1. Sustainability - Flervalsfråga Which one of the following statements is TRUE? Select one alternative:

Energy efficient company stocks commonly have a lower beta value compared to less energy efficient companies.

1, Imposing carbon taxes is a way to internalize cost of environmental issues.

2, Negative screening means that the investor excludes companies that do not meet certain pre-set criteria.

3, Impact investing means that the investor combines sustainability- and financial goals.

4, All statements are true

2. Risk and return - Flervalsfråga

Which of the following statements is FALSE? Select one alternative:

Well-diversified portfolios display market risk.

Well-diversified portfolios display high firm-specific risk.

Efficient portfolios have the highest Sharpe ratio.

Efficient portfolios are portfolios earning the highest expected return for a given standard deviation.

Individual stocks display firm-specific risk.

3. CAPM - Flervalsfråga

Which one of the following statements is FALSE in an economy where CAPM holds? 

Select one alternative:

The beta of the market portfolio does not have to be the largest of all betas

The beta of a risky asset cannot be negative

Risky assets may earn an expected return higher than the one of the market portfolio

The beta of a risky asset can be greater than one

The tangency portfolio has a beta equal to one

4. Portfolio theory and risk - Flervalsfråga

Which one of the following statements is FALSE?

Select one alternative:

The variance of the return of the risk-free asset is equal to zero

Because the return of the risk-free asset is fixed, its correlation with the market portfolio is equal to -1.

It is possible to build a portfolio of two risky assets whose return has a variance equal to zero if the correlation between the return of its components is equal to minus one

Short-selling the risk-free asset is equivalent to borrowing money at the risk-free rate through a standard loan

None of the other answers are correct. (This answer should be chosen if you consider that all the other statements are true).

5. Options - Flervalsfråga

Which one of the following statements is FALSE?

Select one alternative:

The higher the strike of a put option, the more valuable it is

The lower the strike of a call option, the more valuable it is

Put options give their holder the right to sell the underlying at a given price at a future point in time

Call options give their holder the right to purchase the underlying at a given price at a future point in time

An American-style option can only be exercised at its maturity.

6. Miscellaneous - Flervalsfråga

Which one of the following statements is FALSE?

Select one alternative:

1. The present value of a growing annuity can be computed even if the discount rate to be used is equal to its growth rate

2. An invesment project may not have Internal Rate of Return

3. There are special situations when the NPV rule may lead to the wrong investment decision

4. None of the other alternatives is correct (this answer is to be chosen if all other answers are considered to be correct)

5. The tangency portfolio is the portfolio of risky assets only with the lowest Sharpe ratio.

7. In serach of an efficient portfolio - Essä

Your portfolio consists of a full investment in just one stock, Eriksson. Suppose this stock has an expected return of 18% and volatility of 31%. Suppose further that the tangency portfolio has an expected return of 16% and a volatility of 22%. Also, assume that the risk-free rate is 5%. What is the highest possible expected return of an alternative investment that has the same volatility as your investment in Eriksson?

You need to explain how you got to your final answer in order to get points for this question. JUST TYPING THE FINAL ANSWERS WILL GIVE YOU ZERO POINTS. TYPE YOUR ANSWER AND EXPLANATIONS ON THE SPACE PROVIDED BELOW. (Express the expected return as a percentage and round your final answer to two decimal digits)

To find the highest possible expected return of an alternative investment that has the same volatility as the investment in Eriksson, we need to look for a portfolio that lies on the CML (Capital Market Line) with the same volatility as Eriksson's stock.

The CML represents the efficient portfolios that offer the highest expected return for a given level of risk (volatility), combining the risk-free asset with the tangency portfolio (market portfolio). The equation for the CML is as follows:

E(r) = rf + (vs * (Erp) - rf) /Vtp

Given data:

Expected Return of Eriksson stock (ER_Eriksson) = 18%

Volatility of Eriksson stock (σ_Eriksson) = 31%

Expected Return of Tangency Portfolio (ER_Tangency) = 16%

Volatility of Tangency Portfolio (σ_Tangency) = 22%

Risk-Free Rate (RFR) = 5%

Now, we can plug these values into the CML equation:

Expected Return (ER) = 5% + [31% * (16% - 5%) / 22%]

Expected Return (ER) = 5% + [31% * 0.5]

Expected Return (ER) = 5% + 15.5%

Expected Return (ER) = 20.5%

So, the highest possible expected return of an alternative investment with the same volatility as Eriksson's stock is 20.5%.

8. Dividend policy - Essä

A company announces a change of dividend policy soon after paying a dividend equal to 8 per share. The company decides to retain part of the dividends for next year in order to invest in a project which will create a higher dividend growth. Its dividend next year will thus be equal to 3 per share and it will grow at a rate of 4% in subsequent years. Just before the announcement (but right after the dividend was paid) the stock of the company had a price equal to 100 and its previous dividend growth rate was equal to 1%. What is the price of the stock after the announcement if the cost of equity remains unchanged?

(Round your answer to the nearest whole number)
You need to explain how you got to your final answer in order to get points for this question. JUST TYPING THE FINAL ANSWERS WILL GIVE YOU ZERO POINTS. ANSWER ON THE SPACE PROVIDED BELOW.

to calculate the stock price after the announcement of the new dividend policy, we can use the "Constant Dividend Growth Model".

The formula for it is:

Po = Div1 / (rE - g)

Po = current stock price.

Div1 = dividend expected to be paid at the end of the next period.

rE = "Cost of equity" (required rate of return)

g = dividend growth rate

Step 1:

Po (current stock price) =

(Dividend equal to 8 per share) * (1 + previous dividend growth rate) / (Stock price before dividend)

= Cost of equity

Po = 8 * (1+0.01) / 100 = 0.09

Step 2:

Po = (next year dividend (3 per share)) / (Cost of equity - New dividend growth rate)

Po = 3 / (0.09 - 0.04) = 3 / 0.05 = 60

Answer: current stock price is 60.

9. Time value of money -

What is the present value of recieving 3500 SEK in 6 years and 6 months from now, assuming an annual discount rate of 4.2 percent? (Answers are rounded to the nearest integer) Select one alternative:

PV = FV / (1+r)^n

PV = 3500 / (1+0.042)^6,5

PV = 3500 / 1,311215

PV = 2678, 723398

PV = 2679 SEK 

10. The security market line

Assume that CAPM applies. Suppose that you know that the Stock of a company called "Not at all" has a beta equal to 0.9 and a risk premium equal to 12%. The risk-free rate happens to be equal to 2%.

What is the risk premium of the stock of another company called "Nothing to worry about" if it has a beta equal to 1.5?

The CAPM formula to calculate the expected return of a stock is as follows:

E(R) = Rf + B * (E(Rm)) - Rf)

E(R) = expected return of the stock.

E(Rm) = expected return of the market

Rf = risk-free rate

B = beta coefficient of the stock.

Info from the question:

Beta (B) of “Not at all” company´s stock: 0.9

Beta of “Nothing to worry about” company's stock: 1.5

Risk premium of “Not at all”: 12%

Risk-free rate: 2%

Step 1:

You can first calculate the expected return of the market (E(Rm)) using the risk-free rate and the risk premium of “Not at all” company´s stock:

E(Rm) = Rf + risk premium = 

2 + 12 = 14%

Step 2:

Now you can use the CAPM formula to calculate the expected return of “nothing to worry about”.

E(R) = Rf + B * (E(Rm) - Rf) =

E(R) = 2% + 1.5 * (14% - 2%) = 20%

11. FCF Model (Free Cash Flow Model):

A company is expected to generate the following free cash flows over the next four years:

Year                 |1  |       2|     3 | 4 |

FCF (in millions) | 51.5 | 69.7 | 77.3 | 76.5 |

After that, the free cash flows are expected to grow at the industry average of 3.6% per year (g). If the weighted average cost of capital (WACC) is equal to 13.1%, what is the firm's value?

(Answers in millions rounded to the closest whole number)

Step 2:

FCF year 1 / (1 + WACC)^1 + 

FCF year 2 / (1 + WACC)^2 + 

FCF year 3 / (1 + WACC)^3 + 

FCF year 4 / (1 + WACC)^4 = A

Step 3:

PV = 51.5 / (1+0.131)^1 = 45.53492485

PV = 69.7 / (1+0.131)^2 = 54.48884073

PV = 77.3 / (1+0.131)^3 = 53.43080029

PV = 76.5 / (0.131 - 0.036) = 805.2631579

805.2631579 * 1 / (1+0.131)^3 = 556.6087319

Value of the firm = 45.53492485 + 54.48884073 + 53.43080029 + 556.6087319 = 710. 0632978

12. Zero-coupon bond and YTM - Flervalsfråga

A zero-coupon bond with maturity in six years and face value 1000 SEK has a price equal to 733 SEK. What is its yield-to-maturity? (Answers rounded to two decimal digits)

Yield-to-maturity (YTM) för en nollkupongobligation kan beräknas med följande formel:

P = F / (1 + r)^n

där:

P = är nuvärdet (priset) på obligationen.

F = är obligationens nominella värde (face value).

r = är den årliga räntan (yield-to-maturity).

n = är antal år till förfall.

I det här fallet har vi:

P = 733 SEK

F = 1000 SEK

n = 6

Vi behöver lösa för r:

733 = 1000 / (1 + r)^6

Låt oss nu lösa denna ekvation för r:

Isolera (1 + r)^6

(1 + r)^6 = 1000 / 733

Beräkna 1000 / 733

1000 / 733 = 1.364

3. Ta den sjätte roten ur båda sidorna för att lösa för r:

1 + r = (1.364)^1/6

4. Beräkna (1.364)^1/6

Beräkna först på miniräknaren eller excel (1/6) som är = 0,1666666667.

(1.364)^0,1666666667

1 + r = ca 1.0531

5. Subtrahera 1 från båda sidor:

1 + r = ca 1.0531

r = ca 0.0531

6. Konvertera till procent:

r = ca 5.31%

Så yield-to-maturity (YTM) för denna nollkupongobligation är 5.31%, vilket stämmer med facit.

13. Payback period - Flervalsfråga

You are a real estate agent thinking of placing a sign advertising your services at a local bus stop. The sign will cost 5050 and it will be posted for one year. You expect that it will generate additional revenue of 645 per month. The discount rate is 5%.

What is the payback period?

(Answers rounded to two decimal digits)

To calculate the payback period for the investment:

1. Identify the initial investment and monthly revenues: 

Initial investment: 5050

Monthly revenues: 645 per month

2. Calculate the payback period:

Payback period =

Initial investment / Cash flows (monthly revenues)

Payback period =

5050 / 645 = ca 7.83 (months)

3. Perform the division:

   Payback period = 5050 / 645 = ca 7.83 (months)

Answer:

payback period is approximately 7.83 months.

14. Equivalent Annual Annuity - Flervalsfråga

A company is considering a project that requires an initial outlay of 2050 SEK. The project will produce a first cash-flow of 500 SEK at the end of year 1 and then the subsequent yearly cash-flows will grow at a rate of 1% per year. The project has a lifespan of 8 years. Suppose that you know that the EAR rate is equal to 3.5%.

What is the EAA of this project? (Answers rounded to two decimal digits)

To calculate the Equivalent Annual Annuity (EAA) of a project, we need to find the equal annual cash flow that would be equivalent to the cash flows of the project over its lifespan, given a specific interest rate.

Given:

Initial outlay = 2050 SEK

First cash flow = 500 SEK

Cash flows grow at a rate of 1% per year Project lifespan = 8 years Effective Annual Rate (EAR) = 3.5%

Step 1:

Calculate the growth factor The growth factor represents the increase in cash flows each year.

Growth Factor = 1 + Growth Rate Growth Factor

= 1 + 0.01 = 1.01

Step 2:

Calculate the present value of the cash flows. We calculate the present value of each cash flow using the EAR as the discount rate.

Present Value (PV) = Cash Flow / (1 + EAR)^n PV of the first cash flow (Year 1) =

500 / (1 + 0.035)^1 PV of the second cash flow (Year 2) =

500 * (1.01) / (1 + 0.035)^2 PV of the third cash flow (Year 3) =

500 * (1.01)^2 / (1 + 0.035)^3

Continue this calculation for all 8 years.

Step 3:

Calculate the Equivalent Annual Annuity (EAA) The EAA is the equal annual cash flow that is equivalent to the present value of the project's cash flows over its lifespan.

EAA = PV of Cash Flows / Annuity Factor Annuity Factor = (1 - (1 + EAR)^(-n)) / EAR

Calculate the PV of the cash flows and the annuity factor, and then divide the PV by the annuity factor to find the EAA.

After performing the calculations, the EAA of this project is approximately 218.70 SEK.

Therefore, the correct answer is 218.70.

Please note that the EAA represents the equal annual cash flow required to have the same present value as the project's cash flows, considering the given interest rate.

Förslag två:

Step 1: calculate the present value (PV) of cash flows. We need to the PV for each year´s cash flow:

PV year 1:

500 / (1+0,035)^1

PV year 2:

(500 * 1,01) / (1+0,035)^2

PV year 3:

(500 * 1,01)^2 / (1+0,035)^3

PV year 4:

(500 * 1,01)^3 / (1+0,035)^4

PV year 5:

(500 * 1,01)^4 / (1+0,035)^5

PV year 6:

(500 * 1,01)^5 / (1+0,035)^6

PV year 7:

(500 * 1,01)^6 / (1+0,035)^7

PV year 8:

(500 * 1,01)^7 / (1+0,035)^8

Sum all PV:s

Step 2:

15. Coupon bond - Flervalsfråga

Suppose a bond with maturity in 7 years and semi-annual coupons has a face value equal to 1000. Its coupon rate is 8% and it has a yield-to-maturity (YTM) equal 12% (expressed as an APR with semi-annual compounding).

To calculate the price of a bond, we can use the present value formula for bond pricing. The formula is as follows: Price =

∑ [C / (1 + YTM/2)^(2t)] + (F / (1 + YTM/2)^(2n))

Where: C is the coupon payment YTM is the yield-to-maturity F is the face value of the bond t represents each semiannual period (from 1 to n)

Given the information provided:

Face value (F) = 1000 Coupon rate = 8% (0.08) Yield-to-maturity (YTM) = 12% (0.12)

Maturity period (n) = 7 years Semiannual compounding (2 periods per year)

Step 1: Calculate the semiannual coupon payment Coupon payment = (Coupon rate * Face value) / 2 Coupon payment = (0.08 * 1000) / 2 = 40 SEK

Step 2: Calculate the present value of the bond

Price = ∑ [40 / (1 + 0.12/2)^(2t)] + (1000 / (1 + 0.12/2)^(2n))

Perform the calculation for each semiannual period from

t = 1 to t = 2n, and sum up the present values.

Price =

[40 / (1 + 0.06)^(21)] +

[40 / (1 + 0.06)^(22)] +

[40 / (1 + 0.06)^(23)] +

[40 / (1 + 0.06)^(24)] +

[40 / (1 + 0.06)^(25)] +

[40 / (1 + 0.06)^(26)] +

[40 / (1 + 0.06)^(27)] +

[1000 / (1 + 0.06)^(27)]

After performing the calculation, the price of the bond is approximately 814.10 SEK. Therefore, the correct answer is 814.10 SEK.

17. Options - Flervalsfråga

You own 1 put options with strike-price equal to 70 and 2 call options with strike-price equal to 50. They both have the same maturity and the same underlying stock whose current price is 100. What will be the total payoff of your options at maturity if the price of the stock at that point is equal to 62?

To calculate the total payoff of your options at maturity, we need to consider the payoff of each individual option and then sum them up.

Stock price at maturity - Strike price = Call option payoff

Call option payoff: 62 - 50 = 12

 Put option payoff: 70 - 62 = 8

To calculate the total payoff, we sum up the payoffs of the put option and the call options:

Put option payoff + Call option payoff + Call option payoff = Total payoff

8 + 12 + 12 = 32 = Total payoff 

Therefore, the correct answer is 32.

19. Portfolio Theory - (ej klar)

A portfolio has two elements: stock A and stock B. The weight on stock A is equal 0.2. The correlation between the return of stock A and B is 0.7. The table below shows (possibly relevant) additional information. The variance for each stock was computed by using rates of returns and not percentages. What is the expected return of the portfolio? What is its standard deviation? (Round your answer to two decimal digits)

Stocks:     Expected return:     Variance:

A:                     15%           0.0227

B:                11%                0.0123

Answer: 11.80% and 11.19%

20. Beta of a portfolio

Suppose you hold a portfolio of the market portfolio and the risk-free asset. Your portfolio weight on the risk-free asset is equal to -0.5.

What is the Beta of your portfolio?

 Chat-GPT answer:

In finance, when discussing portfolio weights, a weight of -0.5 for the risk-free asset indicates that you have a short position (i.e., borrowing) in the risk-free asset. This means you're borrowing money at the risk-free rate to invest in the market portfolio.

The sum of the weights in a two-asset portfolio (risk-free asset and market portfolio) should equal 1. Therefore, if your weight on the risk-free asset is -0.5, the weight on the market portfolio should be 1 - (-0.5) = 1.5.

This ensures that the total portfolio weight adds up to 1, with the negative weight indicating a short position in the risk-free asset. So, in this case, the correct weight on the market portfolio is indeed 1.5.

Answer: 1.5