Question 1

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 $25 a month for the next 6 months.In keeping with his reputation,he requires that the first payment be paid today.He also charges you 1.65 percent interest per month.How much money are you borrowing?

Accepted Answer

PV_ADue = $25{[1 - 1 / (1.0165)⁶] / 0.0165} × 1.0165 = $144.04 2^nd BGN 2^nd SET 11ea5bb7_de37_c108_8724_7fea38ba720f_TB1005_00

Question 2

Your credit card company quotes you a rate of 17.9 percent,compounded daily.What actual rate of interest you are paying? Assume a 365-day year.

Accepted Answer

EAR = [1 + (0.179 / 365)]³⁶⁵ - 1 = 0.1960,or 19.60% 11ea5bb7_de37_24c0_8724_5f43f13feba0_TB1005_00

Question 3

The Life Trust Co.purchased an investment that will pay $5,000 next year.Every year thereafter,the payment will increase by 1.25 percent.What is the value of this investment if the required rate of return is 8.3 percent?

Accepted Answer

PV_{Growing Perpetuity} = $5,000 / (0.083 - 0.0125)= $70,921.99

Question 4

East Coast Investors invested $28,000 a year into a project for the past 7 years.Today,the project was sold for a net of $324,000.What is the rate of return,ignoring taxes?

Accepted Answer

11ea5bb7_de37_4bd1_8724_2d87236412c4_TB1005_00

Question 5

Today,the Future Trust Co.purchased an investment that will pay $6,000 at the end of 5 years.Every year thereafter,the payment will increase by 1.6 percent.What is the value of this investment today if the required rate of return is 7.4 percent?

Accepted Answer

PV_{Growing Perpetuity Year 4} = $6,000 / (0.074 - 0.016)= $103,448.28 PV = $103,448.28 / (1.074⁴)= $77,751.03

Question 6

You are comparing two annuities with equal present values.The applicable discount rate is 6.65 percent,compounded annually.One annuity pays $4,500 on the first day of each year for 25 years.How much does the second annuity pay each year for 25 years if it pays at the end of each year?

Accepted Answer

Payment = $4,500 × 1.0665 = $4,799.25
Each payment is received 1 year later,so every payment will earn one additional year of interest.

Question 7

Jensen's Shipping wants to expand as soon as it can save $112 million.Towards that goal,the firm started saving 3 years ago and currently has $38.2 million saved.Starting today,the firm will add $15,000 a month to this savings account.The rate of return is 7.1 percent,compounded monthly.How long will it be from now before the company can expand?

Accepted Answer

2^nd BGN 2^nd Set 11ea5bb7_de37_72e4_8724_4dbdba6d365b_TB1005_00 Number of years = 175.20 / 12 = 14.60 years

Question 8

Rodget's is saving $2,500 a month,starting today,and continuing for 4 years.The firm expects to earn 5.6 percent,compounded monthly.If the firm 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 + (.056 / 12)]⁴^×12} / (.056 / 12))× [(1 + (.056 / 12)] = $107,787.25 2^nd BGN 2^nd SET 11ea5bb7_de37_c107_8724_256411bfc6aa_TB1005_00

Question 9

Today,you are retiring.You have a total of $387,419 in your retirement savings and have the funds invested at a guaranteed 3.68 percent,compounded monthly.You want to withdraw $1,500 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 11ea5bb7_de38_5d50_8724_c3a084082fc4_TB1005_00 Number of years = 434.68 / 12 = 36.22 years

Question 10

Walt can afford monthly car payments of $140 for 3 years,starting 1 month from now.The interest rate is 4.6 percent,compounded monthly.How much can he afford to borrow to buy a car?

Accepted Answer

PV = $140({1 - 1 / [1 + (0.046 / 12)]³^×12} / (0.046 / 12))= $4,699.31 11ea5bb7_de37_99f6_8724_fbc5832ea59c_TB1005_00

Question 11

An investment will pay $5,500 every 2 years for the next 40 years.The annual rate of interest is 12 percent.What is the value of this investment at the end of Year 40?

Accepted Answer

2-year rate = 1.12² - 1 = 0.2544,or 25.44% FV = $5,500{[(1.2544)^40/2 - 1] / 0.2544} = $1,990,095.67 11ea5bb7_de38_363f_8724_7bb942b84c23_TB1005_00

Question 12

Suzie just won the lottery! As her prize,she will receive $2,500 a month for 10 years.The first payment will be paid today.At 6 percent,compounded monthly,what is this prize worth to her today?

Accepted Answer

PV = [$2,500({1 - 1 / [1 + (0.06 / 12)]¹⁰^×12} / (0.06 / 12))× [1 + (0.06 / 12)] = $226,309.55 2^nd PMT 2^nd SET 11ea5bb7_de37_99f5_8724_f530c6eb0af3_TB1005_00

Question 13

An investment will pay $1,200 per quarter for 15 years.You require a return of 12 percent,compounded quarterly,for this type of investment.How much is this investment worth to you today?

Accepted Answer

PV = $1,200({1 - 1 / [1 + (0.12 / 4)]¹⁵^×4} / (0.12 / 4)) C = $33,210.68 11ea5bb7_de37_4bd2_8724_7704a85341e1_TB1005_00

Question 14

A bank is loaning $5,000 for 3 years at an interest rate of 7.5 percent.How much additional interest can the bank earn if it compounds interest continuously rather than annually?

Accepted Answer

FV = $5,000 × 1.075³ = $6,211.48 FV = $5,000 × e^0.075×3 = $6,261.61 Difference = $6,261.61 - $6,211.48 = $50.13

Question 15

Your parents have been investing $25 a week for the past 18 years into an account for you.Today,this investment account is worth $60,762.53.Interest is compounded weekly.What is the annual rate of return?

Accepted Answer

11ea5bb7_de37_24bf_8724_13c0b772a477_TB1005_00 APR = 52 × 0.1797% = 9.34%

Question 16

Theo just won a prize that will pay him $10,000 a year for 10 years,starting at the end of Year 10.What is the current value of this prize if the discount rate is 7 percent,compounded annually?

Accepted Answer

PV₉ = $10,000{[1 - (1 / 1.07¹⁰)] / 0.07} = $70,235.82 PV = $70,235.82 / (1.07)⁹ = $38,203.63 11ea5bb7_de37_e819_8724_c9818145e81b_TB1005_00 11ea5bb7_de37_e81a_8724_81ba10691aca_TB1005_00

Question 17

Clint just won a prize that will pay him $15,000 a year for 15 years,starting at the end of Year 5.What is the current value of this prize if the discount rate is 7 percent,compounded annually?

Accepted Answer

PV₉ = $15,000{[1 - (1 / 1.07¹⁵)] / .07} = $136,618.71 PV = $136,618.71 / (1.07)⁴ = $104,225.76 11ea5bb7_de37_e81b_8724_a1d026971d8e_TB1005_00 11ea5bb7_de38_0f2c_8724_cf4461e2c66d_TB1005_00

Question 18

An annuity costs $185,000 today and provides monthly payments of $950 for 40 years.The first payment occurs 1 month from today.What annual rate of return does this annuity offer?

Accepted Answer

11ea5bb7_de36_fdae_8724_f1b509ae3e4e_TB1005_00 APR = 12 × 0.4556% = 5.47%

Question 19

Martha receives $200 on the first of each month.Stewart receives $200 on the last day of each month.Both Martha and Stewart will receive payments for 30 years.The discount rate is 9 percent,compounded monthly.What is the difference in the present value of these two sets of payments?

Accepted Answer

PV_ADue = $200({1 - 1 / [1 + (0.09 / 12)]³⁰^×12} / (0.09 / 12))× [1 + (0.09 / 12)] = $25,042.80 2^nd BGN 2^nd SET 11ea5bb7_de38_0f2d_8724_c90815083b8c_TB1005_00 PV = $200({1 - 1 / [1 + (0.09 / 12)]³⁰^×12} / (0.09 / 12))= $24,856.37 11ea5bb7_de38_363e_8724_c9d91bfdab32_TB1005_00 Difference = $25,042.80 - $24,856.37 = $186.43

Question 20

Angela expects to save $500 a year and earn an average annual return of 5.2 percent.How much will her savings be worth 35 years from now?

Accepted Answer

FV = $500[(1.052³⁵ - 1)/ 0.052] = $47,076.06 11ea5bb7_de37_72e3_8724_f908845b91c0_TB1005_00

Quiz 4: Discounted Cash Flow Valuation