Question 1

Juniper Stores borrowed $98,000 for 5 years at an interest rate of 6.7 percent,compounded annually.The loan requires the payment of the annual interest plus $19,600 of principal each year.What is the amount of the total loan payment in Year 3?

Accepted Answer

Loan payment _{Year 3} = $19,600 + 0.067[$98,000 - (2 × $19,600)] = $23,539.60

Question 2

A 5-year loan in the amount of $48,000 is to be repaid in equal annual payments.What is the remaining principal balance after the third payment if the interest rate is 5 percent,compounded annually?

Accepted Answer

$48,000 = C{[1 - (1 / 1.05⁵)] / 0.05} C = $11,086.79 11ea6c22_9309_eb56_9716_61df105330ee_TB1200_00 11ea6c22_9309_eb57_9716_1fb83b194dc4_TB1200_00

Question 3

A loan in the amount of $212,000 is to be repaid in equal annual payments over 15 years.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

$212,000 = C{[1 - (1 / 1.07¹⁵)] / 0.07} C = $23,276.46 11ea6c22_9309_eb58_9716_df9eae77c007_TB1200_00 11ea6c22_9309_eb59_9716_f543531da53d_TB1200_00

Question 4

Alex estimates that he will have $47,500 in student loans by the time he graduates.The interest rate is 7.2 percent,compounded monthly.If he wants to have this debt paid in full within 5 years following graduation,how much must he pay each month?

Accepted Answer

$47,500 = C({1 - 1 / [1 + (0.072 / 12)]^5×12} / (0.072 / 12)) C = $945.05 11ea6c22_9309_7621_9716_155a9e24559d_TB1200_00

Question 5

Tracie invested $60,000 in exchange for payments of $2,500 a year forever.What rate of return is she earning?

Accepted Answer

r = $2,500 / $60,000 = 0.0417,or 4.17%

Question 6

You have just obtained a 5-year pure discount loan in the amount of $75,000 at 6.28 percent interest,compounded monthly.What total amount will you have to repay?

Accepted Answer

FV = $75,000[1 + (0.0628 / 12)]⁵^×12 = $102,582.70 11ea6c22_9309_4f0f_9716_f59b70033cf2_TB1200_00

Question 7

You retire at age 66 and expect to live another 25 years.On the day you retire,you have $128,500 saved.You expect to earn 4.5 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

$128,500 = C{1 - 1 / [1 + (0.045 / 12)]^25×12} / (0.045 / 12) C = $714.24 11ea6c22_9309_27fe_9716_fd998ae34e97_TB1200_00

Question 8

Jensen's Shipping is expected to produce an annual cash flow of $218,900 next year.Thereafter,this cash flow is expected to decrease by 1.6 percent per year indefinitely.What is this firm worth today at a discount rate of 18 percent?

Accepted Answer

PV_{Growing Perpetuity} = $218,900 / [0.18 - (-0.016)] = $1,116,836.74

Question 9

Texas Foods has a loan that requires one lump sum payment at the end of 12 years in the amount of $139,000.The interest rate is 5.8 percent,compounded monthly.What amount did the firm borrow?

Accepted Answer

PV = $139,000 / [1 + (0.058 / 12)]¹²^×12 = $69,418.30 11ea6c22_9309_9d34_9716_d9b19d03aef6_TB1200_00

Question 10

Today,the Corner Store borrowed $11,680 at 6.3 percent,compounded monthly.The loan payment is $195.23 a month.How many loan payments must the firm make before the loan is paid in full?

Accepted Answer

$11,680 = $195.23({1 - 1 / [1 + (0.063 / 12)]^T} / (0.063 / 12)) T = 72 months 11ea6c22_9309_c445_9716_0d91fd0fccfe_TB1200_00

Question 11

Shawn borrowed $132,600 at 4.25 percent for 30 years to purchase a home.Payments are to be paid monthly.If all payments are paid as agreed,how much total interest will be paid? (Round the monthly payment to two decimal places when computing the total interest paid.)

Accepted Answer

$132,600 = C({1 - 1 / [1 + (0.0425 / 12)]^30×12} / (0.0425 / 12)) C = $652.31 11ea6c22_9309_9d33_9716_b373dcb4852f_TB1200_00 Total interest = (30 × 12 × $652.31)- $132,600 = $102,231.60

Question 12

Aeron Electrics borrowed $160,000 for 4 years at an interest rate of 6 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 3?

Accepted Answer

Annual principal payment = $160,000 / 4 = $40,000 Loan payment for Year 3 = $40,000 + 0.06 [$160,000 - (2 × $40,000)] = $44,800

Question 13

The Uptown Development project is expected to provide a cash flow of $18,600 next year with annual increases of 3.5 percent for 15 years.After that,the project will be worthless.What is the present value of this project at a discount rate of 17 percent,compounded annually?

Accepted Answer

PV = $18,600({1 - [(1 + 0.035)/ (1 + 0.17)]¹⁵} / (0.17 - 0.035))= $115,875.14

Question 14

Beta preferred stock pays an annual dividend of $4.80 a share.How much should you pay to purchase one share if you require a rate of return of 15.6 percent?

Accepted Answer

PV = $4.80 / 0.156 = $30.77

Question 15

Wings and More purchased a piece of property for $1.8 million.It paid a down payment of 20 percent in cash and financed the balance.The loan terms require monthly payments for 15 years at an annual percentage rate of 4.60 percent,compounded monthly.What is the amount of each mortgage payment?

Accepted Answer

Amount borrowed = $1,800,000 × (1 - 0.20)= $1,440,000 $1,440,000 = C({1 - 1 / [1 + (.046 / 12)]^15×12} / (0.046 / 12)) C = $11,089.64 11ea6c22_9309_7620_9716_09e8c8ff5db9_TB1200_00

Question 16

You have $187,620 saved today and plan to withdraw $9,000 a year.How long can you make these withdrawals if you earn an annual percentage rate of 4.8 percent?

Accepted Answer

C = 0.048 × $187,620 C = $9,005.76 Since you plan to withdraw less than you expect to earn,you can make these withdrawals forever.

Question 17

Westover Ridge has a management contract with its president that requires a lump sum payment of $15 million to be paid upon the completion of the president's first 5 years of service.The company can earn 6.5 percent on its investments and wants to set aside an equal amount of money each year over the next 5 years to fund this obligation.How much money must the firm save each year?

Accepted Answer

$15,000,000 = C{[(1 + 0.065)⁵ - 1] / 0.065} C = $2,634,518.06 11ea6c22_9309_00ed_9716_4b5453bf6fa1_TB1200_00

Question 18

Outreach Funds established a trust that provides $150,000 in scholarships each year forever.The trust fund earns a rate of return of 4.03 percent.How much money was contributed to the fund 20 years ago,assuming that only the interest income is distributed?

Accepted Answer

PV = $150,000 / 0.0403 = $3,722,084.37

Question 19

You are the recipient of an inheritance that will pay you and your heirs $13,000 a year forever.What is this inheritance worth today at a discount rate of 5.85 percent?

Accepted Answer

PV = $13,000 / 0.0585 = $222,222.22

Question 20

Keane just borrowed $38,700 for 5 years at an interest rate of 5.9 percent,compounded monthly.What is the amount of each monthly loan payment?

Accepted Answer

$38,700 = C({1 - 1 / [1 + (0.059 / 12)]^5×12} / (0.059 / 12)) C = $746.38 11ea6c22_9309_7622_9716_7db0d992ce61_TB1200_00

Quiz 4: Discounted Cash Flow Valuation