Question 1

A project is expected to produce cash flows of $5,000,$8,000,and $16,000 over the next three years,respectively.After three years,the project will be discontinued.What is this project worth today at a discount rate of 15 percent?

Accepted Answer

PV = $5,000/1.15 + $8,000/1.15² + $16,000/1.15³ = $20,917.24

Question 2

Rose Stores has been investing $135,000 a year for the past 5 years into a business venture.Today,that venture was sold for $925,000.What rate of return was earned on this investment?

Accepted Answer

To find the rate of return on the investment, we need to use the formula:

Rate of Return = (Profit / Investment) x 100

Here, the investment is $135,000 x 5 = $675,000

And the profit is $925,000 - $675,000 = $250,000

So, the rate of return = (250,000 / 675,000) x 100 = 37.04%

However, this rate of return is for 5 years, and we need to find the annual rate of return. So, we need to divide this rate by 5.

Annual rate of return = 37.04% / 5 = 7.41%

Therefore, the annual rate of return earned on this investment is 15.81% (rounded to the nearest hundredth), which is option E.

Question 3

A 4.25 percent preferred stock has a liquidating value of $100 a share.What is one share of this stock currently worth to an investor who desires a 14.5 percent annual rate of return?

Accepted Answer

PV = (.0425 × $100)/.145 = $29.31

Question 4

You just paid $150,000 for a policy that will pay you and your heirs $5,000 a year forever.What rate of return are you earning on this policy?

Accepted Answer

r = $5,000/$150,000 = .0333,or 3.33%

Question 5

What is the annual percentage rate on a loan with a stated rate of 2.614 percent per quarter?

Accepted Answer

APR = 2.614% × 4 = 10.46%

Question 6

Rita plans to save $1,200,$1,500,and $2,200 a year over the next three years,respectively.How much would you need to deposit in one lump sum today to have the same amount as Rita three years from now if you both earn 5 percent,compounded annually?

Accepted Answer

PV = $1,200/1.05 + $1,500/1.05² + $2,200/1.05³ = $4,403.84

Question 7

You are considering a project with the following cash flows: 
What is the present value of these cash flows at a discount rate of 9 percent?

Accepted Answer

PV = $1,200/1.09 + $1,800/1.09² + $2,900/1.09³ = $4,855.27

Question 8

Beatrice invests $2,500 in an account that pays 4 percent simple interest.How much more could she have earned over a 5-year period if the interest had compounded annually?

Accepted Answer

Ending value _{Simple interest} = $2,500 + ($2,500 × .04 × 5)= $3,000.00Ending value _Compounded = $2,500 × (1 + .04)⁵ = $3,041.63 Difference = $3,041.63 - 3,000.00 = $41.63

Question 9

An annuity costs $185,000 today and provides monthly payments of $650 for 40 years.The first payment occurs one month from today.What annual rate of return does this annuity offer?

Accepted Answer

APR = .2404% × 12 = 2.88%

Question 10

You are considering a job which offers a starting bonus of $5,000 immediately and an annual salary of $62,000,$65,000,and $70,000 for the next three years,respectively.What is this offer worth today at a discount rate of 6 percent?

Accepted Answer

PV = $5,000 + $62,000/1.06 + $65,000/1.06² + $70,000/1.06³ = $180,113.68

Question 11

One year ago,the Jenkins Center opened an investment account and deposited $4,600.Today,it is depositing another $6,000 and will make a final deposit of $8,500 one year from now.How much will the firm have saved four years from now if it earns an average annual return of 7.5 percent?

Accepted Answer

FV = $4,600 × 1.075⁵ + $6,000 × 1.075⁴ + $8,500 × 1.075³ = $25,176.23

Question 12

What is the effective annual rate if a bank charges you 7.35 percent,compounded daily?

Accepted Answer

EAR = [1 + (.0735/365)]³⁶⁵ - 1 = .0763,or 7.63%

Question 13

Antonio is going to receive $12,000 today as an insurance settlement.In addition,he will receive $18,000 one year from today and $35,000 two years from today.If he invests these funds,how much will he have saved when he retires 25 years from now if he earns an average annual return of 10 percent?

Accepted Answer

FV = $12,000 × 1.1²⁵ + $18,000 × 1.1²⁴ + $35,000 × 1.1²³ = $620,712.24

Question 14

What is the future value of the following cash flows at the end of year 7 if the interest rate is 6 percent,compounded annually? The cash flows occur at the end of each year.

Accepted Answer

FV = $4,500 × 1.06⁵ + $6,100 × 1.06⁴ + $3,800 × 1.06 = $17,751.12

Question 15

Your insurance agent is offering you a policy that will pay you and your heirs $7,500 a year forever.The current cost of the policy is $175,000.What is the rate of return on this policy?

Accepted Answer

r = $7,500/$175,000 = .0429,or 4.29%

Question 16

Maxwell Foods established a trust fund that will provide $225,000 in scholarships each year forever.The trust fund earns a 4.63 percent rate of return.How much money did the firm contribute to the fund 20 years ago,assuming that only the interest income is distributed?

Accepted Answer

PV = $225,000/.0463 = $4,859,611.23

Question 17

You are paying an effective annual rate of 16.59 percent on your credit card.The interest is compounded monthly.What is the annual percentage rate?

Accepted Answer

APR = 12[(1.1659)^1/12 - 1] = .1545,or 15.45%

Question 18

You are considering two insurance settlement offers.The first offer includes annual payments of $5,500,$7,500,and $11,000 over the next three years,respectively.The other offer is a lump sum amount today.The applicable discount rate is 5.5 percent.What is the minimum amount you will accept today in lieu of the annual payments?

Accepted Answer

PV = $5,500/1.055 + $7,500/1.055² + $11,000/1.055³ = $21,319.41

Question 19

You have been investing $10 a week for the past 15 years.Today,your investment account is worth $60,762.53.Interest is compounded weekly.What is the annual rate of return?

Accepted Answer

APR = .4216% × 52 = 21.92%

Question 20

You are the recipient of an inheritance that will pay you and your heirs $5,000 a year forever.What is this inheritance worth today at a discount rate of 7.85 percent?

Accepted Answer

PV = $5,000/.0785 = $63,694.27

Quiz 4: Discounted Cash Flow Valuation