Exam 2 Practice-Math

You've observed the following returns on Bennington Corporation's stock over the past five years: 11 percent, −10 percent, 19 percent, 18 percent, and 10 percent. What is the arithmetic average, variance, and standard deviation?

this is when you do 2nd 7, enter them in as the "x's", then 2nd 8, xbar is average, variance is the deviation/100^2 average: 7 variance: 0.01496 sd: 12.23

Cavo Corp. has 7 percent coupon bonds making annual payments with a YTM of 6.2 percent. The current yield on these bonds is 6.55 percent. How many years do these bonds have left until they mature?

0.0655=70/P0 so 70/0.0655=1068.70=P0 I/Y=6.2, PV=-1068.70, PMT=70, FV=1000, CPT N=12.64

A stock has an expected return of 14 percent, the risk-free rate is 6 percent, and the market risk premium is 10 percent. What must the beta of this stock be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

14=6+10*Beta so you do 14-6(=8) and solve for beta, which means 8/10= .8

A stock has had returns of 7 percent, 25 percent, 17 percent, −13 percent, 25 percent, and −6 percent over the last six years. What are the arithmetic and geometric average returns for the stock? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

2nd7, input all and enter, 2nd 8, xbar= 9.16 [(1+0.07)(1+0.17)(1-0.13)(1+0.25)(1-0.06)]^(1/6)-1=8.16%

Stuart Software has 12 percent coupon bonds on the market with 16 years to maturity. The bonds make semiannual payments and currently sell for 108.8 percent of par. a. What is the current yield on the bonds? b. What is the YTM of the bonds? c. What is the effective annual yield?

A: (1000*.12)=120 then 1.088*1000=1088, now take 120/1088=.11029 or 11.03% B: N=16*2, PV=-1088, PMT=120/2,FV=1000, CPT I/Y=5.415*2=10.83% C: 2nd 2, NOM=10.83, C/Y=2, CPT EFF=11.12

What are the portfolio weights for a portfolio that has 146 shares of Stock A that sell for $30 per share and 105 shares of Stock B that sell for $22 per share? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .3216.)

A=146*30=4380 and B=105*22=2310 A+B=6690 A/A+B= .6547 B/A+B= .34529

You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.05 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Bp=1.0=1/3(0)+1/3(1.05)+1/3(Bx), when solve for Bx you get 1.95 So it would be one third*1.05 and take that and subtract it from 1 and then multiple by 3.

Suppose a stock had an initial price of $84 per share, paid a dividend of $1.50 per share during the year, and had an ending share price of $92. What was the dividend yield and the capital gains yield? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Dividend yield= 1.50/84=0.0178 or 1.78% Capital yield=92-84/84=0.0952= 9.52%

You have $12,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 11 percent and Stock Y with an expected return of 8 percent. If your goal is to create a portfolio with an expected return of 9.59 percent, how much money will you invest in Stock X and Stock Y? (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.)

E(Rp)=0.0959=.11Xx+.080(1-Xx) Weight of X: .959=.11Xx+.080-.080Xx .0159=0.30Xx so x=.5300 Investment X=.5300(12000)=6360 Dollar amount invested in Y= (1-.5300)(12,000)= 5,640

A stock has an expected return of 11.5 percent, its beta is 1.65, and the expected return on the market is 9.2 percent. What must the risk-free rate be? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected return=risk free rate+(expected return on the market-risk free rate)*beta .115= risk free + (.092 risk free)*1.65 so multiply both by 1.65 and get .115=risk free-1.65*risk free+.1518 And get .0566 or 5.66%

A stock has a beta of 1.30, the expected return on the market is 10 percent, and the risk-free rate is 4.6 percent. What must the expected return on this stock be? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected return=risk free rate+(expected return on the market-risk free rate)*beta so 4.6+(10-4.6)*1.30=11.62

Lei Corporation has bonds on the market with 15.5 years to maturity, a YTM of 6.2 percent, a par value of $1,000, and a current price of $1,039. The bonds make semiannual payments. What must the coupon rate be on these bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

I/Y= 6.2/2=3.1, N=15.5*2=31, PV=-1,039, FV= 1,000, CPT PMT=32.98 Coupon Rate= (2* semi annual)/par value, so (2*32.98)/1,000=0.06595 or 6.60%

Qin Corp. issued 10-year bonds 2 years ago at a coupon rate of 8.1 percent. The bonds make semiannual payments. If these bonds currently sell for 102 percent of par value, what is the YTM

P = $1,020 = $40.50(PVIFAR%,16) + $1,000(PVIFR%,16) Assume $1,000 FV Coupon: (0.081*1,000)/2= 40.5 # of periods: 8*2=16 Price: 1.02 od 1 1000=1020 FV=1,000, PV=-1,020, I/Y=2, PMT=40.5, N=16, CPT I/Y=3.8789*2=7.76

Antiques R Us is a mature manufacturing firm. The company just paid a dividend of $11.40, but management expects to reduce the payout by 5 percent per year indefinitely. If you require a return of 14 percent on this stock, what will you pay for a share today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

P0=D0*(1+g)/(R-g) so P0=11.4*(1-0.05)/[0.14-(-0.05)]=57 or $57

You own a stock portfolio invested 35 percent in Stock Q, 20 percent in Stock R, 30 percent in Stock S, and 15 percent in Stock T. The betas for these four stocks are .77, 1.15, 1.16, and 1.33, respectively. What is the portfolio beta? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Portfolio beta= weighted average of all betas= 0.77*35%+1.15*20%+1.16*30%+1.33*15=1.05

Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company has a bond outstanding with a par value of €1,000, 20 years to maturity, and a coupon rate of 7 percent paid annually. If the yield to maturity is 8.1 percent, what is the current price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Price of the Bond=present value of coupon payments + present value of face value N=20, I/Y=8.1, PMT=(7%*1,000)70, FV=-1000 CPT PV=892.80

Maddon Corporation stock currently sells for $30 per share. The market requires a return of 11.4 percent on the firm's stock. If the company maintains a constant 3.7 percent growth rate in dividends, what was the most recent dividend per share paid on the stock? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Required Return=(D1/Current Price)+Growth Rate or 0.114=(D1/30)+0.037 D1=(0.114-0.037)*30=2.31 NEXT 2.31/1.037=2.23

Douglas, Inc., is expected to maintain a constant 6.8 percent growth rate in its dividend indefinitely. If the company has a dividend yield of 8.6 percent, what is the required return on the company's stock? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Required return on the company's stock=Dividend Yield + Growth Rate so 6.8+8.6=15.4%

The next dividend payment by Zone, Inc., will be $1.92 per share. The dividends are anticipated to maintain a growth rate of 6 percent forever. If the stock currently sells for $38 per share, what is the required return? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Required return=[Next Dividend/Current Stock Price)+Growth Rate = 1.92/38+0.06=0.1105 or 11.05%

Suppose a stock had an initial price of $56 per share, paid a dividend of $1.60 per share during the year, and had an ending share price of $66. Compute the total percentage return. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Total return=(End price-Beg price+Dividends)=(66-56+1.6)=11.6 % total return=(Total return/Beg price)=(11.6/56)=20.71%

Ollie, Inc., has an issue of preferred stock outstanding that pays a dividend of $5.35 every year in perpetuity. If this issue currently sells for $93 per share, what is the required return? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Value of stock=Dividend/Required Rate of Return so Required Rate of Return=Dividend/Value of Stock 5.35/93=0.0575 or 5.75%

You own a portfolio that has $3,900 invested in Stock A and $4,900 invested in Stock B. If the expected returns on these stocks are 11 percent and 14 percent, respectively, what is the expected return on the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

[11%* (3900/3900+4900)]+[14%*(4900/3900+4900)]= 0.04875 + 0.07795 = 0.1267 or 12.67%

The Cricket Co. just paid a dividend of $1.60 per share on its stock. The dividends are expected to grow at a constant rate of 6 percent per year indefinitely. Investors require a return of 10 percent on the company's stock. What is the current stock price, what will it be in 3 years, what will it be in 12 years?

a. What is the current stock price? Current Price=D1/(Required Return - Growth Rate) =(1.6*1.06)/(0.1-0.06)=$42.4 b. What will the stock price be in 3 years? P3=Current Price*(1+Growth Rate)^3 =42.2*(1.06)^3= $50.50 c. What will the stock price be in 12 years? P12=Current Price*(1+Growth Rate)^12 =42.4*)1.06)^12=$85.32

Treasury bills are currently paying 6 percent and the inflation rate is 2.8 percent. a. What is the approximate real rate of interest? b. What is the exact real rate?

a: 6-2.8=3.2% b: =[(1+.06)/(1+.028)]-1=.03113 or 3.11%