**Practice Questions for Exam III (Time Value of Money and Valuation and Rates of Return)**

**Chapter 9 – Time Value of Money**

- An amount of money to be received in the future is worth less today than the stated amount.
__TRUE__ - Discounting refers to the growth process that turns $1 today into a greater value several periods in the future.
__FALSE__

- Compounding refers to the growth process that turns $1 today into a greater value several periods in the future.
__TRUE__ - The interest factor for the future value of a single sum is equal to (1 + n)
^{i}.__FALSE__ - The time value of money concept is fundamental to the analysis of cash inflow and outflow decisions covering periods of over one year.
__TRUE__

- The future value is the same concept as the way money grows in a bank account.
__TRUE__ - The present value of a positive future inflow can become negative as discount rates become higher and higher.
__FALSE__

- The formula PV = FV(1 + n)
^{i}will determine the present value of $1.__FALSE__

- The interest factor for the present value of a single amount is the inverse of the future value interest factor.
__TRUE__

- Higher interest rates (discount rates) reduce the present value of amounts to be received in the future.
__TRUE__ - In determining the future value of an annuity, the final payment is not compounded at all.
__TRUE__ - The future value of an annuity assumes that the payments are received at the end of the year and that the last payment does not compound.
__TRUE__ - The amount of annual payments necessary to accumulate a desired total can be found by reference to the present value of an annuity table.
__FALSE__ - If an individual's cost of capital were 10%, he/she would prefer to receive $107 at the end of one year rather than $100 right now.
__FALSE__ - Using semi-annual compounding rather than annual compounding will increase the future value of an annuity.
__TRUE__ - In paying off a mortgage loan, the amount of the periodic payment that goes toward the reduction of principal increases over the life of the mortgage.
__TRUE__ - The time value of money concept becomes less critical as the prime rate increases.
__FALSE__ - Discounted at 6%, $1000 received three years from now is worth less than $800 received today.
__FALSE__

- Discounted at 6%, $1000 received at the end of each year for three years is worth less than $2,700 received today.
__TRUE__

- Under what conditions must a distinction be made between money to be received today and money to be received in the future?

A.A period of recession.When idle money can earn a positive return.__B.__

C. When there is no risk of nonpayment in the future.

D. When current interest rates are different from expected future rates.

- As the compounding rate becomes lower and lower, the future value of inflows approaches

A.0the present value of the inflows__B.__

C. infinity

D. need more information - If you invest $8,000 at 12% interest, how much will you have in 7 years?

A. $18,016$17,688__B.__

C. $3616

D. $80,712

- In determining the future value of a single amount, one measures

A.the future value of periodic payments at a given interest rate.

B. the present value of an amount discounted at a given interest rate.the future value of an amount allowed to grow at a given interest rate.__C.__

D. the present value of periodic payments at a given interest rate.

- The concept of time value of money is important to financial decision making because

A. it emphasizes earning a return on invested capital.

B. it recognizes that earning a return makes $1 worth more today than $1 received in the future.

C. it can be applied to future cash flows in order to compare different streams of income.all of these__D.__

- As the discount rate becomes higher and higher, the present value of inflows approaches
0__A.__

B. minus infinity

C. plus infinity

D. need more information

How much must you invest at 10% interest in order to see your investment grow to $5,000 in 5 years?

A. $3,070

B. $3,415$3,105__C.__

D. none of these

- An annuity may be defined as

A.a payment at a fixed interest rate.

B. a series of payments of unequal amount.

C. a series of yearly payments.a series of consecutive payments of equal amounts.__D.__ - You are to receive $12,000 at the end of 5 years. The available yield on investments is 6%. What is the present value?
- $8,950

B.$9,000$8,967__C.__

D. $8,230 - As the interest rate increases, the present value of an amount to be received at the end of a fixed period

A. increases.decreases.__B.__

C. remains the same.

D. Not enough information to tell.

As the time period until receipt increases, the present value of an amount at a fixed interest ratedecreases.__A.__

B. remains the same.

C. increases.

D. Not enough information to tell.

- To save for her newborn son's college education, Lea Wilson will invest $1,000 at the beginning of each year for the next 18 years. The interest rate is 12 percent. What is the future value?

A.$7,690.

B. $34,931.$63,440.__C.__

D. $55,750.

- The IF for the future value of an annuity is 4.641 at 10% for 4 years. If we wish to accumulate $8,000 by the end of 4 years, how much should the annual payments be?

A.$2,500

B. $2,000$1,724__C.__

D. none of these55. - Mr. Blochirt is creating a college investment fund for his daughter. He will put in $850 per year for the next 15 years and expects to earn an 8% annual rate of return. How much money will his daughter have when she starts college?

A.$11,250

B.$12,263

C. $24,003$23,079__D.__

- Mr. Nailor invests $5,000 in a money market account at his local bank. He receives annual interest of 8% for 7 years. How much return will his investment earn during this time period?

A.$2,915$3,570__B.__

C. $6,254

D. $8,570

- Lou Lewis borrows $10,000 to be repaid over 10 years at 9 percent. Repayment of principal in the first year is:

A. $1,558$658__B.__

C. $742

D. $88536. Sharon Smith will receive $1 million in 50 years. The discount rate is 14%. As an alternative, she can receive $2,000 today. Which should she choose?

A. the $1 million dollars in 50 years.$2,000 today.__B.__

C. she should be indifferent.

D. need more information.

- Pedro Gonzalez will invest $5,000 at the beginning of each year for the next 9 years. The interest rate is 8 percent. What is the future value?

A. $58,471.

B. $62,440.

C. $67,435.$72,435.__D.__

- Ambrin Corp. expects to receive $2,000 per year for 10 years and $3,500 per year for the next 10 years. What is the present value of this 20 year cash flow? Use an 11% discount rate.
$19,033__A.__

B. $27,870

C. $32,389

D. none of these - Dr. J. wants to buy a Dell computer which will cost $2,788 four years from today. He would like to set aside an equal amount at the end of each year in order to accumulate the amount needed. He can earn 7% annual return. How much should he set aside?

A.$697.00$627.93__B.__

C. $823.15

D. $531.81 - Mr. Fish wants to build a house in 10 years. He estimates that the total cost will be $170,000. If he can put aside $10,000 at the end of each year, what rate of return must he earn in order to have the amount needed?
Between 11% and 12%__A.__

B. Between 8% and 9%

C. 17%

D. None of these - The shorter the length of time between a present value and its corresponding future value,

A.the lower the present value, relative to the future value.the higher the present value, relative to the future value.__B.__

C. the higher the interest rate used in the present-valuation.

D. none of these. - A dollar today is worth more than a dollar to be received in the future because

A. risk of nonpayment in the future.the dollar can be invested today and earn interest.__B.__

C. inflation will reduce purchasing power of a future dollar.

D. None of these.

Mr. Darden is selling his house for $165,000. He bought it for $55,000 nine years ago. What is the annual return on his investment?

A. 3%

B. Between 14% and 16%13%__C.__

D. None of these

Increasing the number of periods will increase all of the following except

A. the present value of an annuity.the present value of $1.__B.__

C. the future value of $1.

D. the future value of an annuity.

Joe Nautilus has $120,000 and wants to retire. What return must his money earn so he may receive annual benefits of $20,000 for the next 14 years.

A. 12%

B. Between 12% and 13%14%__C.__

D. Greater than 15%

You will deposit $2,000 today. It will grow for 6 years at 10% interest compounded semiannually. You will then withdraw the funds annually over the next 4 years. The annual interest rate is 8%. Your annual withdrawal will be:

A.$2,340

B. $4,332

C. $797$1,085__D.__

Carol Thomas will pay out $6,000 at the end of the year 2, $8,000 at the end of year 3, and receive $10,000 at the end of year 4. With an interest rate of 13 percent, what is the net value of the payments vs. receipts in today's dollars?

A. $ 7,326.

B. $10,242.

C. $16,372.$ 4,112.__D.__- John Doeber borrowed $125,000 to buy a house. His loan cost was 11% and he promised to repay the loan in 15 equal annual payments. How much are the annual payments?

A.$3,633

B. $9,250

C. $13,113$17,383__D.__ - John Doeber borrowed $125,000 to buy a house. His loan cost was 11% and he promised to repay the loan in 15 equal annual payments. What is the principal outstanding after the first loan payment?
$121,367__A.__

B. $123,088

C. $107,617

D. None of these

- A home buyer signed a 20-year, 8% mortgage for $72,500. How much should the annual loan payments be?

A.$1,584$7,384__B.__

C. $15,555

D. $15,588

- After 20 years, 100 shares of stock originally purchased for $1000 was sold for $5,000. What was the yield on the investment? Choose the closest answer.

A.19%

B. 5%

C. 12%8%__D.__ - The future value of a $1000 investment today at 8 percent annual interest compounded semiannually for 5 years is

A.$1,469$1,480__B.__

C. $1,520

D. $1,555 - Dan would like to save $2,000,000 by the time he retires in 40 years and believes he can earn an annual return of 8%. How much does he need to invest today to achieve his goal?

A. $136,000$92,000__B.__

C. $134,000

D. $625,000

E. $92,060

- Sydney saved $50,000 during her first year of work after college and plans to invest it for her retirement in 40 years. How much will she have available for retirement if she can make 8% on her investment?

A.$596,250

B. $12,953,000

C. $2,345,100$1,086,250__D.__

Luke believes that he can invest $5,000 per year for his retirement in 30 years. How much will he have available for retirement if he can earn 8% on his investment?$566,400__A.__

B. $681,550

C. $150,000

D. $162,000

- Ian would like to save $1,500,000 by the time he retires in 40 years. If he believes that he can achieve a 7% rate of return, how much does he need to deposit each year to achieve his goal?

A.$9,692

B. $37,500

C. $5,790$7,514__D.__

Jeff believes he will need $60,000 annual income during retirement. If he can achieve a 5% return during retirement and believes he will live 30 years after retirement, how much does he need to save by the time he retires?

A.$1,029,540

B. $3,986,340$922,320__C.__

D. $259,320

If Allison has saved $1,000,000 upon retirement, how much can she live on each year if she can earn 5% per year and will end with $0 when she expects to die 25 years after retirement?

A. $295,334

B. $20,953

C. $371,885$70,952__D.__

- Kathy has $60,000 to invest today and would like to determine whether it is realistic for her to achieve her goal of buying a home for $150,000 in 10 years with this investment. What return must she achieve in order to buy her home in 10 years?

A.between 7% and 8%

B. between 8% and 9%between 9% and 10%__C.__

D. between 10% and 11%

If Gerry makes a deposit of $1,500 at the end of each quarter for 5 years, how much will he have at the end of the 5 years assuming a 12% annual return and quarterly compounding?$40,305__A.__

B. $30,000

C. $108,078

D. $161,220

- Sara would like to evaluate the performance of her portfolio over the past 5 years. What compound annual rate of return has she achieved is she invested $12,000 5 years ago and now has $25,000?

A.between 8% and 9%

B. between 10% and 11%

C. between 13% and 14%between 15% and 16%__D.__

**Chapter 10 – Valuation and Rates of Return**

- The valuation of a financial asset is based on the concept of determining the present value of future cash flows.
__TRUE__ - The prices of financial assets are based on the expected value of future cash flows, discount rate, and past dividends.
__FALSE__ - The discount rate depends on the market's perceived level of risk associated with an individual security.
__TRUE__ - By using different discount rates, the market allocates capital to companies based on their risk, efficiency, and expected returns.
__TRUE__ - The price of a bond is equal to the present value of all future interest payments added to the present value of the principal.
__TRUE__ - An increase in yield to maturity would be associated with an increase in the price of a bond.
__FALSE__ - You hold a long-term bond yielding ten percent. If interest rates fall shortly before you sell the bond, you will sell at a higher price than if interest rates had been constant.
__TRUE__ - The appropriate discount rate for bonds is called the yield to maturity.
__TRUE__

- The total required real rate of return is equal to the real rate of return plus the inflation premium.
__FALSE__

The required rate of return is payment demanded by the investor for foregoing present consumption.__TRUE__

- The inflation premium is based on past and current inflation levels.
__FALSE__

- The risk-free rate of return is equal to the inflation premium plus the real rate of return.
__TRUE__ - The risk premium is equal to the required yield to maturity minus both the real rate of return and the inflation premium.
__TRUE__

- Business risk relates to the inability of the firm to meet its debt obligations as they come due.
__FALSE__

Risk premiums are higher for riskier securities, but the risk premium cannot be higher than the required return.__TRUE__

High-risk corporate bonds are as risky as junk bonds.__TRUE__

- When inflation rises, bond prices fall.
__TRUE__

- An increase in inflation will cause a bond's required return to rise.
__TRUE__

- The higher the yield to maturity on a bond, the closer to par the bond will trade.
__FALSE__

- The longer the maturity of a bond, the greater the impact on price to changes in market interest rates.
__TRUE__

- The further the yield to maturity of a bond moves away from the bond's coupon rate the greater the price-change effect will be.
__TRUE__

- When inflation rises, preferred stock prices fall.
__TRUE__

- The variable growth model is useful for firms in emerging industries.
__TRUE__

- The value of a share of stock is the present value of the expected stream of future dividends.
__TRUE__

- Valuation of a common stock with no dividend growth potential is treated in the same manner as preferred stock.
__TRUE__

- Firms with an expectation for great potential tend to trade at low P/E ratios.
__FALSE__ - The price-earnings ratio is another tool used to measure the value of common stock.
__TRUE__

- Firm's with bright expectations for the future, tend to trade at high P/E ratios.
__TRUE__ - The fact that small businesses are usually illiquid does not affect their valuation process.
__FALSE__ - Valuation of financial assets requires knowledge of

A.future cash flows.

B. appropriate discount rate.

C. past asset performance.a and b.__D.__

- The market allocates capital to companies based on

A.risk.

B. efficiency.

C. expected returns.all of these__D.__

- In a general sense, the value of any asset is the

A.value of the dividends received from the asset.present value of the cash flows received from the asset.__B.__

C. value of past dividends and price increases for the asset.

D. future value of the expected earnings discounted by the asset's cost of capital.

- Which of the following financial assets is likely to have the highest required rate of return based on risk?

A.Corporate bond.

B. Treasury bill.

C. Certificate of Deposit.Common stock.__D.__

- A bond which has a yield to maturity greater than its coupon interest rate will sell for a price
below par.__A.__

B. at par.

C. above par.

D. what is equal to the face value of the bond plus the value of all interest payments.

- Which of the following is not one of the components that makes up the required rate of return on a bond?

A.risk premium

B. real rate of return

C. inflation premiummaturity payment__D.__

- A 20-year bond pays 12% on a face value of $1,000. If similar bonds are currently yielding 9%, What is the market value of the bond?

A.over $1,000

B. under $1,000over $1,200__C.__

D. not enough information given to tell

- A ten-year bond, with par value equals $1000, pays 10% annually. If similar bonds are currently yielding 6% annually, what is the market value of the bond? Use semi-annual analysis.

A.$1000.00

B. $1127.50$1297.85__C.__

D. $2549.85

- A 30-year zero-coupon bond that yields 12% percent is issued with a $1000 par value. What is the issuance price of the bond (round to the nearest dollar)?
$33__A.__

B. $83

C. $8333

D. $none of these

- A 14-year zero-coupon bond was issued with a $1000 par value to yield 12%. What is the approximate market value of the bond?

A.$597$205__B.__

C. $275

D. $482

- Which of the following does not influence the yield to maturity for a security?

A. required real rate of return

B. risk free rate

C. business riskhistoric yields__D.__

- An increase in the riskiness of a particular security would NOT affect

A.the risk premium for that security.the premium for expected inflation.__B.__

C. the total required return for the security.

D. investors' willingness to buy the security.

If the inflation premium for a bond goes up, the price of the bond

A.is unaffected.goes down.__B.__

C. goes up.

D. need more information.

- If the yield to maturity on a bond is greater than the coupon rate, you can assume:

A.interest rates have decreasedthe price is below the par__B.__

C. the price is above the par

D. risk premiums have decreased

- The risk premium is likely to be highest for

A.U.S. government bonds.

B. corporate bonds.utility company stock.__C.__

D. either b or c.

- The return measure that an investor demands for giving up current use of funds, without adjusting for purchasing power changes or the real rate of return, is the
risk premium.__A.__

B. inflation premium.

C. dividend yield.

D. discount rate.

- A ten-year bond pays 11% interest on a $1000 face value annually. If it currently sells for $1,195, what is its approximate yield to maturity?

A. 9.33%

B. 7.94%

C. 12.66%8.10%__D.__

- The relationship between a bond's price and the yield to maturity

A.changes at a constant level for each percentage change of yield to maturity.is an inverse relationship.__B.__

C. is a linear relationship.

D. a and b. - The longer the time to maturity:

A. the greater the price increase from an increase in interest rates.

B. the less the price increase from an increase in interest rates.the greater the price increase from a decrease in interest rates.__C.__

D. the less the price decrease from a decrease in interest rates.

- What is the approximate yield to maturity for a seven-year bond that pays 11% interest on a $1000 face value annually if the bond sells for $952

A.10.5%

B. 10.6%

C. 11.5%12.1%__D.__

A higher interest rate (discount rate) would

A. reduce the price of corporate bonds.

B. reduce the price of preferred stock.

C. reduce the price of common stock.all of these.__D.__- A 15-year bond pays 11% on a face value of $1,000. If similar bonds are currently yielding 8%, what is the market value of the bond?

A.Over $1,000

B. Under $1,000Over $1,200__C.__

D. Not enough information to tell - A 10-year bond pays 8% on a face value of $1,000. If similar bonds are currently yielding 10%, what is the market value of the bond?
Less than $900__A.__

B. More than $900 and less than $1100

C. More than $1100

D. Not enough information to tell - An issue of preferred stock is paying an annual dividend of $5. The growth rate for the firm's common stock is 14%. What is the preferred stock price if the required rate of return is 11%?
$45.45__A.__

B. $41.67

C. $35.71

D. none of these

- Which is a characteristic of the price of preferred stock?

A.Since preferred stock dividends are fixed, they are tax deductible.

B. Because preferred stock has no maturity, the price analysis is similar to that of debt.Preferred stock is valued as a perpetuity.__C.__

D. None of these. - Preferred stock has all but which of the following characteristics?

A.no stated maturity

B. a fixed dividend payment that carries a higher precedence than common stock dividendsthe same binding contractual obligation as debt__C.__

D. preferred lacks the ownership privilege of common stock - The price of preferred stock may react strongly to a change in k
_{p }because

A. preferred stock may be cumulative.

B. preferred stock dividends have to be paid before common stock dividends.there is no maturity date.__C.__

D. corporate recipients of preferred stock dividends may receive a partial tax exemption.

- The growth rate for the firm's common stock is 7%. The firm's preferred stock is paying an annual dividend of $5. What is the preferred stock price if the required rate of return is 8%?

A. $5$62.5__B.__

C. $500

D. none of these

- Will an increase in inflation have a larger impact on the price of a bond or preferred stock?

A.The bond.The preferred stock.__B.__

C. The impact will be the same.

D. There is not enough information to determine the relative impact.

- The dividend valuation model stresses the

A.importance of earnings per share.

B. importance of dividends and legal rules for maximum payment.relationship of dividends to market prices.__C.__

D. relationship of dividends to earnings per share.

- A common stock which pays a constant dividend can be valued as if it were

A.corporate bond.

B. stock paying a growing dividend.preferred stock.__C.__

D. discount bond.

- The dividend on preferred stock is most similar to:
common stock with no growth in dividends.__A.__

B. common stock with constant growth in dividends.

C. common stock with variable growth in dividends.

D. certificate of Deposit. - An issue of common stock's most recent dividend is $3.75. Its growth rate is 8%. What is its price if the market's rate of return is 16%?

A. $25.01

B. $46.88$50.63__C.__

D. none of these

An issue of common stock is selling for $57.20. The year-end dividend is expected to be $2.32 assuming a constant growth rate of 6%. What is the required rate of return?

A.10.3%10.1%__B.__

C. 4.1%

D. none of these

- An issue of common stock is expected to pay a dividend of $4.80 at the end of the year. Its growth rate is equal to 8%. If the required rate of return is 13%, what is its current price?

A.$103.68

B. $36.92$96.00__C.__

D. none of these

- If expected dividends grow at 8% and the appropriate discount rate is 12%, what is the value of a stock with an expected dividend of $2.33?

A.$62.88

B. $19.41

C. $29.12$58.25__D.__

- Stock valuation models are dependent upon
expected dividends, future dividend growth and an appropriate discount rate.__A.__

B. past dividends, flotation costs and bond yields.

C. historical dividends, historical growth and an appropriate discount rate.

D. all of these.

- If a company's stock price (Po) goes up, and nothing else changes, Ke (the required rate of return) should

A. go up.go down.__B.__

C. remain unchanged.

D. need more information. - An issue of common stock has just paid a dividend of $4.00. Its growth rate is equal to 8%. If the required rate of return is 13%, what is its current price?

A. $19.04

B. $80$86.40__C.__

D. none of these

An issue of common stock is expected to pay a dividend of $4 at the end of the year. Its growth rate is equal to 3%, and the current share price is $40. What is the required rate of return on the stock?

A.between 7% and 10%

B. between 10% and 12%between 12% and 14%__C.__

D. between 14% and 17%

- The cost of capital for common stock is k
_{e}= (D_{1}/P_{o}) + g. What are the assumptions of the model?

A.Growth (g) is constant to infinity.

B. The price earnings ratio stays the same.

C. The firm must pay a dividend to use this model.All of these are assumptions of the model.__D.__

- Required return by investors is directly influenced by all of the following except:

A.Inflation

B. U.S. Treasury ratesDividends__C.__

D. Risk

- The market allocates capital to firms based on all of the following except:
Higher risk requires lower returns due to higher expectations__A.__

B. Level of efficiency

C. Expected returns

D. Degree of past performance

- Market Enterprises would like to issue bonds and needs to determine the approximate rate they would need to pay investors. A firm with similar risk recently issued bonds with the following current features a 7% coupon rate, 20 years until maturity, and a current price of $1,150. At what rate would Market Enterprises expect to issue their bonds, assuming annual interest payments?
5.7%__A.__

B. 5.9%

C. 7%

D. 7.1%

- Star Corp. issued bonds 2 years ago with a 9% coupon rate. Their bonds are currently trading for $928 in the market. Which of the following most likely has occurred since the time of issue?

A.Interest rates decreasedInflation increased__B.__

C. Risk decreased

D. Real rates of return decreased

- Doug has been approached by his broker to purchase a bond for $850. He believes the bond should yield 10%. The bond pays 7% annual coupon rate and has 12 years left until maturity. What should Doug's analysis of the bond indicate to him?

A.The bond is undervalued, purchase

B. The bond is undervalued, do not purchase

C. The bond is overvalued, purchaseThe bond is overvalued, do not purchase__D.__

- Which of the following regarding preferred stock is true?

A.If the price decreases, required rate of return has decreasedIf the required rate of return increases, the price decreases__B.__

C. If the required rate of return increases, the price increases

D. The price in the market remains at par

**End of the chapter problems**

**Chapter 9**

9.2. What is the present value of:

*a*. $9,000 in 7 years at 8 percent?*b*. $20,000 in 5 years at 10 percent?*c*. $10,000 in 25 years at 6 percent?*d*. $1,000 in 50 years at 16 percent?

**Solution**

- $5,247 [ FV=9000; N=7; I=8; PMT=0; PV=?=5247]
- $12,420
- $2,330
- $1

9.4 If you invest $9,000 today, how much will you have:

*a*. In 2 years at 9 percent?*b*. In 7 years at 12 percent?*c*. In 25 years at 14 percent?*d*. In 25 years at 14 percent (compounded semiannually)?

- $ 10,692 [PV=-9000; N=2; I=9; PMT=0; FV=?=10,692]
- $ 19,899
- $238,158
- $265,113 (7%, 50 periods)

- 14. Carrie Tune will receive $19,500 for the next 20 years as a payment for a new song she has written. If a 10 percent rate is applied, should she be willing to sell out her future rights now for $160,000?

No, the present value of the annuity is worth more than $160,000.

9.23. Juan Garza invested $20,000 10 years ago at 12 percent, compounded quarterly. How much has he accumulated?

$65,240

- 24. Determine the amount of money in a savings account at the end of five years, given an initial deposit of $5,000 and a 12 percent annual interest rate when interest is compounded (
*a*) annually, (*b*) semiannually, and (*c*) quarterly.

- $8,810 (12%, 5 periods)
- $8,955 (6%, 10 periods)
- $5,000 (3%, 20 periods)

9.41. If your uncle borrows $60,000 from the bank at 10 percent interest over the seven-year life of the loan, what equal annual payments must be made to discharge the loan, plus pay the bank its required rate of interest (round to the nearest dollar)? How much of his first payment will be applied to interest? To principal? How much of his second payment will be applied to each?

FV = 0; PV = 60,000; I/Y = 10; N = 7; PMT = ? = 12,325

So, yearly you are paying 12, 325 which include both interest and principal.

First payment:

$60,000 × .10 = $6,000 interest

$12,325 – $6,000 = $6,325 applied to principal

Second payment:

First determine remaining principal and then the interest and principal payment.

$60,000 – $6,325 = $53,675 remaining principal

$53,675 × .10 = $ 5,368 interest

$12,325 – $5,368 = $ 6,957 applied to principal

**Chapter 10**

10.5. Harrison Ford Auto Company has a $ 1,000 par value bond outstanding that pays

11 percent interest. The current yield to maturity on each bond in the market is

8 percent. Compute the price of these bonds for these maturity dates:

*a*. 30 years.*b*. 15 years.*c*. 1 year.

**Solution**

- 30 years to maturity

FV = 1000; PMT = 110; N = 30; I/Y = 8; PV = ? = $1,338

- 15 years to maturity

FV = 1000; PMT = 110; N = 15; I/Y = 8; PV = ? = $1,257

- 1 year maturity

Answer: $ 1,028 (N = 1)

- 12. Tom Cruise Lines, Inc., issued bonds five years ago at $1,000 per bond. These bonds had a 25-year life when issued and the annual interest payment was then

12 percent. This return was in line with the required returns by bondholders at that point as described below:

Real rate of return........... 3%

Inflation premium........... 5

Risk premium.................. __ 4__

Total return.................. 12%

Assume that five years later the inflation premium is only 3 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds.

The bonds have 20 years remaining until maturity. Compute the new price of

the bond.

First compute the new required rate of return (yield to maturity).

Real rate of return 3%

Inflation premium 3

Risk premium __ 4__

Total return 10%

Now, FV = 1,000; I/Y = 10; N = 20; PMT = 120; PV = ? = $1,170.

- 14. Good News Razor Co. issued bonds 10 years ago at $1,000 per bond. These bonds had a 40 year life when issued and the annual interest payment was then 12 percent. This return was in line with the required returns by bondholders at that point in time as described below:

Real rate of return........... 2%

Inflation premium........... 4

Risk premium.................. __ 5__

Total return.................. 11%

Assume that 10 years later, due to favorable publicity, the risk premium is now

3 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 30 years remaining until maturity. Compute the new price of the bond.

**Solution**

First compute the new required rate of return (yield to maturity)

Real rate of return 2%

Inflation premium 4%

Risk premium __3%__

N = 30; I/Y = 9; PMT = 120; FV = 1000; PV = ? = $1,308.

- 17. Bonds issued by the Crane Optical Company have a par value of $1,000, which

is also the amount of principal to be paid at maturity. The bonds are currently selling for $850. They have 10 years remaining to maturity. The annual interest payment is 9 percent ($90).

**Solution**

PV = -850; N = 10; PMT = 90; FV = 1,000; I/Y = ? = 11.61%

- 18. Bonds issued by the West Motel Chain have a par value of $1,000, are selling

for $1,100, and have 20 years remaining to maturity. The annual interest payment

is 13.5 percent ($135).

**Solution**

PV = -1,100; N = 20; PMT = 135; FV = 1,000; I/Y = 12.15%

- 20. Robert Brown III is considering a bond investment in Southwest Technology Company. The $1,000 bonds have a quoted annual interest rate of 8 percent and the interest is paid semiannually. The yield to maturity on the bonds is 10 percent annual interest. There are 25 years to maturity. Compute the price of the bonds based on semiannual analysis.

**Solution**

N = 25x2=50; PMT = 80/2=40; FV = 1,000; I/Y = 10/2=5; PV = ? = 817.44

- 22. The preferred stock of Ultra Corporation pays an annual dividend of $6.30. It has a required rate of return of 9 percent. Compute the price of the preferred stock.

- 23. North Pole Cruise Lines issued preferred stock many years ago. It carries a fixed dividend of $6 per share. With the passage of time, yields have soared from the original 6 percent to 14 percent (yield is the same as required rate of return).
*a*. What was the original issue price?*b*. What is the current value of this preferred stock?*c*. If the yield on the Standard & Poor’s Preferred Stock Index declines, how will the price of the preferred stock be affected?

- Original price
- Current value
- The price of preferred stock will increase as yields decline. Since preferred stock is a fixed income security, its price is inversely related to yields as would be true with bond prices. The present value of an income stream has a higher present value as the discount rate declines, and a lower present value as the discount rate increases.

- 24. Venus Sportswear Corporation has preferred stock outstanding that pays an annual dividend of $12. It has a price of $110. What is the required rate of return (yield)

on the preferred stock?

- 25. Analogue Technology has preferred stock outstanding that pays a $9 annual dividend. It has a price of $76. What is the required rate of return (yield) on the preferred stock?

- 26. Static Electric Co. currently pays a $2.10 annual cash dividend (D
_{0}). It plans to maintain the dividend at this level for the foreseeable future as no future growth

is anticipated. If the required rate of return by common stockholders (K_{e}) is

12 percent, what is the price of the common stock?

- 27. BioScience, Inc., will pay a common stock dividend of $3.20 at the end of the year (D
_{1}). The required return on common stock (K_{e}) is 14 percent. The firm has a constant growth rate (g) of 9 percent. Compute the current price of the stock (P_{0}).

- 28. Friedman Steel Company will pay a dividend of $1.50 per share in the next

12 months (D_{1}). The required rate of return (K_{e}) is 10 percent and the constant growth rate is 5 percent. *a*. Compute P_{0}.

*(For parts b, c, and d in this problem all variables remain the same except the one specifically changed. Each question is independent of the others.)*

*b*. Assume K_{e}, the required rate of return, goes up to 12 percent; what will be the new value of P_{0}?*c*. Assume the growth rate (g) goes up to 7 percent; what will be the new value

of P_{0}?*d*. Assume D_{1}is $2, what will be the new value of P_{0}?

- 29. Maxwell Communications paid a dividend of $3 last year. Over the next 12 months, the dividend is expected to grow at 8 percent, which is the constant growth rate for the firm (g). The new dividend after 12 months will represent D
_{1}. The required rate of return (K_{e}) is 14 percent. Compute the price of the stock (P_{0}).

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