Finance 301 exam 2

A bond's yield can be

decomposed into inflation premium, maturity risk premium, default risk premium and liquidity risk premium.

Bonds A, B, and C all have a maturity of 10 years and a yield to maturity of 7%. Bond A's price exceeds its par value, Bond B's price equals its par value, and Bond C's price is less than its par value. None of the bonds can be called. Which of the following statements is CORRECT?

f the yield to maturity on each bond increases to 8%, the prices of all three bonds will decline.

The periodic interest rate

i =APR/m

amortized loan

is designed to have equal loan payment each period, with the portion of the payment allocated to the interest gradually decreasing, while the portion allocated to the principal paid gradually increasing

APR

is quoted simple annual percentage rate without compounding

Effective Annual Rate of Interest (EAR)

is the annualized true cost of borrowing/rate of return considering the effect of compounding

m=

is the number of compounding in a year

where i is the

periodic (e.g. monthly) interest rate NOT APR

A bond will sell at__________, that is, above the face value, when its coupon rate is _____________ than the bond yield to maturity

premium(discount)/ greater (smaller)

A semi-annual coupon bond with 10 years to maturity and 10% annual coupon rate. The annual market required interest rate is 8%. Assume the bond's face value is $1000. Based on semiannual compounding, the bond price should be ______

rate=semi-annual market yield=0.08/2 nper=total number of coupons= 10*2 pmt=coupon rate*1000/2 (semi-annual coupon payment) FV= 1000 (face value) =PV(0.08/2,10*2,10%*1000/2,1000,0) = $1135.90

To reach the same future value, the periodic payment in an ordinary annuity needs to be what?

× (1+i) times larger than the payment in an otherwise equivalent annuity due.

Continued with previous question. What is total amount needed on the day she retires?

$1,364,669.41 use PVA due formula: 80,000*(1+3.5%)* (1- 1/1.035^25)/0.035 = 1,364,669.41

Continued with previous question. What is her required annual saving at the end of each year?

$12,046.53 use FVA ordinary annuity to solve for CF 1,364,669= CF* (1.0830 - 1)/0.08 CF= 12,046.53

To be able to afford her desired retirement living, her goal of total saving in 30 years is $

$1364669.41

for a 10-year, 5% APR interest-only loan of $200,000, the annual interest=

$200000 x 5% = $10,000

Continued with previous question. What should be the fair price of the deferred annuity today?

$557,105.65 PV6= 50,000*(1- 1/1.037520)/0.0375=694,810.21 PV0= 694,810.21/1.03756=557,105.65

A 60-year old considers an annuity that will provide $50,000 per year for 20 years. She is willing to wait until 7 years later to receive the first payment. Assume the interest rate is 3.75%. What is the price of the deferred annuity at the year 6, one year before the annuity begins?

$694,810.21 PV6= 50,000*(1- 1/1.037520)/0.0375=694,810.21 PV0= 694,810.21/1.03756=557,105.65

The loan payment is

$C in PVA formula

Both A and B saved $C each year for n years. Suppose the interest rate on their saving is the same. A saved his money at the end of each year and accumulates a total saving of $M in n years. If B saved at the beginning each year, what is B's total saving in n years?

$M*(1+i) B is annuity due so B's FV= M*(1+i)

If the price of an ordinary annuity is _______,the price of an annuity due with the same periodic payment will be ________

$P, $P(1+i)

What's the price of a 4-year bond of $2,250 per year plus an additional $1,550 at the end of Year 4 if the interest rate is 5%?

(2250/0.05)*(1-1/1.054)+1550/1.054=9253.58

Bond's interest rate risk

-All else equal, value of long-term bonds is more sensitive to interest rate changes. -All else equal, value of low-coupon bonds is more sensitive to interest rate changes. -All else equal, bond's re-investment risk is greater for short-term bonds. -All else equal, bond's re-investment risk is greater for high-coupon bonds

The table below shows the CD annual percentage yield offered by four banks: Bank Compounding APY A Annually 5% B Quarterly 5% C Monthly 4.8% D Daily 4.85% Which of the following statements are correct? There are more than one correct.

-Bank A's EAY is the same as its APY 5% because it's annual compounding -Bank D's EAY is 4.969% -Bank C's EAY is 4.907% Calculate EAY for each bank A is annual compounding so EAY=APY=5% B : (1+5%/2)2 -1=5.062% C: (1+4.8%/12)12-1=4.907% D: (1+4.85%/365)365 -1=4.969%

John Deere, an equipment manufacturer, offered buyers a payment choice between the following two: (1)receiving $4,000 off a base price of $88,745 if the buyer pays cash (2) receiving 0 percent financing on a four-year loan and the buyer will pay the base price. That is, the buyer is offer a loan of $88,745 to purchase the equipment today and will repay $88,745 four years later. The buyer should always choose option 1 if ____________________ (multiple answers, choose all correct ones)

-If the buyer has $84,745 cash and an investment opportunity with expected rate of return less than 1.16%. -If the buyer doesn't have $84,745 cash and can get a bank loan with 0.5% interest rate

Consider two equally risky securities. A will provide three payments: $500 now, $800 a year later and $1,000 two years later. B will provide a single payment of $2600 three years from now. The appropriate interest rate is 7.5%. How would you evaluate the two securities? Choose all the right answers.

-You should pay a higher price for A because A's PV of multiple CFs is higher than B's PV of single CF. -If you re-invest it upon receiving A's each payment, the future value of your investment at the end of year 3 will be greater than $2,620.65 A's PV= 500+800/1.075+1000/1.075^2=2109.52 B's PV= 2600/1.075^3=2092.90 A's FV3= 500*1.075^3+1.075^2+1000*1.075=2620.65

Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero

. Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).

Suppose you deposited $8,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months (240 days), assuming each month has 30 days?

8000*(1+5.25%/360)240 =8284.94

Principal paid

= $C - Interest paid

Mary is going to law school in a year. The first year tuition $80,675 is due a year from now. The second and third tuition is $85,300 and $90,225, respectively. Assuming the discount rate is 4% What is the total cost in terms of present value? Do not include thousand separator and $.

=NPV(4%,CF1:CF3)= 236646.46

Your answer to the previous is your financial goal. If you can contribute a constant amount to your investment account and are able to earn 8% on your investment each year for 35 years, how much do you need to contribute to your retirement account at the end of each year to achieve the financial goal? Round your answer to two decimals without thousand separator and $ sign.

=PMT(0.08,35,0,FV,0)=7493.67

If you want your retirement saving be large enough to allow you to withdraw $80,000 at the beginning of each year for 30 year, with 5% annual compounding interest rate, how much saving do you need to have on the day your retire? Rounded your answer to two decimals without thousand separators and $.

=PV(0.05,30,-80000,0,1) =$1291285.89

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual percentage rate of 19.50%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year. What is the effective annual rate on the loan?

EAR= (1+0.195/4)^4 -1=20.97%

EAR formula

EAR= (1+i)m -1 or EAR=(1+APR/m)m -1

You made multiple savings in the past several years. At an interest rate of 5.0%, what is your total amount at the end of year 4? Years: 0 1 2 3 4 Saving $0 $75 $225 $0 $300

FV= 75*1.053 +225*1.052 +300 =635

Which Excel function can allow you to calculate the implied interest rate on a financial asset that is tied to a stream of non-constant payments?

IRR

A 12-year bond has an annual coupon of 9%. The coupon rate will remain fixed until the bond matures. The bond has a yield to maturity of 7%. Which of the following statements is CORRECT?

If market interest rates remain unchanged, the bond's price one year from now will be lower than it is today.

Which of the following are correct? There may be more than one answer.

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the quoted annual percentage rate rate on the deposit (or loan)

A company is expected to generate $50 million cash flow next year and the cash flow is predicted to grow at 5% each year. Assume the required return for the company is 11%. What is the estimated intrinsic value of the company

P= C1/(i-g) = 50/(0.11-0.05)=833.33 The correct answer is: $833.33 million

Which Excel function can you use to compute the bond price?

PV

A Bond has 10 years to maturity and coupon rate of 6.5%. The face value of the bond $1000 and the coupon payment is payable annually. If the current market yield for the bond is 7%, the fair price of the bond is $

Use Excel: PV=(0.07,10,65,1000,0) Use Formula: 65*(1- 1/1.0710)/0.07 +1000/1.0710 =964.88

X and Y are equally risky n-payment annuities, with identical annual payment $C and the same market required interest rate i. The only difference is that X will make the first payment today and Y will make the first payment one year from now. If the market price of X is $P, what should the price of Y?

X is annuity due and Y is ordinary annuity. if the price of X is $P, the price of Y must be $P/(1+i) The correct answer is: $P/(1+i)

A yield curve is

a line that plots the yields of bonds against their maturity for a given quality of bond

If Maria sells the bond, what is her capital gain ?

8.52%

The expected inflation rate is 1.5%. If you earn 7.5% on stocks, what is your rate of return in terms of purchasing power?

1.075/1.015 -1= 5.91%

Assume the average expected annual inflation rate for next 30 years is 2%. A $100,000 income in 30 years in today's purchasing power is

100,000/1.02^30 = 55,207.09

Continued with previous question. A year later, the market yield for the same bond falls by 0.8 percentage point. The bond price at this point should be $

1000

Annual Precentage Rate is 12%, imonthly is....

12%/12 = 1

What Maria's holding period return on the bond?

16.34%

Mr. Smith has $600,000 total retirement saving. Assume he can earn 4.5% on his money and he withdraw $50,000 at the end of each year. How long will it last before he runs out of his saving?

17.64 compute n in the annuity equation 600,000=50,000*(1-1/1.045n)/0.045 n=17.64

What's the rate of return you would earn if you paid $2,880 for a perpetuity that pays $85 per year?

2.95%

You want to quit your job and go back to school for a law degree 4 years from now, and you plan to save $2,100 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. Under these a

2100*1.057*(1.0574-1)/0.057=9667.20

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a PV of $2,600?

2600*0.065=169

You want to buy a new ski boat 2 years from now, and you plan to save $2,900 per year, beginning one year from today. You will deposit your savings in an account that pays 6.2% interest. How much will you have just after you make the 2nd deposit, 2 years from now?

2900*(1.0622-1)/0.062=5,980

Suppose you just won the state lottery, and you have a choice between receiving $3,025,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity?

3,025,000= (250,000/i)*[1-1/(1+i)^20], 5.53%

Suppose you inherited $575,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?

575,000= (CF/0.0825)*(1- 1/1.082520) CF=59,658.76

Maria bought a 20-year, 7.2% annual coupon bond at a market price of $921.45. The face value of te bond is $1,000. What is the bond's yield to maturity?

8%

Suppose your credit card issuer charges an effective annual rate of 26.51%. You must make monthly credit card payments, which amounts to monthly compounding. The bank's nominal quoted annual percentage rate is

APR =[(1+0.2351)1/12 -1]*12=23.75% The correct answer is: 23.75

Which of the following statements is CORRECT?

All else equal, if a bond's yield to maturity increases, its price will fall.

Which of the following descriptions are correct? There are more than one answer.

All else equal, the price of a deferred annuity is lower than an otherwise ordinary annuity that makes the first payment in a year. All other things held constant, the future value of a given annuity increases as the number of compounding periods per year increases.

Interest paid=

Beginning loan balance× i

End-of period loan balance=

Beginning-of-period loan balance - Principal paid for the period

The bond price is inversely related to the

Bond's yeild

You hold an annuity that pays $24,000 at the end of each year for 5 years. The on going interest rate on the annuity is 4.5%. Now you are thinking selling this 5-year annuity and use the proceeds to buy a longer term annuity. Assume the interest rate on the new annuity due is the same and ignore the transaction fees. If you can accept annual payment of $10,306 at the end of each year, how many annual payment can you expect from the longer annuity?

Compute the PV of the annuity: (24000/0.045)*(1-1/1.0455)=105,359.44 Solve n in the new annuity: (10306.29/0.045)*(1-1/1.045n)=105,359.44, n= 14

You hold an annuity that pays $24,000 at the end of each year for 5 years. The on going interest rate on the annuity is 4.5%. Now you are thinking selling this 5-year annuity and use the proceeds to buy a 10-year annuity due. Assume the interest rate on the new annuity due is the same and ignore the transaction fees. What is the annual payment can you expect for the annuity due?

PV of the 5-year annuity= (24000/0.045)*(1-1/1.045^5)=105,359.44 Solve the CF in a 10-year annuity due with the same PV 105,359.44= CF*(1.045/0.045)*(1-1/1.045^10), CF= 12,741.82

What is the price of a deferred annuity with 5 payments of $8,500 that starts 5 years from now and the appropriate interest rate is 4.5%?

PV4= (8500/0.045)*(1-1/1.0455)= 37314.8 PV=37314.8/1.0454=31,290.75

What is the present value of the following cash flow stream at a rate of 11.00%? Year 0 1 2 3 4 $75 $225 $0 $300

PV= 75/1.11+ 225/1.112+ 300/1.114=447.8

Your aunt is about to retire, and she wants to sell some of her stock and buy an annuity that will provide her with income of $78,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost her to buy such an annuity today?

PVA due= (78,000*1.0725/0.0725)*(1-1/1.072530)=944,085.69

Loan balance is the ________ of remaining loan payments

Present Value

You want to accumulate $X in N years. You figure that you will need to save $C at the end of each year to reach the financial goal. If you make the saving at the beginning of each year, what should be your annual saving to accumulate the same amount $X in N years? Assume the interest rate is the same as i.

Start earlier, you can save less: $C/(1+i) The correct answer is: $C/(1+i)

Suppose you want to create a perpetual family trust fund with plan to offer $50,000 each year, beginning 10 years later. Suppose you can lock in a fixed interest rate of 4%. Which of the following statements is NOT correct?

The amount needed 10 years from now is $1,250,000

How to calculate the annual-coupon bond value and semi-annual coupon bond value?

The bond's yield to maturity (that is, the market required interest rate for the bond) is the annualized discount rate in the bond pricing equation.

State of California 10-year zero coupon bond with $1,000 face value was issued two years ago. If the going interest rate on these bonds is 6.6%, the bond is worth

The payment of $1,000 will be made 8 years from now. PV=1000/1.066^8 = 599.71 The correct answer is: 599.71

You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would increase the calculated value of the investment?

The riskiness of the investment decreases

Your friend needs your help for retirement planning. The following information is what you gather from your conversations. She wants to retire at 65. Her financial goal is to save enough money before then, so she can enjoy a living standard of $80,000 a year for 25 years. Her employer provides a 401 account. She will contribute a fixed amount of money each year for 30 years to the account. Currently she has no money in the account and her first contribution will be made in a year. You think an annual expected return of 8% on her retirement saving is reasonable. On the day she retire, she needs to withdraw all the money from the account. You suggest her to retain $80,000 for the first year living expense and use the rest money to buy an annuity, which can pay her $80,000 at the end of each year for the rest 24 years. In other words, the saving should be enough to provide 25 annual payments of $80,000, with the first payment due immediately on the day she retires. The expected interest rate on the annuity is 3.5%. You need to figure out her required annual contribution to 401 account in order to reach her financial goal. Which of the following statements is correct?

The total amount needed for the 25-year retirement period, is also the target future value in 30- year investing period.

Total interest payments=

Total loan payments - Original loan principal

Pure discount loan

the principal and all compounding interest are paid at maturity. Examples: T-bills, zero-coupon bonds.

Interest-only loan

the principal is not paid until maturity

The bond's yield also called

yield to maturity (YTM) is the expected rate of return on the bond assuming investors purchase the bond at the given the market price and hold the bond until maturity.