Question 1

Aeron Electrics borrowed $120,000 for five years at an interest rate of 8 percent,compounded annually.The loan requires repayment of the interest annually.In addition,the principal must be repaid in equal annual payments.What is the amount of the total loan payment in year three?

Accepted Answer

Annual principal payment = $120,000/5 = $24,000Loan payment for Year 3 = $24,000 + .08 [$120,000 - (2 × $24,000)] = $29,760

Question 2

Terrence has an investment that will pay $250 to him next year and increase that amount by 1.25 percent annually.The payments are expected to go on indefinitely and the discount rate is 6.5 percent,compounded annually.What is the value of this investment?

Accepted Answer

PV_{Growing Perpetuity} = $250/(.065 - .0125)= $4,761.90

Question 3

There are three factors that affect the present value of an annuity.Explain what these three factors are and discuss how an increase in each will impact the present value of the annuity.

Accepted Answer

The answer of There are three factors that affect the...

Question 4

What is the effective annual rate of 16.5 percent,compounded continuously?

Accepted Answer

EAR = e^.165 - 1 = .1794,or 17.94%

Question 5

Wilt's Mart is expected to produce a cash flow of $38,900 at the end of next year with increases of 1.5 percent annually for a total of 25 years.What is the present value of this business at a discount rate of 14.5 percent,compounded annually?

Accepted Answer

PV = $38,900{[1 - (1.015/1.145)²⁵]/(.145 - .015)} = $284,523.90

Question 6

A project is expected to provide a cash flow of $15,600 next year with annual increases of 4.5 percent for a total of 12 cash flows.After that,the project will be worthless.What is the present value of this project at a discount rate of 13 percent,compounded annually?

Accepted Answer

PV = $15,600{[1 - (1.045/1.13)¹²]/(.13 - .045)} = $111,723.56

Question 7

You have just obtained a 6-year pure discount loan in the amount of $275,000 at 5.78 percent interest,compounded semiannually.What amount will you have to repay at the end of the six years?

Accepted Answer

FV = $275,000 × [1 + (.0578/2)]^{6 × 2} = $387,088.88

Question 8

What is the difference between an ordinary annuity and an annuity due? Which type of annuity would you prefer if you are making the payments? Explain your reasoning.

Accepted Answer

The answer of What is the difference between an ordinary...

Question 9

Countrywide Oil has a well that will produce an annual cash flow of $36,900 next year.The cash flow is expected to increase by 2 percent per year indefinitely.What is this well worth today if the discount rate is 17 percent?

Accepted Answer

PV_{Growing Perpetuity} = $36,900/(.17 - .02)= $246,000

Question 10

A 10-year loan in the amount of $238,000 is to be repaid in equal annual payments.The interest rate is 7 percent,compounded annually.What is the amount of interest that is included in the loan payment for Year 3?

Accepted Answer

$238,000 = C{[1 - (1/1.07¹⁰)]/.07};C = $33,885.85

Question 11

You have been awarded monthly payments of $2,800 for 15 years as an insurance settlement.ABC Finance has offered to pay you a lump sum amount today in exchange for your annuity stream.When determining the price to be paid today,will you or will ABC prefer a lower discount rate over a higher discount rate? Explain your reasoning.

Accepted Answer

The answer of You have been awarded monthly payments of...

Question 12

Your credit card company quotes you a rate of 16.5 percent,compounded daily.What is the actual rate of interest you are paying?

Accepted Answer

EAR = [1 + (.165/365)]³⁶⁵ - 1 = .1793,or 17.93%

Question 13

Identify a type of loan that is a pure discount loan and explain which features of the loan qualify it to be classified as a pure discount loan.

Accepted Answer

The answer of Identify a type of loan that is...

Question 14

You just invested $13,000 for seven years at 14 percent,compounded continuously.What will the value of your investment be at the end of the seven years?

Accepted Answer

$13,000 × e^{.14 × 7} = $34,637.93

Question 15

You are loaning $1,000 for one year at a 6 percent rate of interest.How much additional interest can you earn if you compound the rate continuously rather than annually?

Accepted Answer

FV = $1,000 × 1.06 = $1,060FV = $1,000 × (1 + e^.06)= $1,061.84Difference = $1,061.84 - 1,060 = $1.84

Question 16

Greedy and Friends loans money at an annual rate of 21 percent,compounded daily.What is the actual rate borrowers are paying?

Accepted Answer

EAR = [1 + (.21/365)]³⁶⁵ - 1 = .2336,or 23.36%

Question 17

Texas Foods has a loan that requires one lump sum payment at the end of 12 years in the amount of $389,000.The interest rate is 6.5 percent,compounded monthly.What amount did the firm borrow?

Accepted Answer

PV = $389,000/[1 + (.065/12)]^{12 × 12} = $178,695.68

Question 18

What circumstances are required for an APR to equal an EAR?

Accepted Answer

The answer of What circumstances are required for an APR...

Question 19

A 5-year loan in the amount of $169,000 is to be repaid in equal annual payments.What is the remaining principal balance after the third payment if the interest rate is 3 percent,compounded annually?

Accepted Answer

$169,000 = C{[1 - (1/1.03⁵)]/.03};C = $36,901.92

Question 20

Juniper Stores borrowed $80,000 for four years at an interest rate of 9 percent,compounded annually.The loan requires the payment of the annual interest plus $20,000 of principal each year.What is the amount of the total loan payment in Year 2?

Accepted Answer

Loan payment for Year 2 = $20,000 + .09 ($80,000 - 20,000)= $25,400

Quiz 4: Discounted Cash Flow Valuation