Question 1

Noel Klinger is planning to invest in an insurance company product. The product will pay $12,500 at the end of this year. Thereafter, the payments will grow annually at a 2.5 percent rate forever. Jack will be able to invest his cash flows at a rate of 5.5 percent. What is the present value of this investment cash flow stream? (Round to the nearest dollar.)

Accepted Answer

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Question 2

Shelton 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 percent for the next 15 years. What is the present value of this growing annuity if the firm uses a discount rate of 18 percent on its investments? (Round to the nearest dollar.)

Accepted Answer

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Question 3

Beautinator Cosmetics borrowed $152,300 from a bank for three years. If the quoted rate (APR) is 11.75 percent, and the compounding is daily, what is the effective annual rate (EAR)? (Round to one decimal place.)

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Question 4

James Perkins wants to have a million dollars at retirement, which is 15 years away. He already has $200,000 in an IRA earning 8 percent 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 percent on any investment he makes. (Round to the nearest dollar.)

Accepted Answer

To find the annual savings needed, calculate the future value of the current $200,000 and subtract it from $1,000,000. Then, use the future value of an annuity formula to find the annual savings required to make up the difference. The correct calculation results in approximately $13,464.

Question 5

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 percent, how much will you have at the end of four years? Round to the nearest dollar.

Accepted Answer

Using the compound interest formula: A = P(1+r/n)^(nt), 
where A is the amount at the end of the investment period, 
P is the initial investment (in this case, $1,400), r is the annual interest rate (6% or 0.06), 
n is the number of times interest is compounded per year (assuming annually), 
and t is the number of years (4).
So, A = 1400(1+0.06/1)^(1*4) = $1,836.82. 
Rounding to the nearest dollar gives the answer D: $6,492.

Question 6

Surreal Corp. has borrowed to invest in a project. The loan calls for a payment of $17,500 every month for three years. The lender quoted Surreal a rate of 8.40 percent with monthly compounding. At what rate would you discount the payments to find amount borrowed by Surreal Corp.? (Round to two decimal places.)

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Question 7

Sid Phillips has funded a retirement investment with $250,000 earning a return of 6.75 percent. What is the value of the payment that he can receive in perpetuity? (Round to the nearest dollar.)

Accepted Answer

The value of a perpetuity can be found by dividing the annual payment by the interest rate. 
Thus, the annual payment that Sid Phillips can receive in perpetuity is: 
250,000 x 0.0675 = $16,875

Therefore, the answer is choice C, $16,875.

Question 8

Bryant Investments is putting out a new product. The product will pay out $32,000 in the first year, and after that the payouts will grow by an annual rate of 2.75 percent forever. If you can invest the cash flows at 7.25 percent, how much will you be willing to pay for this perpetuity? (Round to the nearest dollar.)

Accepted Answer

To find the price of the perpetuity, we need to find the present value of all the cash flows. 
PV = CF1/(r-g)
where PV = present value
CF1 = cash flow in the first year = $32,000
r = discount rate = 7.25%
g = growth rate = 2.75%
PV = $32,000/(0.0725-0.0275)
PV = $711,111 (rounded to the nearest dollar)
Therefore, the best choice is D, as it is the closest to the calculated present value.

Question 9

Foodelicious Corp. 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 percent growth for the last several years. Foodelicious Corp. 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 percent, what is the present value of this investment? (Round to the nearest dollar.)

Accepted Answer

To calculate the present value of the investment, we need to use the formula for the present value of an annuity: PV = C * [(1 - (1 + r)^-n) / r], where PV is the present value, C is the annual cash flow, r is the discount rate (15% in this case), and n is the number of periods (16 in this case). Plugging in the numbers, we get: PV = $310,000 * [(1 - (1 + 0.15)^-16) / 0.15] = $2,838,182 (rounded to the nearest dollar). Therefore, the best choice is B.

Question 10

Brandon Ramirez wants to set up a scholarship at his alma mater. He is willing to invest $320,000 in an account earning 11 percent. What will be the annual scholarship that can be given from this investment? (Round to the nearest dollar.)

Accepted Answer

The annual scholarship amount can be calculated by multiplying the investment amount by the interest rate: $320,000 * 0.11 = $35,200.

Question 11

Tim Dodson has borrowed $8,600 to pay for his new car. The annual interest rate on the loan is 9.4 percent, and the loan needs to be repaid in four payments. What will be his annual payment if he begins his payment beginning now? (Round to the nearest dollar.)

Accepted Answer

The first step is to calculate the monthly interest rate by dividing the annual rate by 12:

9.4% / 12 = 0.7833%

The second step is to use the loan formula, which is:

Payment = (P × r) / (1 − (1 + r)^−n)

Where:
- P = the principal or amount borrowed
- r = the monthly interest rate (in decimal form)
- n = the total number of payments

Plugging in the given values, we get:

Payment = (8,600 × 0.007833) / (1 − (1 + 0.007833)^−4) = $2,448

Therefore, the annual payment will be $2,448. The answer is D.

Question 12

: Ann Chang is investing $2,500 today and will do so at the beginning of each of the next six years for a total of seven payments. If her investment can earn 12 percent, how much will she have at the end of seven years? (Round to the nearest dollar.)

Accepted Answer

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Question 13

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

Accepted Answer

To calculate the present value of the inheritance, we need to use the formula for the present value of an annuity:

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

Where PV is the present value, PMT is the payment received each year, r is the interest rate per period, and n is the number of periods.

In this case, PMT = $100,000, r = 7.75%, and n = 5. Plugging these values into the formula, we get:

PV = $100,000 x [(1 - (1+0.0775)^-5) / 0.0775] = $433,064

Therefore, the best choice is C.

Question 14

Cassandra Dawson 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 percent annually. How much will she have to invest annually to reach her target? (Round to the nearest dollar.)

Accepted Answer

We can solve this problem using the formula for the future value of an annuity:

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

where FV is the future value, PMT is the annual deposit, r is the interest rate, and n is the number of years.

Plugging in the given values, we get:

12,000 = PMT x ((1 + 0.068)^4 - 1) / 0.068

Solving for PMT, we get:

PMT = 2,537.84

Rounding to the nearest dollar, the answer is $2,538, which is choice C.

Question 15

Jeff Lovett 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 percent, what is the present value of this annuity? (Round to the nearest dollar.)

Accepted Answer

The present value of an annuity is the sum of the present values of each of the individual payments. The present value of each payment is calculated by dividing the payment amount by the discount factor, which is (1 + r)^n, where r is the interest rate and n is the number of periods. In this case, the interest rate is 8.3% and the number of periods is 5. So, the discount factor is (1 + 0.083)^5 = 1.4693. The present value of each payment is $2,235 / 1.4693 = $1,520. The present value of the annuity is the sum of the present values of each of the individual payments, which is $1,520 * 5 = $7,600.

Question 16

Ralf Wilson wants to receive $25,000 in perpetuity and will invest his money in an investment that will earn a return of 14 percent 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 using the formula: Present Value = Annual Cash Flow / Interest Rate. Therefore, the value of the investment needed today is $25,000 / 0.14 = $178,571 (rounded to the nearest dollar).

Question 17

A lottery winner was given a perpetual payment of $25,362. She could invest the cash flows at 7.5 percent. What is the present value of this perpetuity? (Round to the nearest dollar.)

Accepted Answer

The present value of a perpetuity can be calculated using the formula PV = PMT/i, where PV is the present value, PMT is the annual cash flow, and i is the interest rate. 
Plugging in the values given, we get PV = 25,362/0.075 = 338,160. Rounded to the nearest dollar, the answer is A, $338,160.

Question 18

Stuart Weddle's father is 55 years old and wants to set up a cash flow stream that would be forever. He would like to receive $15,000 every year, beginning at the end of this year. If he could invest in account earning 9 percent, how much would he have to invest today to receive his perpetual cash flow? (Round to the nearest dollar.)

Accepted Answer

To calculate the present value of a perpetuity, use the formula: PV = C / r, where C is the annual cash flow ($15,000) and r is the interest rate (9% or 0.09). Thus, PV = $15,000 / 0.09 = $166,667.

Question 19

How is an annuity due different from the ordinary annuity?

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Question 20

Dawson Electricals has borrowed $27,850 from its bank at an annual rate of 8.5 percent. It plans to repay the loan in eight equal installments, beginning at the end of next in a year. What is its annual loan payment? (Round to the nearest dollar.)

Accepted Answer

We can solve this problem using the formula for the present value of an annuity:

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

where PV is the present value of the loan, Pmt is the equal payment, r is the annual interest rate, and n is the number of payments.

In this case, we have:

PV = $27,850
r = 8.5% = 0.085
n = 8

Solving for Pmt, we get:

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

Pmt = $27,850 x 0.085 / [1 - (1 + 0.085)^-8]

Pmt = $4,938.9

Rounding this to the nearest dollar, we get:

Pmt = $4,939

Therefore, the annual loan payment for Dawson Electricals is $4,939, which corresponds to choice C.

Quiz 6: Discounted Cash Flows and Valuation

Beautinator Cosmetics borrowed $152,300 from a bank for three years. If the quoted rate (APR) is 11.75 percent, and the compounding is daily, what is the effective annual rate (EAR) ? (Round to one decimal place.)