# Finance: Price, Salary, Funds, Discounts

1. In 2012, the average vehicle in the US sold for $42,830. In 2002 (10 years earlier) the average selling price was $25,313. What was the annual increase in the selling price over this time period?

a) 3.89 percent

b) 4.20 percent

c) 4.56 percent

d) 5.01 percent - not correct answer

e) 5.40 percent

2. You have taken a new job at a start-up company. You agreed to a modest salary for the first two years, but if the company is successful you will be paid $32,000 bonus at the end of the 2nd year of employment. When you receive it you plan to invest it for 5 more years and conservatively believe you can earn no less than 4.5 percent per year. Based on this assumption, how much money will you have 7 years from now?

a) $39,877.82

b) $41,687.14

c) $44,079.84 - not correct answer

d) $47,908.12

e) $52,002.67

3. You are trying to save to buy a new $45,000 Lexus. You have $28,000 today that can be invested and you believe you can reasonably earn a 5 percent return on funds. How many years will it be before you can drive off in your new Lexus? (assume the price of the vehicle remains constant)

a) 3.55 years

b) 5.68 years

c) 7.98 years - not correct answer

d) 9.72 years

d) 11.29 years

4. You have just received notification that you have won the $600,000 first prize in the Centennial Lottery to be awarded on your 100th birthday which is 70 years from now. However, you have an option to take a lump sum now, which is the discounted present value of the prize. The lottery commission uses a 5% discount rate to determine the present value of your winnings. What is the lump sum you can collect now if not waiting until your 100th birthday?

a) $6,404.20

b) $12,876.50

c) $19,719.70

d) $26,333.33

e) $37,418.69 - not correct answer

5. This morning, Louise opened a savings account that will earn 2.2 percent interest, compounded annually. After five years, her savings account will be worth $5,600. Assume Louise will not make any withdrawals or additional deposits. Given this, which one of the following statements is false?

a) Louise deposited less than $5,600 this morning

b) The present value of Louise's account is less than $5,600 - not correct answer

c) Louise could have deposited less money and still had $5,600 in five years if she could have earned more than 2.2 percent interest

d) Louise would have had to deposit more money to have $5,600 in five years if she were to earn less than 2.2 percent interest

e) Louise will earn an equal dollar amount of interest every year for the next five years

6. Your grandfather just gave you a $10,000 cash gift. You would like to start a new family tradition and have decided to invest this money so that you can gift it to your grandchildren 50 years from now. How much additional money will you have to gift to your grandchildren if you can earn an average of 6.0 percent instead of just 5.5 percent on our savings?

a) $26,486.12

b) $31,592.10

c) $38,781.93

d) $47,239.01 - not correct answer

e) $55,872.98

7. Barnacle Manufacturing, Inc. has an unfunded pension liability of $850 million that must be paid in 25 years. To assess the value of Barnacle's stock, financial analysis want to discount this liability back to its present value. The relevant discount is 6.3 percent. What is the percent value of this liability?

a) $159,803.469

b) $171,834,907

c) $176,067,311 - not correct answer

d) $184,538,639

e) $191,620,445

8. Charles has been purchasing $25,000 worth of liquid ink stock annually for the past 11 years. His holdings are now worth $587,959. What is his annual rate of return on this investment?

a) 14.06 percent

b) 14.18 percent

c) 14.29 percent

d) 14.37 percent

e) 14.68 percent - not correct answer

9. A(n) _________ is an example of a monthly interest rate expressed as an annual rate.

a) stated rate

b) discounted annual rate

c) effective annual rate

d) periodic monthly rate - not correct answer

e) consolidated monthly rate

10. Your broker has offered you two investment options. Each pays 5 percent interest, compounded annually. Option A pays three annual payments of $4,000 each. Option B pays three annual payments starting with $2,000 the first year followed by two annual payments of $5,000 each. Which one of the following statements is correct given these two investment options?

a) Both options are of equal value given that they both provide $12,000 of income

b) Option A has the higher present value at time of investment

c) Option B has the higher present value future value at the end of year three - not correct answer

d) Option A is perpetuity

e) Option B is an annuity

11. Beginning three months from now, you want to be able to withdraw $1,500 each quarter from your bank account to cover college expenses over the next 4 years. The account pays 0.8 percent interest per quarter. How much do you need to have your account today to meet expense needs over the next 4 years?

a) $21,630.44

b) $21,994.06

c) $22,045.26 - not correct answer

d) $22,256.09

e) $22,443.45

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#### Solution Preview

1. In 2012, the average vehicle in the US sold for $42,830. In 2002 (10 years earlier) the average selling price was $25,313. What was the annual increase in the selling price over this time period?

Average price of vehicle in 2002=Po=$25,313

Average price of vehicle in 2012=P=$42,830

Number of periods=n=10

Annual increase in selling price=(P/Po)^(1/n)-1=(42830/25313)^(1/10)-1=5.40%

Correct option is e) 5.40 percent

2. You have taken a new job at a start-up company. You agreed to a modest salary for the first two years, but if the company is successful you will be paid $32,000 bonus at the end of the 2nd year of employment. When you receive it you plan to invest it for 5 more years and conservatively believe you can earn no less than 4.5 percent per year. Based on this assumption, how much money will you have 7 years from now?

Rate of interest, r >=4.5%

Number of periods=n=5

Amount to be invested after 2 years=P2=$32,000

Future Value at the end of seven years from now=P2*(1+r)^n=32000*(1+4.5%)^5=$39,877.82

Minimum Value at the end of 7 years=$39,877.82

3. You are trying to save to buy a new $45,000 Lexus. You have $28,000 today that can be invested and you believe you can reasonably earn a 5 percent return on funds. How many years will it be before you can drive off in your new Lexus? (assume the price of the vehicle remains constant)

Price of a new Lexus=P=$45,000

Current amount=Po=$28,000

Rate of return=r=5%

Number of periods=n=?

We know that

P=Po*(1+r)^n

(1+r)^n=(P/Po)

Taking Ln both sides

n*Ln(1+r)=Ln(P/Po)

n=Ln(P/Po)/Ln(1+r)=Ln(45000/28000)/Ln(1+5%)=9.72 years

Correct option ...

#### Solution Summary

There are 11 questions related to time value of money concepts. Solution to each problem provides adequate support in terms of explanation/calculations.

Finance Problems: Risk Free Rate of Return

Find attached finance problems I appreciate helping and solving in advance.

1. The risk free rate of return is 8 percent; the expected rate of return on the market is 12 percent. Stock X has a beta coefficient of 1.3, an earnings and dividend growth rate of 7 percent, and a current dividend of $2.40. If the stock is selling for $35, what should you do?

2. Presently, Stock A pays a dividend of $2.00 a share, and you expect the dividend to grow rapidly for the next four years at 20 percent. Thus the dividend payments will be:

Year Dividend

1 $1.20

2 1.44

3 1.73

4 2.07

After this initial period of super growth, the rate of increase in the dividend should decline to 8 percent. If you want to earn 12 percent on investments in common stock, what is the maximum you should pay for this stock?

3. You are hurt in a car accident and your lawyer wins a RM100,000 settlement to be distributed as follows:

? RM20,000 immediate payment

? RM5,000 a year for ten years starting now

? RM30,000 after ten years.

If the lawyer's fee is RM10,000, what is the value of this settlement if the interest rate is

10 percent?

4. A state lotto awarded a prize of RM560,000 a year for the next 20 years starting today. If the state sold RM21,900,000 in lotto tickets, what proportion of the sales will the state distribute if it earns 8% annually on invested funds?

5. A firm has a RM1,000,000 debt (e.g., a bond) outstanding that matures after 10 years.

The sinking fund requires the firm to set aside annually an amount so the debt may be

retired at maturity. If the firm can earn 10% annually on these funds, how much must it

invest annually to meet the sinking fund?

Describe the relationship between following variables:

i) future value and interest rate;

ii) future value and time period;

iii) present value and interest rate; and

iv) present value and time period

6. The risk-free rate of return is 8 percent; the expected rate of return on the market is 12

percent. Stock X has a beta coefficient of 1.3, an earnings and dividend-growth rate of 7

percent, and a current dividend of RM2.40. If the stock is selling for RM35, what should

you do?

7. Two stocks each pay a RM1 dividend that is growing annually at 8 percent. Stock A has

a beta of 1.3; stock B's beta is 0.8.

i) Which stock is more volatile?

ii) If treasury bills yield 6 percent and you expect the market to rise by 12 percent, what

is your risk-adjusted required rate of return?

iii) Using the dividend-growth model, what is the maximum amount you would be willing

to pay for each stock?

iv) Why are your valuations different

8. Presently, Stock A pays a dividend of $2.00 a share, and you expect the dividend to

grow rapidly for the next four years at 20 percent. Thus the dividend payments will be:

Year Dividend

1 RM1.20

2 1.44

3 1.73

4 2.07

After this initial period of super growth, the rate of increase in the dividend should decline

to 8 percent. If you want to earn 12 percent on investments in common stock, what is the

maximum you should pay for this stock?

9. As an investor you have a required rate of return of 14 percent for investments in risky

stocks. You have analyzed three risky firms and must decide which (if any) to purchase.

Your information is:

Firm A B C

Current dividends RM1.00 RM3.00 RM7.50

Expected annual growth

rate in dividends 7% 2% (-1%)

Current market price RM23 RM47 RM60

i) What is the maximum price? Which (if any) should you buy?

ii) If you bought Stock A, what is your implied rate of return?

iii) If your required rate of return were 10 percent, what should be the price necessary to

induce you to buy Stock A?

10. What does an inventory turnover of 3.0 suggest? If inventory is sold for cash instead of

on credit, how will this affect the inventory turnover? If a firm's inventory turnover is 4.0

and its receivables turnover is 6.0, how long will it take for the company to generate cash

from the newly acquired inventory?

11. The inventory turnover for an industry is 6 (every two months) but Silauan Cahaya Bhd.

turns over its inventory 4 times a year (every three months). If annual sales are

RM1,000,000 and the interest cost to carry inventory is 12 percent, what is the potential

savings in interest expense if the firm achieves the industry for the turnover of its

inventory?

12. A homeowner has been offered three alternative mortgage loans to finance the purchase of a RM300,000 house. The interest rate on the first alternative is 8 percent for twenty-five years, and the loan requires a 20 percent down payment. The second mortgage loan is also for twenty-five years with an interest rate of 7 percent but requires a down payment of a third of the cost of the house. The third loan also requires a third down but is for 20 years at 6 percent. What are the annual mortgage payments required by each loan?

13. If you purchase a RM5 preferred stock for RM40 a share, what is the current yield? If you anticipate that yields will decline to 10 percent, what will be the anticipated capital gain on this investment?

14. What is the value of a RM1,000 zero coupon government bond that matures after eight years, if comparable yields are 7%?

Reference Book

1. Financial Management-Theory and practice by Eugene F. Brigham, Michael C. ehrhardt 11 Edition.