Question 1

Perpetuity: Chris Collinge has funded a retirement investment with $250,000 earning a return of 5.75 per cent. What is the value of the payment that he can receive in perpetuity? (Round to the nearest dollar.)

Accepted Answer

To calculate the value of a perpetuity, we use the formula:

Perpetuity Value = Annual Payment / Interest Rate

In this case, Chris has funded the investment with $250,000 and the return is 5.75%. Therefore, the annual payment he can receive in perpetuity is:

Annual Payment = $250,000 x 5.75% = $14,375

Dividing this by the interest rate, we get:

Perpetuity Value = $14,375 / 5.75% = $250,000

Therefore, Chris can receive an annual payment of $14,375 in perpetuity.

Question 2

If your investment pays the same amount at the end of each year forever, the cash flow stream is called

Accepted Answer

A cash flow stream that pays the same amount at the end of each year forever is called a perpetuity. This is because the payments continue perpetually, or indefinitely. An ordinary annuity, on the other hand, has a finite number of payments and ends after a certain period of time. An annuity due is similar to an ordinary annuity but the payments are made at the beginning of each period instead of at the end. Therefore, the best choice for this scenario is A, which is a perpetuity.

Question 3

Growing annuity: Wilbon Company is evaluating whether it should take over the lease of an ethnic restaurant in Manhattan. The current owner had originally signed a 25-year lease, of which 16 years still remain. The restaurant has been growing steadily at a 7 per cent growth for the last several years. Wilbon Company expects the restaurant to continue to grow at the same rate for the remaining lease term. Last year, the restaurant brought in net cash flows of $310,000. If the firm evaluates similar investments at 15 per cent, what is the present value of this investment? (Round to the nearest dollar.)

Accepted Answer

The present value of a growing annuity can be calculated using the formula for the present value of a growing annuity. Given the cash flow of $310,000, a growth rate of 7%, a discount rate of 15%, and a period of 16 years, the present value is approximately $2,838,182.

Question 4

Annuity due: Mark Holcomb has a five-year loan on which he will make annual payments of $2,235, beginning now. If the interest rate on the loan is 8.3 per cent, what is the present value of this annuity? (Round to the nearest dollar.)

Accepted Answer

The present value of an annuity due can be calculated using the formula for the present value of an ordinary annuity and then multiplying by (1 + r) to account for the payments starting immediately. The present value of an ordinary annuity is calculated using the formula: PV = PMT * [(1 - (1 + r)^-n) / r]. For this problem, PMT = $2,235, r = 0.083, and n = 5. After calculating the present value of the ordinary annuity, multiply by (1 + 0.083) to adjust for the annuity due. The result is approximately $9,588.

Question 5

Perpetuity: Jeff Conway wants to receive $25,000 in perpetuity and will invest his money in an investment that will earn a return of 13.5 per cent annually. What is the value of the investment that he needs to make today to receive his perpetual cash flow stream? (Round to the nearest dollar.)

Accepted Answer

The value of a perpetuity is calculated by dividing the annual cash flow by the annual interest rate. Here, $25,000 / 0.135 = $185,185.

Question 6

Perpetuity: A lottery winner was given a perpetual payment of $11, 444. She could invest the cash flows at 7 per cent. What is the present value of this perpetuity? (Round to the nearest dollar.)

Accepted Answer

The answer of Perpetuity: A lottery winner was given a...

Question 7

Your investment in a small business venture will produce cash flows that increase by 15 per cent every year for the next 25 years. This cash flow stream is called

Accepted Answer

The cash flow stream is increasing by 15% every year for 25 years, making it a growing annuity. A growing perpetuity would continue indefinitely, so it is not the correct answer. An ordinary annuity would have a constant cash flow stream, so it is also not the correct answer. An annuity due would have payments made at the beginning of each period, but the problem does not mention when the payments are made.

Question 8

Perpetuity: Your father is 60 years old and wants to set up a cash flow stream that would be forever. He would like to receive $20,000 every year, beginning at the end of this year. If he could invest in account earning 9 per cent, how much would he have to invest today to receive his perpetual cash flow? (Round to the nearest dollar.)

Accepted Answer

The present value of a perpetuity is the amount of money that must be invested today to generate a constant stream of cash flows forever. The formula for the present value of a perpetuity is:PV = CF / rwhere:PV is the present valueCF is the annual cash flowr is the annual interest rateIn this case, the annual cash flow is $20,000 and the annual interest rate is 9%. Therefore, the present value of the perpetuity is:PV = $20,000 / 0.09 = $222,222

Question 9

Computing annuity payment: Trevor Smith wants to have a million dollars at retirement, which is 15 years away. He already has $200,000 in an investment account earning 8 per cent annually. How much does he need to save each year, beginning at the end of this year to reach his target? Assume he could earn 8 per cent on any investment he makes. (Round to the nearest dollar.)

Accepted Answer

The correct answer is A. $13,464.To calculate the annuity payment, we can use the formula:PMT = (FV * r) / ((1 + r)^n - 1)where:PMT is the annuity paymentFV is the future valuer is the annual interest raten is the number of yearsIn this case, we have:FV = $1,000,000r = 8% = 0.08n = 15Plugging these values into the formula, we get:PMT = (1,000,000 * 0.08) / ((1 + 0.08)^15 - 1)PMT = $13,464.06Therefore, Trevor needs to save $13,464 each year to reach his target of $1 million at retirement.

Question 10

Growing perpetuity: Norwood Investments is putting out a new product. The product will pay out $25,000 in the first year, and after that the payouts will grow by an annual rate of 2.5 per cent forever. If you can invest the cash flows at 7.5 per cent, how much will you be willing to pay for this perpetuity? (Round to the nearest dollar.)

Accepted Answer

The answer of Growing perpetuity: Norwood Investments is putting out...

Question 11

Annuity due: Your inheritance will pay you $100,000 a year for five years beginning now. You can invest it in a bank account that will pay 7.75 per cent annually. What is the present value of your inheritance? (Round to the nearest dollar.)

Accepted Answer

The answer of Annuity due: Your inheritance will pay you...

Question 12

Annuity due: You plan to save $1,400 for the next four years, beginning now, to pay for a vacation. If you can invest it at 6 per cent, how much will you have at the end of four years? Round to the nearest dollar.

Accepted Answer

Since this is an annuity due, we must use the formula for present value of an annuity due instead of the formula for regular present value. The formula is:

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

where PV is the present value, PMT is the recurring payment, r is the interest rate per period, and n is the number of periods.

Plugging in the values, we get:

PV = $1,400 x [(1 + 0.06) x ((1 + 0.06)^4 - 1) / 0.06]
PV = $5,820.98

Since we are asked for the future value, we can simply multiply this by (1 + r)^(n-1):

FV = $5,820.98 x (1 + 0.06)^3
FV = $6,491.69

Rounding to the nearest dollar gives us choice D, $6,492.

Question 13

A firm receives a cash flow from an investment that will increase by 10 per cent annually for an infinite number of years. This cash flow stream is called

Accepted Answer

The cash flow described is a growing perpetuity because it is a constant cash flow stream that never ends and grows at a constant rate each year. An ordinary annuity has a fixed cash flow stream for a finite period of time, whereas a growing annuity has a cash flow stream that grows at a constant rate for a finite period of time. An annuity due has payments made at the beginning of each period, rather than at the end of each period.

Question 14

Computing annuity payment: Jackson Electricals has borrowed $27,850 from its bank at an annual rate of 8.5 per cent. It plans to repay the loan in eight equal instalments, beginning at the end of next year. What is its annual loan payment? (Round to the nearest dollar.)

Accepted Answer

To calculate the annual loan payment, we use the formula for an annuity payment: P = [r*PV] / [1 - (1 + r)^-n], where P is the payment, r is the interest rate per period, PV is the present value of the loan, and n is the number of periods. Plugging in the values: r = 0.085, PV = $27,850, n = 8, we find P ≈ $4,939.

Question 15

Growing annuity: Hill Enterprises is expecting tremendous growth from its newest boutique store. Next year the store is expected to bring in net cash flows of $675,000. The company expects its earnings to grow annually at a rate of 13 per cent for the next 15 years. What is the present value of this growing annuity if the firm uses a discount rate of 18 per cent on its investments? (Round to the nearest dollar.)

Accepted Answer

The present value of a growing annuity can be calculated using the formula: PV = C * [(1 - ((1 + g) / (1 + r))^n) / (r - g)], where C is the initial cash flow, g is the growth rate, r is the discount rate, and n is the number of periods. Plugging in the values: C = $675,000, g = 0.13, r = 0.18, n = 15, the present value is approximately $6,448,519.

Question 16

Perpetuity: Roger Barkley wants to set up a scholarship at his alma mater. He is willing to invest $500,000 in an account earning 10 per cent. What will be the annual scholarship that can be given from this investment? (Round to the nearest dollar.)

Accepted Answer

To find the annual scholarship from a perpetuity, you need to multiply the initial investment by the interest rate in percentage form. Then, divide that by 100. 
Annual scholarship = ($500,000 x 10%)/100 = $50,000 
Therefore, the annual scholarship that can be given from this investment is $50,000.

Question 17

Computing annuity payment: Jane Ogden wants to save for a trip to Australia. She will need $12,000 at the end of four years. She can invest a certain amount at the beginning of each of the next four years in a bank account that will pay her 6.8 per cent annually. How much will she have to invest annually to reach her target? (Round to the nearest dollar.)

Accepted Answer

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Question 18

Which one of the following statements is TRUE about the effective annual rate (EAR)?

Accepted Answer

All of the statements are true about the effective annual rate (EAR). The EAR takes into account the effects of compounding and adjusts the annualised interest rate for the time value of money. It is the true cost of borrowing or lending, as it reflects the total amount of interest that will be earned or paid over the course of a year. Therefore, choice D is correct.

Question 19

Computing annuity payment: John Harper has borrowed $17,400 to pay for his new truck. The annual interest rate on the loan is 9.4 per cent, and the loan needs to be repaid in four years. What will be his annual payment if he begins his payment beginning now? (Round to the nearest dollar.)

Accepted Answer

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Question 20

Growing perpetuity: Jack Benny is planning to invest in an insurance company product. The product will pay $10,000 at the end of this year. Thereafter, the payments will grow annually at a 3 per cent rate forever. Jack will be able to invest his cash flows at a rate of 6.5 per cent. What is the present value of this investment cash flow stream? (Round to the nearest dollar.)

Accepted Answer

The answer of Growing perpetuity: Jack Benny is planning to...

Quiz 6: Discounted Cash Flows and Valuation