, we get:

PV = 2000 / 0.06
PV = 33333.33

Therefore, Ally must provide $33,333.33 in her will for this perpetuity. The correct answer is C.

Question 5

Consider the following timeline detailing a stream of cash flows: 
If the current market rate of interest is 10%,then the present value (PV)of this stream of cash flows is closest to:

Accepted Answer

To find the present value of the stream of cash flows, we need to discount each cash flow based on the time at which it is received. Using a financial calculator, we can calculate the present value of the cash flows as follows:

N = 5 (number of cash flows)
I/Y = 10 (market rate of interest)
CF0 = 0
CF1 = 100
CF2 = 150
CF3 = 200
CF4 = 250
CF5 = 300

Solving for PV gives us $459.97, which is closest to $460. Therefore, the best choice is C.

Question 6

Which of the following investments has a higher present value,assuming the same (strictly positive)interest rate applies to both investments?

Accepted Answer

Investment Y has a higher present value because it has higher cash flows in the earlier years, which are valued more highly due to the effect of compounding at a positive interest rate. Therefore, even though the total cash flows for both investments are the same, the timing and size of those cash flows affects the present value calculation. Without knowing the interest rate, we cannot calculate the exact present value, but we can still compare the relative present values of the two investments based on the timing and size of their cash flows.

Question 7

What is the present value (PV)of an investment that will pay $400 in one year's time,and $400 every year after that,when the interest rate is 5%?

Accepted Answer

The answer of What is the present value (PV)of an...

Question 8

Salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of each of the next 5 years.He must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first year.What is the present value of this investment if the interest rate is 4%?

Accepted Answer

The answer of Salvatore has the opportunity to invest in...

Question 9

Consider the following timeline detailing a stream of cash flows: 
If the current market rate of interest is 8%,then the future value (FV)of this stream of cash flows is closest to:

Accepted Answer

The answer of Consider the following timeline detailing a stream...

Question 10

If $10,000 is invested in a certain business at the start of the year,the investor will receive $3000 at the end of each of the next four years.What is the present value of this business opportunity if the interest rate is 7% per year?

Accepted Answer

The answer of If $10,000 is invested in a certain...

Question 11

A business promises to pay the investor of $2000 today for a payment of $500 in one year's time,$1000 in two years' time and $1000 in three years' time.What is the present value of this business opportunity if the interest rate is 5% per year?

Accepted Answer

The answer of A business promises to pay the investor...

Question 12

You are given two choices of investments,Investment A and Investment B.Both investments have the same future cash flows.Investment A has a discount rate of 4%,and Investment B has a discount rate of 5%.Which of the following is true?

Accepted Answer

Investment A has a lower discount rate than Investment B, meaning that the present value of its cash flows will be higher. This is because the lower discount rate implies a higher value for money today compared to money in the future. Therefore, Investment A is the better choice.

Question 13

The present value (PV)of a stream of cash flows is just the sum of the present values of each individual cash flow.

Accepted Answer

This is the basic principle of time value of money, where we discount future cash flows to their present values and then add them up to get the present value of the entire stream of cash flows.

Question 14

A homeowner in a sunny climate has the opportunity to install a solar water heater in his home for a cost of $2400.After installation the solar water heater will produce a small amount of hot water every day,forever,and will require no maintenance.How much must the homeowner save on water heating costs every year if this is to be a sound investment? (The interest rate is 9% per year. )

Accepted Answer

The answer of A homeowner in a sunny climate has...

Question 15

Suppose you invest $1000 into a mutual fund that is expected to earn a rate of return of 10%.The amount of money will you have in ten years is closest to which of the following? The amount you will have in 50 years is closest to which of the following?

Accepted Answer

Using the compound interest formula, we can calculate the amount of money you will have after 10 years:

A = P(1 + r/n)^(nt)
A = 1000(1 + 0.1/1)^(1*10)
A = $2,593.74

Therefore, we choose answer choice C.

For 50 years, we have:

A = 1000(1 + 0.1/1)^(1*50)
A = $117,391.13

Therefore, we choose answer choice C again.

Question 16

A perpetuity has a PV of $32,000.If the interest rate is 10%,how much will the perpetuity pay every year?

Accepted Answer

PV = C / r
$32,000 = C / 0.10
C = $3,200. Therefore, the perpetuity will pay $3,200 every year.

Question 17

Consider the following timeline detailing a stream of cash flows: 
If the current market rate of interest is 8%,then the present value (PV)of this stream of cash flows is closest to:

Accepted Answer

To find the present value (PV) of the stream of cash flows, we need to discount each cash flow back to its present value using the market rate of interest of 8%. Using the PV formula, we get:

PV = 10,000/(1+0.08)^1 + 6,000/(1+0.08)^2 + 5,000/(1+0.08)^3 + 4,000/(1+0.08)^4

PV = 9,259.26 + 5,249.81 + 3,732.24 + 2,705.15

PV = $21,211.46

Therefore, the best choice is B.

Question 18

An investment pays you $20,000 at the end of this year,and $10,000 at the end of each of the four following years.What is the present value (PV)of this investment,given that the interest rate is 4% per year?

Accepted Answer

We can use the formula for the present value of an annuity to calculate the PV of this investment:

PV = 20,000/(1+0.04) + 10,000/(1+0.04)^2 + 10,000/(1+0.04)^3 + 10,000/(1+0.04)^4 + 10,000/(1+0.04)^5

PV = 20,000/1.04 + 10,000/1.04^2 + 10,000/1.04^3 + 10,000/1.04^4 + 10,000/1.04^5

PV = 19,230.77 + 9,157.81 + 8,717.43 + 8,295.78 + 7,892.11

PV = 54,133.91

Therefore, the present value of this investment is $54,133.91. Thus, the best choice is (C).

Question 19

Use the information for the question(s)below.
Joe just inherited the family business,and having no desire to run the family business,he has decided to sell it to an entrepreneur.In exchange for the family business,Joe has been offered an immediate payment of $100,000.Joe will also receive payments of $50,000 in one year,$50,000 in two years,and $75,000 in three years.The current market rate of interest for Joe is 6%.
-In terms of present value (PV),how much will Joe receive for selling the family business?

Accepted Answer

The answer of Use the information for the question(s)below.
Joe just...

Question 20

Consider the following timeline detailing a stream of cash flows: 
If the current market rate of interest is 6%,then the future value (FV)of this stream of cash flows is closest to:

Accepted Answer

The answer of Consider the following timeline detailing a stream...

Quiz 4: Time Value of Money: Valuing Cash Flow Streams

If a few intermediate cash flows in valuing a stream of cash flows are zero can we delete those points on the timeline and squeeze the timeline to show only nonzero cash flows?

A perpetuity will pay $1000 per year,starting five years after the perpetuity is purchased.What is the present value (PV) of this perpetuity on the date that it is purchased,given that the interest rate is 4%?

A lottery winner will receive $1 million at the end of each of the next ten years.What is the future value (FV) of her winnings at the time of her final payment,given that the interest rate is 8.5% per year?

Ally wishes to leave a provision in her will that $2000 will be paid annually in perpetuity to a local charity.How much must she provide in her will for this perpetuity if the interest rate is 6%?

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 10%,then the present value (PV) of this stream of cash flows is closest to:

Which of the following investments has a higher present value,assuming the same (strictly positive) interest rate applies to both investments?

What is the present value (PV) of an investment that will pay $400 in one year's time,and $400 every year after that,when the interest rate is 5%?

Salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of each of the next 5 years.He must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first year.What is the present value of this investment if the interest rate is 4%?

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 8%,then the future value (FV) of this stream of cash flows is closest to:

If $10,000 is invested in a certain business at the start of the year,the investor will receive $3000 at the end of each of the next four years.What is the present value of this business opportunity if the interest rate is 7% per year?

A business promises to pay the investor of $2000 today for a payment of $500 in one year's time,$1000 in two years' time and $1000 in three years' time.What is the present value of this business opportunity if the interest rate is 5% per year?

You are given two choices of investments,Investment A and Investment B.Both investments have the same future cash flows.Investment A has a discount rate of 4%,and Investment B has a discount rate of 5%.Which of the following is true?

The present value (PV)of a stream of cash flows is just the sum of the present values of each individual cash flow.

Suppose you invest $1000 into a mutual fund that is expected to earn a rate of return of 10%.The amount of money will you have in ten years is closest to which of the following? The amount you will have in 50 years is closest to which of the following?

A perpetuity has a PV of $32,000.If the interest rate is 10%,how much will the perpetuity pay every year?

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 8%,then the present value (PV) of this stream of cash flows is closest to:

An investment pays you $20,000 at the end of this year,and $10,000 at the end of each of the four following years.What is the present value (PV) of this investment,given that the interest rate is 4% per year?

Consider the following timeline detailing a stream of cash flows: If the current market rate of interest is 6%,then the future value (FV) of this stream of cash flows is closest to: