Question:

The work below is not the work of a tutor. I am submitting these problems for the first time. The work is my own. It is just me, the problems, and my text book. The work that I have completed is in bold. This is to help the tutor distinguish between the problems (not in bold) and my work to solve the problems (in bold). What I need is assurance that I solved these problems correctly in order to assure me that I am understanding this concepts correctly. If I have not solved them correctly, I request help from a tutor because I am unsure if I solved these problems (#1-10) correctly. If I did not, I request a tutor to show me why I am wrong, to show me my error, and to help me learn from that error and solve the problem correctly. I figure if I solve the problem on my own that I would learn instead of simply posting the problem and having a tutor solve it for me. This way of me solving the problem first and having a tutor check my work, the tutor can show me my error and I can better understand the problem, my error, and solve for the correct answer. This enables me to learn and to help me understand if I am actually understanding the concept correctly. If I have mislead with my initial question below, I apologize. Again, this to help me better understand the concepts so that I can learn. Please help. Did I solve the problems correctly?

Subject: Corporate Finance

Topics: #1-7 Capital Markets and the Pricing of Risk

#8-10 Estimating the Cost

1. The figure below shows the one-year return distribution for RCS stock:

RCS Stock ABCDE

Probability (%)1020152530

Return (%)-30-1001030

Note: Make sure to round all intermediate calculations to at least five decimal places

PR =Probability distribution; R= each possible return

Expected (mean) Return = E[R] = R (PR)*R

E[RRCS] = 10%(-0.30) + 20%(-0.10) + 15%(0) + 25%(0.10) + 30%(0.30) = 0.065 = 6.50%

a.The expected return is ___6.50__%. (Round to two decimal places.)

Var (R) = R (PR)* (R - E[R])^2

Variation

Var (RRCS) = 10%(-0.30-0.065)^2 + 20%(-0.10-0.065)^2 + 15%(0-0.065)^2 + 25%(0.10-0.065)^2 + 30%(0.30-0.065)^2

Var (RRCS) = 0.036275

Standard Deviation

SD (R) = square root (Var(R))

SD (R) = square root (0.036275)

SD (R) = .1904599 = 19.05%

b.The standard deviation is _19.05_________%. (Round to two decimal places.)

2.You bought a stock one year ago for $50.77 per share and sold it today for $56.73 per share. It paid a $1.14 per share dividend today.

Divt+1 = 1.14;Pt = 50.77 ;Pt+1 = 56.73;Rt+1 = realized Rate of Return?

Rt+1 = (Divt+1 / Pt) + ([Pt+1 - Pt] / Pt)

Rt+1 = (1.14 / 50.77) + ([56.73 - 50.77] / 50.77)

Rt+1 = 0.13984 = 13.98 %

a.Your realized rate of return was _13.98___%. (Round to two decimal places.)

b.How much of the return came from dividend yield and how much came from capital gain?

Dividend Yield= (Divt+1 / Pt)

= (1.14 / 50.77) = 0.022454 = 2.25%

The return that came from dividend yield is __2.25________%. (Round to two decimal places.)

Capital gain = ([Pt+1 - Pt] / Pt)

= ([56.73 - 50.77] / 50.77) = 0.117392 = 11.74

The return that came from capital gain is ___11.74_______%. (Round to two decimal places.)

3. Using the data in the table below, calculate the return for investing in the stock from January 2, 2003, to January 2, 2004, assuming all dividends are reinvested in the stock immediately.

DatePriceDividend

1/2/03$34.58

2/5/03$30.59$0.22

5/14/03$29.94$0.21

8/13/03$31.24$0.20

11/12/03$38.88$0.18

1/2/04$41.32

The return for the entire period is _22.54_____%. (Round to two decimal places.)

2/5/03:Divt+1 = 0.22;Pt =34.58;Pt+1 = 30.59;Rt+1 = realized Rate of Return?

Rt+1 = [(Divt+1 + Pt+1) / Pt] - 1

Rt+1 = [(0.22 + 30.59) / 34.58]-1 = -.109022 = -10.90%

5/14/03:Divt+1 = 0.21;Pt =30.59;Pt+1 = 29.94;Rt+1 = realized Rate of Return?

Rt+1 = [(Divt+1 + Pt+1) / Pt] - 1

Rt+1 = [(0.21 + 29.94) / 30.59]-1 = -.014383 = -1.44%

8/13/03:Divt+1 = 0.20;Pt =29.94;Pt+1 = 31.24;Rt+1 = realized Rate of Return?

Rt+1 = [(Divt+1 + Pt+1) / Pt] - 1

Rt+1 = [(0.20 + 31.24) / 29.94]-1 = 0.0501002 = 5.01%

11/12/03:Divt+1 = 0.18;Pt =31.24;Pt+1 = 38.88;Rt+1 = realized Rate of Return?

Rt+1 = [(Divt+1 + Pt+1) / Pt] - 1

Rt+1 = [(0.18 + 38.88) / 31.24]-1 = 0.25032 = 25.03%

1/2/04:Divt+1 = 0 ;Pt =38.88;Pt+1 = 41.32;Rt+1 = realized Rate of Return?

Rt+1 = [(Divt+1 + Pt+1) / Pt] - 1

Rt+1 = [(0 + 41.32) / 38.88]-1 = 0.06275 = 6.28%

Realized Annual Return (R annual)

R annual = (1 + Rq1)*(1+Rq2)* (1 + Rq3)*(1+Rq4) - 1

R annual = (1 -.1090)*(1-.0144)* (1 + 0.0501)*(1+0.2503) *(1+0.0628) - 1

R annual = (0.891) (0.9856) (1.0501) (1.2503) (1.0628) - 1

R annual = 1.22539 - 1 = .22539 = 22.54%

4.The last for yours of returns are as follows:

1 3 3 4

-2.4% 28.5% 11.5% 3.9%

Average annual return =

= (1 / T) (R1 + R2 + R3+ R4+RT)

= (1 / 4) (-0.024 + 0.285 + 0.115+ 0.039) = 0.10375 = 10.38

a.The average annual return is __10.38___%. (Round to two decimal places.)

Var(R) = (1/T-1) t (Rt - )^2

Var (R) = (1/4-1) [(-0.024 -.1038)^2 + (0.285 - .1038)^2 + (0.115-.1038)^2+ (0.039-.1038)^2] = (1/3) [0.05349076] = 0.0178302533 = 0.01783

b.The variance of the stock's returns is _0.01783____%. (Round to five decimal places.)

Standard Deviation = SD (R) = square root (Var(R))

SD(R) = square root 0.01783

SD(R) = 0.1335299= 13.35%

c.The standard deviation of the stock's returns is _13.35____%. (Round to two decimal places.)

5. Consider an investment with the following returns over four years:

Year1234

Return19%9%16%13%

CAGR = ([(1+R1)(1+R2)(1+R3)(1+RT)]^(1/T))-1

CAGR = ([(1+.19)(1+.09)(1+.16)(1+0.13)]^(1/4))-1

CAGR = ([(1.19)(1.09)(1.16)(1.13)]^(1/4))-1

CAGR = 0.42505 - 1 = -0.57494 = -57.49

a.The compound annual growth rate (CAGR) for this investment over the four years is -57.49___%. (Round to two decimal places.)

Average annual return =

= (1 / T) (R1 + R2 + R3+ R4+RT)

= (1 / 4) (0.19 + 0.09 + 0.16+ 0.13) = 0.1425= 14.25%

b.The average annual return for this investment over the four years is __14.25____%. (Round to two decimal places.)

c.Which is a better measurement of the investment's performance? If the investment's returns are independent and identically distributed, which is a better measure of the investment's expected return next year?

CAGR / arithmetic average (select one) is a better measurement of the investment's performance while CAGR / arithmetic average (select one) is a better measure of the investment's expected return next year.

6.Consider two local banks. Bank A has 89 loans outstanding; each for $1.0 million that it expects will be repaid today. Each loan has a 5% probability of default, in which case the bank is not repaid anything. The chance of default is independent across all loans. Bank B has only one loan of $89 million outstanding, which it also expects will be repaid today. It also has a 5% probability of not being repaid. Calculate the following:

PR =Probability distribution; R= each possible return

Expected (mean) Return = E[R] = R (PR)*ROR

Expected Payoff = E[Payoff] = payoff (PR)*Payoff

Bank A:E[Payoff] = (0.95) * (89 million) = 84.55

a.The expected payoff of Bank A is $__84.55_____ million. (Round to the nearest million.)

Expected Payoff = E[Payoff] = payoff (PR)*Payoff

Bank B:E[Payoff] = (0.95) * (89 million) = 84.55

b.The expected payoff of Bank B is $__84.55__ million. (Round to the nearest million.)

Var (payoff) = payoff (PR)* (R - E[payoff])^2

Var (payoff) = (.095) * (89 - 84.55)

Var (payoff) =4.2275

SD (payoff) = square root Var (payoff)

SD (payoff) = square root 4.2275 = 2.056088

c.The standard deviation of the overall payoff of Bank A is $_2.0561_million. (Round to four decimal places.)

Var (payoff) = payoff (PR)* (R - E[payoff])^2

Var (payoff) = (.095) * (89 - 84.55)

Var (payoff) =4.2275

SD (payoff) = square root Var (payoff)

SD (payoff) = square root 4.2275 = 2.056088

d.The standard deviation of the overall payoff of Bank B is $_2.0561_ million. (Round to four decimal places.)

7.Suppose the market premium is 4% and the risk-free interest rate is 3%. Using the data in the table below, calculate the expected return of investing in each company's stock.

StarbucksHersheyAutodesk

Beta1.040.192.31

rI= cost of capital (aka expected return); B1=beta;

rI= Risk-free interest rate + (B1 * Market Risk Premium)

Starbucks 0.03 + (1.04 * .04) = 0.0716 = 7.16%

The expected return of Starbuck's stock is _7.16___ %. (Round to two decimal places.)

Hershey's 0.03 + (0.19 * .04) = 0.0376 = 3.76%

The expected return of Hershey's stock is _3.76_ %. (Round to two decimal places.)

Autodesk's 0.03 + (2.31 * .04) = 0.1224 = 12.24%

The expected return of Autodesk's stock is _12.24__ %. (Round to two decimal places.)

Why don't all investors hold Autodesk's stock rather than Hershey's stock?

A.Hershey's stock has less market risk, so investors don't need as high an expected return to hold it.

B.They would if the numbers in the table were reliable. The problem is that they are just estimates, so investors cannot rely on them.

C.Investors make mistakes; nobody should hold Hershey.

D.Investors care about other things besides return; for example, the company's profits.

8.Suppose all possible investment opportunities in the world are limited to the five stocks listed in the table below. What does the market portfolio consist of (what are the portfolio weights)?

Number of Shares

StockPrice/Share($)Outstanding (millions)

A610

B1512

C83

D421

E4320

Enter the percentage that each stock makes up of the total portfolio. (Round to two decimal places.)

Market Value (MV) = (number of shares outstanding) * (price per share)

Portfolio Weights (xi) = MV / total MV

Stock A:MV = 10 * 6 = 60; xi= 60/ 1166 = 0.051457 = 5.15%

Stock B:MV = 12 * 15 = 180; xi = 180 /1166 = 0.154373 = 15.44%

Stock C: MV = 3* 8 = 24;xi = 24 / 1166 = 0.020583 = 2.06%

Stock D:MV = 1 * 42 = 42; xi = 42 / 1166 = 0.036020 = 3.60%

Stock E:MV = 20 * 43 = 860;xi = 860 / 1166 = 0.73756 = 73.76%

Sum = 60 + 180+24+42+860 = 1166

StockPortfolio Weight

A5.15%

B15.44%

C2.06%

D3.60%

E73.76%

9.In June 2009, Cisco Systems had a market capitalization of $135 billion. It had A-rated debt of $5 billion as well as cash and short-term investments of $28 billion, and its estimated equity at the time was 1.18.

Net Debt = Debt - Excess cash and short-term investments;Net debt = 5-28 = -23

Enterprise value= market cap + net debt = 135 -23= 112

a.Cisco's enterprise value is $__112___ billion. (Round to the nearest integer.)

Asset or Unlevered Beta (Bu);Beta equity (BE); Beta debt (BD)

Bu = (E / E+D)(BE) + (D / E+D) (BD)

Bu = (135 / 135-23) (1.18) + (-23 / 135 - 23) (0) = 1.42232

b.Assuming Cisco's debt has a beta of zero, the beta of Cisco's underlying business enterprise is __1.42____. (Round to two decimal places.)

10.Unida Systems has 43 million shares outstanding trading for $9 per share. In addition, Unida has $97 million in outstanding debt. Suppose Unida's equity cost of capital is 17%, its debt cost of capital is 9%, and the corporate tax rate is 33%.

Unlevered Cost of Capital (ru); rE = equity costs of capital;rD = debt costs of capital; E=market capitalization(outstanding shares * market price per share);D=debt

E=43 * 9 = 387 million

ru = (E / E+D)(rE) + (D / E+D)(rD)

ru = (387 / 387 + 97)(.17) + (97 / 387 + 97)(.09)

ru = .153966 = 15.4%

a.Unida's unlevered cost of capital is __15.4%____%. (Round to one decimal place.)

Tc=corporate tax

After-tax debt cost of capital = (rD) (1-Tc)

= (.09) (1-.33) = 0.0603 = 6.03%

b.Unida's after-tax debt cost of capital is ___6.0_______%. (Round to one decimal place.)

rwacc = weighted average cost of capital

rwacc = (E / E+D)(rE) + (D / E+D)(rD)(1-Tc)

=(387 / 387 + 97)(.17) + (97 / 387 + 97)(.09)(1-.33)

=.1359297 + 0.012084917

= .1480146 = 14.8%

c.Unida's weighted average cost of capital is __14.8________%. (Round to one decimal place.)