Question 1

Jensen's Shipping wants to expand as soon as it can save $142 million.Towards that goal,the firm started saving three years ago and currently has $19.6 million saved.Starting today,the firm will add $12,000 a month to this savings account.The rate of return is 13.1 percent,compounded monthly.How long will it be from now before the company can expand?

Accepted Answer

2^nd BGN 2^nd Set Number of years = 178.03/12 = 14.84 years

Question 2

You desperately need some money and only your 'miserly' friend has any.He agrees to loan you the money you need,if you make payments of $20 a month for the next six months.In keeping with his reputation,he requires that the first payment be paid today.He also charges you 1.5 percent interest per month.How much money are you borrowing?

Accepted Answer

PV_ADue = $20{[1 - 1/(1.015)⁶]/.015} × 1.015 = $115.652^nd BGN 2^nd SET

Question 3

Westover Ridge has a management contract with its president that requires a lump sum payment of $20 million to be paid upon the completion of the president's first ten years of service.The company can earn 5.5 percent on its investments and wants to set aside an equal amount of money each year over the next ten years to fund this obligation.How much money must the firm save each year?

Accepted Answer

$20,000,000 = C{[1 + .055)¹⁰ - 1]/.055};C = $1,553,355.37

Question 4

Wings and More purchased a piece of property for $1.4 million.It paid a down payment of 15 percent in cash and financed the balance.The loan terms require monthly payments for 15 years at an annual percentage rate of 7.60 percent,compounded monthly.What is the amount of each mortgage payment?

Accepted Answer

Amount borrowed = $1,400,000 × (1 - .15)= $1,190,000$1,190,000 = C({1 - 1/[1 + (.076/12)]^{15 × 12}}/(.076/12));C = $11,099.18

Question 5

You borrow $150,000 to buy a house.The mortgage rate is 8.5 percent and the loan period is 30 years.Payments are made monthly.If you pay for the house according to the loan agreement,how much total interest will you pay? (Round the payment to two decimal places when computing the total interest. )

Accepted Answer

$150,000 = C ({1 - 1/[1 + (.085/12)]^{12 × 30}}/(.085/12));C = $1,153.37 Total interest = (360 × $1,153.37)- $150,000 = $265,213.20

Question 6

You have $100,000 saved today and plan to withdraw $8,000 a year.How long can you make these withdrawals if you earn an annual percentage rate of 3.5 percent?

Accepted Answer

PV = $100,000 = $8,000[(1 - 1/1.035^T)/.035];T = 16.73 years

Question 7

Rodget's is saving for an expansion project and has decided to save $2,500 a month,starting today and continuing for four years.The firm expects to earn 7.9 percent,compounded monthly.If the company had wanted to deposit an equivalent lump sum today,how much would it have had to deposit?

Accepted Answer

PV_ADue = $2,500({1 - 1/[1 + (.079/12)]^{4 × 12}}/(.079/12))× [(1 + (.079/12)] = $103,277.412^nd BGN 2^nd SET

Question 8

Today,you are retiring.You have a total of $413,926 in your retirement savings and have the funds invested at 4.2 percent,compounded monthly.You want to withdraw $2,500 at the beginning of every month,starting today.You also want the withdrawals to stop when your account balance declines to $100,000.For how many years can you make withdrawals?

Accepted Answer

2^nd BGN 2^nd SET Number of years = 203.57/12 = 16.96 years

Question 9

An investment will pay $6,300 every three years for the next 30 years.The annual rate of interest is 11.4 percent.What is the value of this investment at the end of Year 30?

Accepted Answer

3-year rate = 1.114³ - 1 = .38247FV = $6,300{[(1.38247)^30/3 - 1]/.38247} = $403,576.58

Question 10

Today,the Corner Store borrowed $5,250 at 7.2 percent,compounded monthly.The loan payment is $114.11 a month.How many loan payments must the firm make before the loan is paid in full?

Accepted Answer

$5,250 = $114.11({1 - 1/[1 + (.072/12)]^T}/(.072/12));T = 54 months

Question 11

You estimate that you will have $44,500 in student loans by the time you graduate.The interest rate is 6.5 percent,compounded monthly.If you want to have this debt paid in full within five years,how much must you pay each month?

Accepted Answer

$44,500 = C({1 - 1/[1 + (.065/12)]^{5 × 12}}/(.065/12));C = $870.69

Question 12

Rowynn just signed loan papers to buy a new car.The loan is for $26,700 for four years at an interest rate of 5.8 percent,compounded monthly.What is the amount of each monthly loan payment?

Accepted Answer

$26,700 = C({1 - 1/[1 + (.058/12)]^{4 × 12}}/(.058/12));C = $624.60

Question 13

Erickson's is considering a project with an initial cost of $623,000.The project will produce cash inflows of $33,500 monthly for 21 months.What is the annual rate of return on this project?

Accepted Answer

APR = 1.1322% × 12 = 13.59%

Question 14

Charley wants to sell you an investment that will pay $1,000 per quarter for 25 years.You desire an annual rate of return of 5.5 percent,compounded quarterly.What is the most you would be willing to pay as a lump sum today for this investment?

Accepted Answer

PV = $1,000({1 - 1/[1 + (.055/4)]^{25 × 4}}/(.055/4));C = $54,165.88

Question 15

Theo just won a prize that will pay him $12,000 a year for 12 years,starting at the end of Year 12.What is the current value of this prize if the discount rate is 9 percent,compounded annually?

Accepted Answer

PV₁₁ = $12,000{[1 - (1/1.09¹²)]/.09} = $85,928.70PV = $85,928.70/(1.09)¹¹ = $33,300.20

Question 16

You are buying a previously owned car today at a price of $8,125.You are paying $600 down in cash and financing the balance for 36 months at 7.9 percent,compounded monthly.What is the amount of each loan payment?

Accepted Answer

Amount financed = $8,125 - 600 = $7,525$7,525 = C({1 - 1/[1 + (.079/12)]³⁶}/(.079/12));C = $235.46

Question 17

You are comparing two annuities with equal present values.The applicable discount rate is 7.25 percent,compounded annually.One annuity pays $6,500 on the first day of each year for 20 years.How much does the second annuity pay each year for 20 years if it pays at the end of each year?

Accepted Answer

Payment = $6,500 × 1.0725 = $6,971.25Each payment is received one year later,so every payment will earn one additional year of interest.

Question 18

Clint just won a prize that will pay him $30,000 a year for 30 years,starting at the end of Year 10.What is the current value of this prize if the discount rate is 12 percent,compounded annually?

Accepted Answer

PV₉ = $30,000{[1 - (1/1.12³⁰)]/.12} = $241,655.52PV = $241,655.52/(1.12)⁹ = $87,143.40

Question 19

You retire at age 65 and expect to live another 30 years.On the day you retire,you have $564,500 saved.You expect to earn 3.5 percent,compounded monthly.How much can you withdraw from your savings each month if you plan to die on the day you spend your last penny?

Accepted Answer

$564,500 = C{1 - 1/[1 + (.035/12)]³⁶⁰}/(.035/12));C = $2,534.86

Question 20

Martha receives $100 on the first of each month.Stewart receives $100 on the last day of each month.Both Martha and Stewart will receive payments for five years.The discount rate is 8 percent,compounded monthly.What is the difference in the present value of these two sets of payments?

Accepted Answer

PV_ADue = $100({1 - 1/[1 + (.08/12)]^{5 × 12}}/(.08/12))× [(1 + (.08/12)] = $4,964.722^nd BGN 2^nd SET PV = $100({1 - 1/[1 + (.08/12)]^{5 × 12}}/(.08/12))= $4,931.84 Difference = $4,964.72 - 4,931.84 = $32.88

Quiz 4: Discounted Cash Flow Valuation