Question 1

Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today.What rate of return is built into the annuity? Disregard taxes.

Accepted Answer

To compare the two options, we need to find the present value of the annuity payments. Using the formula for the present value of an annuity, we get:

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

Where PV is the present value, PMT is the payment, r is the annual interest rate, and n is the number of periods.

Substituting PMT = $250,000, n = 20, and PV = $2,550,000, we can solve for r:

$2,550,000 = $250,000 x [1 - (1+r)^-20] / r

Multiplying both sides by r and rearranging, we get:

$2,550,000r = $250,000[1 - (1+r)^-20]

Expanding the brackets and simplifying, we get:

$2,550,000r = $250,000 - $250,000(1+r)^-20

$2,550,000r + $250,000(1+r)^-20 = $250,000

$2,550,000r + $250,000/(1+r)^20 = $250,000

$2,550,000r = $250,000 - $250,000/(1+r)^20

$2,550,000r = $250,000[(1+r)^20 -1]/(1+r)^20

$2,550,000r(1+r)^20 = $250,000[(1+r)^20 -1]

Dividing both sides by (1+r)^20 and simplifying, we get:

r = 7.49%

Therefore, the rate of return built into the annuity is 7.49%. As this is greater than the expected rate of return on other investments, it is better to choose the annuity option.

Question 2

Which of the following statements is CORRECT?

Accepted Answer

The answer of Which of the following statements is CORRECT?
...

Question 3

Your sister paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $10,000 at the end of the 5th year.What is the expected rate of return on this investment?

Accepted Answer

The answer of Your sister paid $10,000 (CF at t...

Question 4

Which of the following statements is CORRECT?

Accepted Answer

To solve for the internal rate of return (IRR), you need to find the rate that equates the present value of positive cash flows to the absolute value of the present value of negative cash flows. This process often involves trial and error, which is facilitated by computers or financial calculators.

Question 5

Ten years ago, Kronan Corporation earned $0.50 per share.Its earnings this year were $2.20.What was the growth rate in earnings per share (EPS) over the 10-year period?

Accepted Answer

The growth rate can be calculated using the formula for compound annual growth rate (CAGR): $$CAGR = \left(\frac{Final Value}{Initial Value}\right)^{\frac{1}{Number of Periods}} - 1$$ Here, the final value is $2.20, the initial value is $0.50, and the number of periods is 10 years. Plugging these values into the formula gives: $$CAGR = \left(\frac{2.20}{0.50}\right)^{\frac{1}{10}} - 1 = 2.44^{\frac{1}{10}} - 1 \approx 0.1597$$ or 15.97%.

Question 6

Which of the following statements is CORRECT?

Accepted Answer

An annuity due is a type of annuity where the cash flows occur at the beginning of each period. This is different from an ordinary (or deferred) annuity where the cash flows occur at the end of each period. Option A is incorrect because variable annuity refers to an annuity where the cash flow varies in amount rather than timing. Option B is incorrect because an ordinary annuity has cash flows occurring at the end of each period. Option C is incorrect because an annuity by definition has equal cash flows occurring at regular intervals, but the cash flows do not have to be equal. Option E is incorrect because the cash flows for an annuity should occur at regular intervals, but they do not have to be of the same amount.

Question 7

Your bank pays 4% interest annually.You have $2,500 invested in the bank.How long will it take for your funds to double?

Accepted Answer

The answer of Your bank pays 4% interest annually.You have...

Question 8

Your Green Investment Tips subscription is about to expire.You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately.Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy?

Accepted Answer

The answer of Your Green Investment Tips subscription is about...

Question 9

Which of the following statements is CORRECT?

Accepted Answer

An annuity is defined by equal cash flows occurring at regular intervals. Choices A, B, C, and D misrepresent the definitions of variable annuities, ordinary annuities, and annuities due.

Question 10

You have purchased a U.S.Treasury bond for $3,000.No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000.What interest rate will you earn on this bond?

Accepted Answer

The answer of You have purchased a U.S.Treasury bond for...

Question 11

You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4.What rate of return would you earn if you bought this asset?

Accepted Answer

The rate of return can be calculated using the Net Present Value (NPV) formula set to zero, because the NPV of investing in the asset should equal the cost of the investment for the investor to earn the expected rate of return. The cash flows are discounted back at the rate of return to find the present value, which should equal the investment cost of $7,250. The correct rate of return is the one that makes the NPV equal to zero. Through financial calculation or using a financial calculator, the rate that fits this criterion is 6.05%.

Question 12

Your aunt has $500,000 invested at 5.5%, and she now wants to retire.She wants to withdraw $45,000 at the beginning of each year, beginning immediately.When she makes her last withdrawal (at the beginning of a year), she also wants to have enough left in the account so that you can make a final withdrawal of $50,000 at the end of that year (her last withdrawal is at the beginning of the year, your withdrawal is at the end of that same year).What is the maximum number of $45,000 withdrawals that she can make and still have enough in the account so that you can make a $50,000 withdrawal at the end of the year of her last withdrawal? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)

Accepted Answer

We can use the formula for the present value of an annuity to solve this problem:
Present Value = Payment x ((1 - (1 + interest rate)^-n) / interest rate)
Where payment is the withdrawal amount, interest rate is the annual interest rate (5.5%), and n is the number of withdrawals.

We can first calculate the present value of the $50,000 withdrawal at the end of the final year:
PV = $50,000 / (1 + 0.055) = $47,393.36

Next, we can use trial and error to find the number of withdrawals that will result in a remaining balance of at least $47,393.36 after the last $45,000 withdrawal. Starting with 15 withdrawals, we get:
PV = $45,000 x ((1 - (1 + 0.055)^-15) / 0.055) = $525,772.43
Remaining balance = $525,772.43 x 1.055 - $45,000 = $484,419.51
This is more than the required $47,393.36, so we can try with 14 withdrawals:
PV = $45,000 x ((1 - (1 + 0.055)^-14) / 0.055) = $480,529.69
Remaining balance = $480,529.69 x 1.055 - $45,000 = $436,101.66
This is less than the required $47,393.36, so we need to try with more than 14 withdrawals. Continuing in this way, we find that 15 withdrawals result in a remaining balance of $484,419.51, which is sufficient for the final $50,000 withdrawal. Therefore, the maximum number of $45,000 withdrawals that she can make is 15.

Question 13

You agree to make 24 deposits of $500 at the beginning of each month into a bank account.At the end of the 24^th month, you will have $13,000 in your account.If the bank compounds interest monthly, what nominal annual interest rate will you be earning?

Accepted Answer

The future value of an annuity formula is used to calculate the nominal annual interest rate. By setting the future value to $13,000, the monthly deposit to $500, and solving for the interest rate, the nominal annual interest rate is approximately 7.62%.

Question 14

Your investment account pays 8.0%, compounded annually.If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?

Accepted Answer

The answer of Your investment account pays 8.0%, compounded annually.If...

Question 15

You have $5,000 invested in a bank that pays 3.8% annually.How long will it take for your funds to triple?

Accepted Answer

The answer of You have $5,000 invested in a bank...

Question 16

Wildwoods, Inc.earned $1.50 per share five years ago.Its earnings this year were $3.20.What was the growth rate in earnings per share (EPS) over the 5-year period?

Accepted Answer

The growth rate can be calculated using the formula for compound annual growth rate (CAGR), which is: $$CAGR = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1$$ where FV is the future value ($3.20), PV is the present value ($1.50), and n is the number of periods (5 years). Plugging in the values gives: $$CAGR = \left(\frac{3.20}{1.50}\right)^{\frac{1}{5}} - 1 \approx 0.1636$$ or 16.36%.

Question 17

Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today.You need money today to open a new restaurant, and your uncle offers to give you $120,000 for the annuity.If you sell it, what rate of return would your uncle earn on his investment?

Accepted Answer

The rate of return your uncle would earn on his investment can be found using the present value of an annuity formula, which is PV = PMT × [(1 - (1 + r)^-n) / r], where PV is the present value, PMT is the payment per period, r is the rate per period, and n is the number of periods. Since the payment is made at the beginning of the period, this is an annuity due. The formula needs to be adjusted slightly or a financial calculator or software that can handle annuity due calculations should be used. Given that the uncle is paying $120,000 for the annuity, and the payments are $15,000 per year for 12 years, we need to find the rate that satisfies this equation. Without going through the complex algebra, using a financial calculator or software designed for these calculations, inputting these values would give us the closest rate to match the present value of $120,000. The correct answer is 8.41%, which indicates that at this rate, the present value of the annuity payments equals the $120,000 offered by the uncle.

Question 18

Your girlfriend just won the Florida lottery.She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today.What rate of return is built into the annuity?

Accepted Answer

The correct answer is A because the rate of return built into the annuity is 3.44%. This can be calculated using the following formula:r = (FV/PV)^(1/n) - 1where:r = rate of returnFV = future value of the annuityPV = present value of the annuityn = number of yearsIn this case, the future value of the annuity is $15,000,000, the present value of the annuity is $10,500,000, and the number of years is 20. Plugging these values into the formula, we get:r = (15,000,000/10,500,000)^(1/20) - 1r = 3.44%

Question 19

Brockman Corporation's earnings per share were $3.50 last year, and its growth rate during the prior 5 years was 9.0% per year.If that growth rate were maintained, how many years would it take for Brockman's EPS to triple?

Accepted Answer

The answer of Brockman Corporation's earnings per share were $3.50...

Question 20

You have just purchased a U.S.Treasury bond for $747.25.No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000.What interest rate will you earn on this bond?

Accepted Answer

The answer of You have just purchased a U.S.Treasury bond...

Quiz 4: Time Value of Money

Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today.What rate of return is built into the annuity? Disregard taxes.

Which of the following statements is CORRECT?

Your sister paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $10,000 at the end of the 5th year.What is the expected rate of return on this investment?

Which of the following statements is CORRECT?

Ten years ago, Kronan Corporation earned $0.50 per share.Its earnings this year were $2.20.What was the growth rate in earnings per share (EPS) over the 10-year period?

Which of the following statements is CORRECT?

Your bank pays 4% interest annually.You have $2,500 invested in the bank.How long will it take for your funds to double?

Which of the following statements is CORRECT?

You have purchased a U.S.Treasury bond for $3,000.No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000.What interest rate will you earn on this bond?

You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4.What rate of return would you earn if you bought this asset?

You agree to make 24 deposits of $500 at the beginning of each month into a bank account.At the end of the 24th month, you will have $13,000 in your account.If the bank compounds interest monthly, what nominal annual interest rate will you be earning?

Your investment account pays 8.0%, compounded annually.If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?

You have $5,000 invested in a bank that pays 3.8% annually.How long will it take for your funds to triple?

Wildwoods, Inc.earned $1.50 per share five years ago.Its earnings this year were $3.20.What was the growth rate in earnings per share (EPS) over the 5-year period?

Your girlfriend just won the Florida lottery.She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today.What rate of return is built into the annuity?

Brockman Corporation's earnings per share were $3.50 last year, and its growth rate during the prior 5 years was 9.0% per year.If that growth rate were maintained, how many years would it take for Brockman's EPS to triple?

You have just purchased a U.S.Treasury bond for $747.25.No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000.What interest rate will you earn on this bond?

You agree to make 24 deposits of $500 at the beginning of each month into a bank account.At the end of the 24^th month, you will have $13,000 in your account.If the bank compounds interest monthly, what nominal annual interest rate will you be earning?