FIN331.101Fall 2010 Exam

Dr. RheeNAME__________________ ID#__________________

1. Which of followings is NOT the characteristics of a perpetuity?

a. A perpetuity continues for a fixed time period.b. Value of a perpetuity can be calculated as “PMT/i”c. In a perpetuity, returns are earned in the form of a series of cash flows.d. A perpetuity is a constant infinite stream of identical cash flows.e. Real estate and preferred stock are effectively perpetuities.Answer: a

2. If a security of $17,200 is worth $20,390 three years in the future and assuming that no withdrawals or deposits are made, what is the implied interest rate that the investor expects to earn on the security?

a. 4.19%b. 5.84%c. 6.78%d. 7.82%e. 8.24%Answer: bN = 3, PV = -17,200, FV = 20,390 ⇨ I = 5.8%

3. You’ve decided to buy a house that is valued at $1 million. You have $500,000 as a down payment on the house and you take out a mortgage for the rest. Your bank is offering you a 30-year standard mortgage at a fixed nominal rate of 9% or a 15-year mortgage at a fixed nominal rate of 9%. How much larger must your monthly payment would be?

a. $1,048.22b. $1,205.45c. $1,519.92d. $1,729.56e. $1,836.69Answer: a30-year: N = 360, I = 9/12, PV = 500,000 ⇨ PMT = $4,023.1115-year: N = 180, I = 9/12, PV = 500,000 ⇨ PMT = $5,071.33Therefore, difference is $1,048.22

4. How long will it take for you to pay off $1,000 charged on your credit card, if you plan to make the minimum payment of $15 per month and the credit card charges 24% per annum?

a. 10 yearsb. 12 yearsc. 15 yearsd. 17 yearse. You may not be able to pay off the debtAnswer: eIf you use a financial calculator, you may get an error message because $15 of monthly payment is too small to pay back $1,000 at 24% per annum. In other words, it takes almost forever to pay back $1,000 at 24% per annum with monthly payment of $15.

5. Which of the following investments would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero.

a. Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments).b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20

payments).c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20

payments).d. Investment D pays $2,500 at the end of 10 years (just one payment).e. Investment E pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).Answer: d

A is smaller than E and B is smaller than C because the money comes in later. A is smaller than B because a larger annuity is received later. So, now the choice comes down to either A or D. Since all of D is received at the end, this is the logical choice. We could also do these calculations to answer the question:

A $1,536.14 EFF% 10.00% 10 250B $1,573.63 NOM% 9.76% 125C $1,650.44 125D $963.86 Smallest 2500E $1,689.76 250

6. Which of the following statements is CORRECT?

a. The cash flows for an ordinary annuity all occur at the beginning of the periods.b. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by

definition an annuity.c. The cash flows for an annuity due must all occur at the beginning of the periods.d. The cash flows for an annuity may vary from period to period, but they must occur at regular intervals,

such as once a year or once a month.e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have

what the textbook defines as a variable annuity.Answer: c

7. You observed an upward-sloping normal yield curve. Which of following statement is the MOST correct?

a. Pure expectation theory must be correct.b. There is a positive maturity risk premium.c. If the pure expectation theory is correct, future (short-term) rates are expected to be higher than current

(short-term) rates.d. Inflation must be expected to change in the future.e. Default risk premium or liquidity premium must be increasing in the future. Answer: c

8. Suppose the interest rate on a 1-year T-bond is 5.0% and that on a 2-year T-bond is 7.0%. Assuming the pure expectations theory is correct, what is the market's forecast for 1-year rates 1 year from now?

a. 7.36%b. 7.75%c. 8.16%d. 8.59%e. 9.04%Answer: e(1 + 0Rn)n = (1 + 0R1) * (1 + 1R2) * (1 + 2R3) * … * (1 + nRn-1) * [1 + E(n-1Rn)](1 + 0R2)2 = (1 + 0R1) * [1 + E(1R2)] ⇨ (1.07)2 = (1.05) * [1 + E(1R2)]

⇨ E(1R2) = (1.07)2 / (1.05) – 1 = 9.04% 9. Assume a scenario in which there is no maturity risk premium (MRP = 0) and the real risk-free rate is

expected to remain constant, and the yield curve is likely to be normal for the next 10 years. Is inflation expected to increase, decrease, or stay the same over the next 10 years? a. Stay the sameb. Decreasec. Increased. Increase at first and then decreasee. None of aboveAnswer: c

10. Crockett Corporation's 5-year bonds yield 6.65%, and 5-year T-bonds yield 4.75%. The real risk-free rate is r* = 3.60%, the default risk premium for Crockett's bonds is DRP = 1.00% versus zero for T-bonds, the liquidity premium on Crockett's bonds is LP = 0.90% versus zero for T-bonds, and the maturity risk premium for all bonds is found with the formula MRP = (t – 1) × 0.1%, where t = number of years to maturity. What inflation premium (IP) is built into 5-year bond yields?

a. 0.68%b. 0.75%c. 0.83%d. 0.91%e. 1.00%Answer: bBasic equation: r = r* + IP + MRP + DRP + LPrCrockett Not needed in this problem 6.35%LP Not needed in this problem 0.90%DRP Not needed in this problem 1.00%rT-bond Required data 4.75%r*Required data 3.60%Years to maturity Required data 5MRP = (t – 1) × (0.1) = 0.40%

IP = rT-bond − r* − MRP 0.75%

11. You have 2 options to buy a membership. One is to pay $5,000 upfront today and the other one is to pay$500 each year starting today. If the prevailing discount rate is 8%, how many years do you remain as a member before the $500 annual payment becomes more expensive than the one-time membership?

a. 14.5 yearsb. 17.5 yearsc. 18.5 yearsd. 19.5 yearse. 21.5 yearsAnswer: bSet it BGN, then I=8, PV=-5000, PMT=500 => N=17.54, 18 after rounding. Alternatively, you can take a difference between the two payment ($4,500), then I=8%, PV=-4500, PMT=500 => N=16.54. Since your membership last for one more year after the current membership fee is paid, your membership ends in 17.54 years.

12. What is the bond contract feature that allows the issuer to redeem bonds under specified terms prior to maturity and when issuers more likely to redeem the outstanding bonds issue?

a. Deferred call, when interest rates are higher than when the bonds are issuedb. Sinking fund provision, when interest rates are higher than when the bonds are issued

c. Indenture, whenever the buyer wants the issuer to redeem the outstanding bondsd. Call provision, when interest rates are lower than when the bonds are issuede. Put provision, when interest rates are lower than when the bonds are issuedAnswer: d

13. Roen is planning to invest in five-year 15% annual coupon bonds with a face value of $1,000 each. Calculate number to fill the blanks in the table and identify which one is the discount bond if the market is at equilibrium.

Bond Discount Rate Bond Value Current YieldBond A 10.00% $1,189.54 (1)Bond B 15.00% (2) 15.00%Bond C (3) $954.58 15.71%

a. 10.00%, $988.76, 14.47%, bond Ab. 11.00%, $1,000.00, 15.71%, bond Bc. 12.61%, $1,000.00, 16.40%, bond Cd. 13.24%, $1,100.00, 16.00%, bond Ae. 14.00%, $1,250.00, 16.40%, bond BAnswer: c(1) CY = Annual Coupon PMT / Price of a Bond = $150 / $1,189.54 = 12.61%(2) Discount rate = coupon rate. Therefore bond value = $1,000(3) N = 5, PV = -954.58, PMT = 150, FV = 1,000 ⇨ I = 16.40%Discount bond = bond C

14. Duff Brewing Co. has 9% annual coupon bonds that are callable and have 18 years left until maturity. The bonds have a par value of $1,000 and their current market price is $1,190.35. However, Duff Brewing Co. may call the bonds in 8 years at a call price of $1,060. What are the YTM and YTC, respectively? Also, if Duff Brewing Co. issues new bonds today, what coupon rate must the bonds to be issued at par?

YTM YTC Coupon Rate a. 6.09%, 5.47%, 6.09%b. 7.09%, 6.47%, 7.09%c. 8.09%, 7.47%, 7.47%d. 8.92%, 8.82%, 8.82%e. 9.23%, 9.32%, 9.32%Answer: bYTM: N = 18, PV = -1,109.35, PMT = 90, FV = 1,000 ⇨ I = 7.09%YTC: N = 18, PV = -1,109.35, PMT = 90, FV = 1,060 ⇨ I = 6.47%The YTM of existing bonds reflects the rate of return required by investors, thus same as current YTM.

15. The following bond list is from the business section of a newspaper on January 1, 2005 (all are semi-annual bonds). Prices are stated relative to the par value of $100. Calculate what number should be in the blank and indicate which bond is trading at premium.

Company Coupon Maturity Last Price Last YieldEST

SpreadUST

(Years)

ESTVolume(1000s)

Schubert, Inc. 8.125%01-01-2015

$82.25 11.11% 6.20 10 72,070

Chapman, Inc.

9.625%01-01-2035

$80.48 12.05% 7.15 30 65,275

Rust, Inc. 4.500%01-01-2010

$95.18 5.62% 1.37 5 59,277

Murphy & 5.375% 01-01- $101.02 5.14% 0.89 5 57,465

Co. 2010

Pickman, Inc. 7.750% 01-01- 2015

$93.11 3.89 10 56,305

Last Price & Last Yield: bond’s price and YTM at the end of trading.EST Spread: bond’s spread above the relevant U.S. Treasury benchmark (percentage).UST: relevant maturity of U.S. Treasury benchmark for each bond.EST Volume: # of bonds traded during the day.

a. 4.40%, Murhpy & Co.b. 6.40%, Rust, Inc.c. 8.80%, Murhpy & Co.d. 10.40%, Pickman, Inc.e. 12.80%, Schubert, Inc.Answer: c

i) Pickman Inc.’s relevant UST maturity is 10 years, which is same as Schubert, Inc.’s maturity. Since EST Spread of Schubert, Inc. is 6.20%, UST yield is 11.11% - 6.20% = 4.91%. Thus, 4.91% + 3.89% (spread of Pickman, Inc.) = 8.80%

ii) N = 20, PV = -93.11, PMT = 3.875, FV = 100 ⇨ I = 4.40 * 2 = 8.80%

16. A 15-year bond with a face value of $1,000 currently sells for $850. Which of the following statements is CORRECT?

a. The bond’s coupon rate exceeds its current yield.b. The bond’s current yield exceeds its yield to maturity.c. The bond’s yield to maturity is greater than its coupon rate.d. The bond’s current yield is equal to its coupon rate.e. If the yield to maturity stays constant until the bond matures, the bond’s price will remain at $850.

Answer: c

17. Taussig Corp.'s bonds currently sell for $1,150. They have a 6.35% annual coupon rate and a 20-year maturity, but they can be called in 5 years at $1,067.50. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. Under these conditions, what rate of return should an investor expect to earn if he or she purchases these bonds?

a. 3.42%b. 3.60%c. 3.79%d. 3.99%e. 4.20%Answer: e

If the coupon rate exceeds the YTM, then it is likely that the bonds will be called and replaced with new, lower coupon bonds. In that case, the YTC will be earned. Otherwise, one should expect to earn the YTM.

If held to maturity: If called:Par value $1,000 Par value $1,000Coupon 6.35% Coupon 6.35%N 20 N 5Price = PV $1,150 PV $1,150PMT = Par × Coupon $63.50 PMT $63.50FV $1,000.00 FV $1,067.50

I/YR = YTM 5.13% I/YR = YTC 4.20%Expected rate of return = YTC if Coupon > YTM (Taussing Corp. is likely to call the bonds. Therefore rate of return is same as YTC). Otherwise, YTM

18. Bill has below portfolio consists of two stocks; Blue Ocean, Inc. and Red Ocean Corp. He invested 75% in Blue Ocean, Inc. and the rest in Red Ocean Corp.

Market Condition Probability Blue Ocean, Inc. Red Ocean Corp.Strong 0.20 38% 53%Normal 0.35 23% 30%Weak 0.45 -30% -38%

Based on the information, calculate expected rate of return of (1) Blue Ocean, Inc., (2) Red Ocean Corp., and (3) portfolio.

a. 1.80%, 2.78%, 1.54%b. 2.15%, 4.00%, 2.61%c. 3.69%, 4.19%, 3.15%d. 4.19%, 5.16%, 3.82%e. 5.16%, 5.49%, 4.42%Answer: b

Blue Ocean, Inc. Read Ocean Corp.Market Condition Probability Blue Ocean, Inc. Read Ocean Corp. Prob * E(r) Prob * E(r)

Strong 0.20 38% 53% 0.076 0.106Normal 0.35 23% 30% 0.0805 0.105Weak 0.45 -30% -38% -0.135 -0.171

2.15% 4.00%sum = E(ri)

Expected Return on Portfolio = sum[w i * E(r i)] = (0.75 * 2.15%) + (0.25 * 4.00%) = 2.61%

19. Below table describes historically realized returns on Towson, Inc.

2005 2006 2007 2008 2009Stock Return 12.50% 8.50% 15.00% 21.00% 6.50%

Calculate (1) average realized return, and coefficient of variation. (Hint: standard deviation is 5.71%)

a. 12.70%, 0.48b. 25.40%, 0.55c. 31.75%, 0.69d. 39.37%, 0.72e. 40.18%, 0.84Answer: a

Average Realized Rate of Return = r=(∑ r t)/n

r=(12.50 %+8.50 %+15.00 %+21.00 %+6.50 %) /5=12.70 %

Standard Deviation

Return Deviation from the Squared Year Average Return Deviation

(1) (2) = (1) - 12.70% (3) = (2)^22005 12.50% -0.20% 0.0004%2006 8.50% -4.20% 0.1764%2007 15.00% 2.30% 0.0529%2008 21.00% 8.30% 0.6889%2009 6.50% -6.20% 0.3844%

Sum 1.3030%Variance 0.0032575Standard Dev. 5.71%

→ sum / (n-1)→ (Variance)^(1/2)

Coefficient of Variation = Standard Deviation / Expected Return = 5.71% / 12% = 0.48

20. Limitless Energy, Inc. is considering to issue 8.8% semi-annual coupon bonds with 15 years to maturity. The bonds are selling at $965.75 with a par value of $1,000. What rate of return are investors expected to earn?

a. 4.61%b. 9.24%c. 9.05%d. 8.79%e. 7.90%Answer: b YTM calculation. N=15*2=30, PV= -965.75, PMT=(0.088*1000)/2, FV=1000 => I=4.62, 4.62*2=9.24%