Question 1

Suppose you are 40 years old and plan to retire in exactly 20 years. 21 years from now you will need to withdraw $5,000 per year from a retirement fund to supplement your social security payments. You expect to live to the age of 85. How much money should you place in the retirement fund each year for the next 20 years to reach your retirement goal if you can earn 12% interest per year from the fund?

Accepted Answer

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Question 2

As a part of your savings plan at work, you have been depositing $250 per quarter in a savings account earning 8% interest compounded quarterly for the last 10 years. You will retire in 15 years and want to increase your contribution each year from $1,000 to $2,000 per year, by increasing your contribution every four months from $250 to $500. Additionally, you have just inherited $10,000, which you plan to invest now to earn interest at 12% compounded annually for the next 15 years. How much money will you have in savings when you retire 15 years from now?

Accepted Answer

First, let's calculate the amount of savings from the quarterly deposits over the last 10 years. We can use the formula for compound interest, where A is the final amount, P is the principal (initial deposit), r is the interest rate, and n is the number of times compounded per year:

A = P(1 + r/n)^(nt)

Quarterly deposits of $250 per quarter for 10 years is a total of 40 deposits. Plugging in the values, we get:

A = 250(1 + 0.08/4)^(4*10) 
A = 250(1.02)^40 
A = 250(2.20804) 
A = $552,011.18

Next, we need to calculate the savings with the increased contributions of $1,000 to $2,000 per year, where the contribution increases every four months from $250 to $500. This will result in a total of 60 deposits (15 years x 4 deposits per year). To simplify the calculation, we can find the average contribution per deposit:

($250 + $500)/2 = $375

Using the same compound interest formula, we can calculate the total savings from these deposits:

A = 375(1 + 0.08/4)^(4*15) 
A = 375(2.70381) 
A = $1,014,056.28

Finally, we need to add the $10,000 inheritance, which will earn interest at 12% compounded annually over the next 15 years. Using the compound interest formula again:

A = 10,000(1 + 0.12)^15 
A = 10,000(4.53161) 
A = $45,316.12

Adding up all three amounts:

$552,011.18 + $1,014,056.28 + $45,316.12 = $1,611,383.58

Therefore, the answer is choice C: $161,307.

Question 3

What is the present value of the following uneven stream of cash flows? Assume a 6% discount rate and end-of-period payments. Round to the nearest whole dollar. Year Cash Flow
1 $3,000
2 $4,000
3 $5,000

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Question 4

The expected after-tax cash flow from an investment property that you are considering is
Year 1 $25,000
Year 2 $27,500
Year 3 $30,250
At the end of year 3 you expect to sell the property for $400,000. If the appropriate discount rate is 12%, what is the most you should pay for this property?

Accepted Answer

The answer of The expected after-tax cash flow from an...

Question 5

The present value of a complex cash flow stream is equal to the sum of the present values of each of the cash flows.

Accepted Answer

This is a fundamental principle of finance known as the time value of money. Each cash flow is discounted back to its present value, and the sum of these values represents the present value of the entire cash flow stream.

Question 6

You are planning to deposit $10,000 today into a bank account. Five years from today you expect to withdraw $7,500. If the account pays 5% interest per year, how much will remain in the account eight years from today? Round to the nearest dollar.

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Question 7

What is the value (price) of a bond that pays $400 semiannually for 10 years and returns $10,000 at the end of 10 years? The market discount rate is 10% paid semiannually.

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The answer of What is the value (price) of a...

Question 8

You are considering purchasing common stock in AMZ Corporation. You anticipate that the company will pay dividends of $5.00 per share next year and $7.50 per share in the following year. You also believe that you can sell the common stock two years from now for $30.00 per share. If you require a 14% rate of return on this investment, what is the maximum price that you would be willing to pay for a share of AMZ common stock?

Accepted Answer

The answer of You are considering purchasing common stock in...

Question 9

The future value of a complex cash flow growing at the rate of i for periods is its present value multiplied by (1+i)n.

Accepted Answer

The future value of a cash flow growing at a rate of i for n periods is calculated by multiplying the present value by (1+i)^n, not (1+i)n.

Question 10

Your parents are planning to retire in Phoenix, AZ in 20 years. Currently, the typical house that pleases your parents costs $200,000, but they expect inflation to increase the price of the house at a rate of 4% over the next 20 years. In order to buy a house upon retirement, what must they save each year in equal annual end-of-year deposits if they can earn 10% annually?

Accepted Answer

To calculate the required yearly savings for your parents, we need to use the future value formula for an annuity:

FV = PMT x [(1 + r)^n - 1] / r

Where:
PMT = the yearly savings required
r = the annual interest rate (10%)
n = the number of years (20)

We need to find PMT, so we can rearrange the formula:

PMT = FV x (r / [(1 + r)^n - 1])

First, we need to calculate the future value of the house in 20 years:

FV = $200,000 x (1 + 0.04)^20
FV = $480,658.64

Now we can calculate the yearly savings required:

PMT = $480,658.64 x (0.10 / [(1 + 0.10)^20 - 1])
PMT =  $7,650.94

Therefore, your parents must save $7,650.94 each year in equal annual end-of-year deposits to purchase the house upon retirement. Answer is B.

Question 11

You have just won a magazine sweepstakes and have a choice of three alternatives. You can get $100,000 now, or $10,000 per year in perpetuity, or $50,000 now and $150,000 at the end of 10 years. If the appropriate discount rate is 12%, which option should you choose?

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The answer of You have just won a magazine sweepstakes...

Question 12

Ronald Slump purchased a real estate investment with the following end-of-year cash flows: Year EOY Cash Flow
1 $200
2 $-350
3 $-430
4 $950
What is the present value of these cash flows if the appropriate discount rate is 20%?

Accepted Answer

To calculate the present value of the cash flows, we need to discount each cash flow by the appropriate discount rate. Using a financial calculator or Excel, we can calculate the present value of these cash flows as follows:

PV = $200/(1+0.20)^1 - $350/(1+0.20)^2 - $430/(1+0.20)^3 + $950/(1+0.20)^4
PV = $133.33

Therefore, the present value of these cash flows is $133.33, which is closest to choice C ($133).

Question 13

You have just purchased an investment that generates the cash flows that are shown below. If you are able to invest your money at 5.75%, compounded annually, by how much is this investment better or worse than your next best investment worth today? 0 $(9,000)
1 $1,250
2 $1,585
3 $1,750
4 $2,225
5 $3,450

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The answer of You have just purchased an investment that...

Question 14

You believe WSU stock will pay dividends of $1.00, $1.25, and $1.50 at the end of each of the next 3 years. Immediately after receiving the third dividend, you will sell the stock for $28.50. If the appropriate discount rate is 12%, you should be willing to pay $20.75 for this stock.

Accepted Answer

To determine the fair value of the stock, we need to calculate the present value of all 3 dividends and the sale price using the appropriate discount rate of 12%.

PV(Dividend Year 1) = $1.00 / (1 + 0.12)^1 = $0.8929
PV(Dividend Year 2) = $1.25 / (1 + 0.12)^2 = $1.0068
PV(Dividend Year 3) = $1.50 / (1 + 0.12)^3 = $1.2605
PV(Sale Price) = $28.50 / (1 + 0.12)^3 = $18.3580

Total Present Value = $0.8929 + $1.0068 + $1.2605 + $18.3580 = $21.5182

Therefore, the fair value of the stock is $21.5182, which is higher than the price of $20.75. Therefore, the statement is false.

Question 15

An investment will pay $500 in three years, $700 in five years, and $1,000 in nine years. If the opportunity rate is 6%, what is the present value of this investment?

Accepted Answer

The answer of An investment will pay $500 in three...

Question 16

To evaluate and compare investment proposals, we must adjust all cash flows to a common date.

Accepted Answer

Adjusting all cash flows to a common date (usually the present) is necessary in order to take into account the time value of money and make accurate comparisons between different investment options.

Question 17

Consider an investment that has cash flows of $500 the first year and $400 for the next four years. If your opportunity cost is 10%, you should be willing to pay $1,607.22 for this investment.

Accepted Answer

The present value of the cash flows, discounted at 10%, is approximately $1,607.22. This is calculated by summing the present values of each cash flow: $500/(1.1)^1 + $400/(1.1)^2 + $400/(1.1)^3 + $400/(1.1)^4 + $400/(1.1)^5.

Question 18

Assume that two investments have a three-year life and generate the cash flows shown below. Which of the two would you prefer? Year Investment A Investment B
1 $5,000 $8,000
2 $5,000 $5,000
3 $5,000 $2,000

Accepted Answer

Investment B generates larger cash flows in the earlier years, which could provide a higher return on investment in a shorter period of time. In addition, the total cash flows for both investments are the same, so Investment B is the preferred choice.

Question 19

You intend to purchase a new car upon graduation in two years. It will have a cost of $29,371, including all extra features and sales tax. You just received a $3,000 pre-graduation gift from your rich uncle that you intend to deposit in a money market account that pays 6% interest, compounded monthly. If you use the amount in the money market account for a down payment, and take out an auto loan for the remainder, how much will you need to borrow? (Round to the nearest dollar.)

Accepted Answer

The answer of You intend to purchase a new car...

Question 20

You have decided to invest $500 in a mutual fund today and make $500 end-of-the-year investments in the fund each year until you retire for 40 years. Assuming an opportunity cost of 12%, what do you estimate that you will have in this account at retirement?

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The answer of You have decided to invest $500 in...

Quiz 6: The Time Value of Money-Annuities and Other Topics

What is the present value of the following uneven stream of cash flows? Assume a 6% discount rate and end-of-period payments. Round to the nearest whole dollar. Year Cash Flow 1 $3,000 2 $4,000 3 $5,000

The expected after-tax cash flow from an investment property that you are considering is Year 1 $25,000 Year 2 $27,500 Year 3 $30,250 At the end of year 3 you expect to sell the property for $400,000. If the appropriate discount rate is 12%, what is the most you should pay for this property?