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# FIN200 Corporate Financial Management Final Examination Assessment Answer

**FIN200 Corporate Financial Management ****T120 Take Home Final Examination:**

Q1. Answer the following questions.

a. What is the Optimal Capital Structure? Explain with a graph.

b. What is diversification in Finance? Explain.

c. Explain the differences between American and European options.

Q2. Provide appropriate answers to the following questions.

a. What are differences between future and forward contracts? Explain.

b. Explain 3 forms of market efficiencies.

c. Explain the term structure of interest rates.

Q3. If government bonds are currently paying 7 per cent and the inflation rate is 2.1 per cent, what is the approximate real rate? What is the exact real rate?

Q4. The following information relates to Rio Tinto Mining Corporation. What is Rio Tinto’s weighted average cost of capital?

● 10 years ago, Rio Tinto issued 80,000 bonds with 16 years maturity and a face value of $1000 each, pays an – annual coupon amount of $100 each. The yield on the bonds is 15% p.a. Rio Tinto’s marginal corporate tax rate is 30%.

● Rio Tinto has 15 million preference shares on issue, which are currently trading for $3.20 each, giving total market value of $48 million. They pay an annual dividend of 30 cents per share.

● Rio Tinto has 21.5 million ordinary shares on issue, which are currently trading for $4 each. These shares are expected to pay an annual dividend of $0.75 next year, and this dividend is expected to grow at the constant rate of 3% in perpetuity.

Q5. Use the following option quotes to answer the questions below.

December, 2019, Alibaba Ltd

Last sale price $16.00

__ Calls – Last ____Puts - Last__

__Strike Price Jun July Aug Jun July Aug__

$16.00 36 cents 48 cents 72 cents 24 cent 27 cents 32 cents

a. Suppose you buy 150 July $16.00 call contracts. How much will you pay, ignoring commissions?

b. Suppose you buy 50 of August 2019 put contracts. What is your maximum net gain?

On the expiration date, Alibaba is selling for $14.00 per share. What are your options worth?

c. In part (b), suppose you sold your 50 August put contracts. What is your net gain or loss if Alibaba is selling for $13.00?

Q6. You would like to invest in two shares A and B. The return on these shares over the next year depends on the state of economy, which will be described as “Boom”, “Normal”, “Slow” and “Recession”. The table below shows the probability of each of these states of economy, and the expected return on each share given each possible state of the economy. The correlation coefficient between shares A and B is 0.5.

State of the economy | Probability | A Return | B Return |

Boom | 0.20 | 0.25 | 0.21 |

Normal | 0.40 | 0.16 | 0.12 |

Slow | 0.25 | 0.10 | 0.08 |

Recession | 0.15 | - 0.06 | 0.05 |

a. What is the expected return on A and B shares?

b. What is the standard deviation of A and B shares?

c. What is the expected return on portfolio comprised of 55% invested in share A and the balance in share B?

d. What is the standard deviation on portfolio comprised of 55% invested in share A and 45% invested in share B?

Q7.** **The risky portfolio Q consists of 2,500 shares of Google and 7,500 shares of Yahoo. Assume that Google has a share price of $4, an expected return of 18 per cent, and a standard deviation of 25 per cent. Yahoo has a share price of $2, an expected return of 15 per cent, and a standard deviation of 20 per cent. The correlation between the two is 0.5, and the risk-free rate of interest is 2 per cent.

What fraction of your portfolio must you invest in risky portfolio of Q and risk-free to have a portfolio standard deviation of 12 per cent?

## Answer

**Q1. Answer the following questions.**

**a. What is the Optimal Capital Structure? Explain with a graph.**

**Answer:**

Capital structure is the combination of different sources of capital to fund the business capital needs. The capital is composed of debt, preference, capital and equity capital. The optimal capital structure is the mix of debts and equity such that the weighted average cost of capital of the firm is lowest and hence the value of the firm is maximum. The cost of capital is directly proportional to the risk attached with it. As the risk increases the cost of capital also increases. Debt is secured against the assets of the company and therefore is less risky as compared to equity which has the residual charge over the assets of the firm. The cost of debt is less than cost of equity. However as the debt increases the cost of debt also increases making it more expensive. There has to be a right combination of debt and equity in the capital structure so that the cost of capital is least to the firm. This combination is known as the optimal capital structure.

The above graph shows that the wacc of the firm with all equity reduces as the debt is added to the capital structure. However if the debt is increased beyond a certain limit the cost of debt also increases and the benefit of low WACC is no more. The WACC is lowest at ascertain combination of debt and equity and that ratio of debt and equity is termed as optimal capital structure.

Source: (CFI, 2020)

**b. What is diversification in Finance? Explain.**

**Answer:**

Investments are subject to risks and hence diversification is preferred to reduce the exposure to risks. Diversification is the strategy in which the capital is invested in different investments with different risks. If the investment is done in only one asset or fund, the change in value of the asset affects the value of the whole investment. Diversification reduces the volatility of the whole investment as the losses from one asset are set off by the profits from another asset.

However diversification can help reduce only the unsystematic risk which is asset/firm specific. The unsystematic risk affects only one or a small group of assets. The investment in different assets or group of assets helps in reducing this risk. Diversification does not affect the systematic risk which is market risk.

**c. Explain the differences between American and European options. **

**Answer:**

Option are the derivatives which allow the option holder to exercise a right in future. The options can be American option or European option depending upon the right given by them.

American option gives the holder the right to exercise the option any time before the expiry date of the option. While the European option can be exercised only on the pre decided expiry date of the option. The premium paid for the European option is less than the premium paid for the American option.

The European options are generally traded over the counter while the American options are traded over the market over an exchange. The European options are generally less risky as the expiry date is fixed and the loss and profit can be estimated. While in American options the risk is high as the holder can exercise the option at any time he finds it profitable.

**Q2. Provide appropriate answers to the following questions. **

**a. What are differences between future and forward contracts? Explain.**

**Answer:**

Futures contracts are the standardized instruments that are traded publically on the exchanges through brokerage firms. The contracts are standardized in terms of the trading volumes, the delivery dates, credit amounts and methods. The standards are set for each contract. Since the contracts are traded on exchanges they have less counter party risks and the profits and losses are settled daily in the account.

Forward contracts are the agreements between the two parties. The terms of the agreement are set by the two parties mutually. The agreement could be sell the asset or buy the asset at the pre- decided time in future. These contracts are customized according to the needs of the customer. The contracts have higher counter party risk as the total profit or loss is determined on the maturity date only.

**b. Explain 3 forms of market efficiencies. **

**Answer:**

The three forms of market efficiencies are as follows:

- Weak Market Hypothesis: in this form of market efficiency, the prices of the stock cannot be determined from past prices. The historical data does not provide any trend which can be used to earn higher profits in future. There are no patterns that are observed in price movements of the assets. The prices follow the random walk theory. The future price movements are completely dependent upon the information that is not present in the past prices of the assets.
- Semi-strong Market Hypothesis: in the form of market efficiency the prices of the stock adjusts very fast to the publically available information. The investors cannot earn high or abnormal profits based upon that information because the market adjusts the prices of the asset very quickly and reaches equilibrium.
- Strong Market Hypothesis: in this form of market efficiency, the share prices reflect all the private and public information and no player can earn higher returns. The prices of the asset are at equilibrium at all the times. The market form is not possible if there are barriers to private information becoming public as it assumes that all the information is available to all the investors and everyone acts in their best interest.

**c. Explain the term structure of interest rates.**

**Answer:**

The structure of interest rates shows the relationship between the interest rates and duration of maturity of investment/bonds. The structure of interest rates is also known as yield curve and helps in assessing the state of economy. Normally the yield increases with the maturity and thus results in upward sloping curve. This is also considered as a normal slope or curve.

However, the slope can be downward sloping with short term investments giving higher yields as compared to long term bonds. This is the inverted yield curve and shows that the economy is in recession.

The flat curve shows very less variation in between the short term and long term yields. The future market is unsure in this state.

**Q3. If government bonds are currently paying 7 per cent and the inflation rate is 2.1 per cent, what is the approximate real rate? What is the exact real rate?**

**Answer:**

Interest rate paid on government bonds (nominal rate ), i = 7%

Inflation rate, π = 2.1%

Real rate of interest s calculated after adjusting the inflation from the nominal rate.

Approximate real rate, r = Nominal rate – inflation rate = i - π

= 7% - 2.1% = 4.9%

The exact real rate can be calculated using the fisher equation:

(1+i) = (1+r) * (1+π)

r = (1+i)/(1+π) – 1

= (1+7%)/(1+2.1%) – 1

= (1.07/1.021) - 1

= 0.04799

= 4.80%

Exact Real rate = 4.80%

**Q4. The following information relates to Rio Tinto Mining Corporation. What is Rio Tinto’s weighted average cost of capital?**

**●**** 10 years ago, Rio Tinto issued 80,000 bonds with 16 years maturity and a face value of $1000 each, pays an – annual coupon amount of $100 each. The yield on the bonds is 15% p.a. Rio Tinto’s marginal corporate tax rate is 30%.**

**● ****Rio Tinto has 15 million preference shares on issue, which are currently trading for $3.20 each, giving total market value of $48 million. They pay an annual dividend of 30 cents per share.**

**● ****Rio Tinto has 21.5 million ordinary shares on issue, which are currently trading for $4 each. These shares are expected to pay an annual dividend of $0.75 next year, and this dividend is expected to grow at the constant rate of 3% in perpetuity. **

**Answer:**

Weighted Average cost of capital = sum of (weights of capitals * cost of capitals)

**Cost of debt (Kd):**

No of bonds issued = 80,000

Face value = $1,000

Maturity value = $1,000

Annual coupon = $100

Yield on bonds = 15%

Tax rate = 30%

Present Value(PV) of bond = PV of maturity value + PV of coupon payments

The bonds are left for 6 years:

Current market value of debt = 1000/((1+15%)^6+ Ʃ_{t = 1to 6 } 100/ ((1+15%)^t)

= $810.78

Total Market Value of Debt = $810.78 * 80,000 = $64.86 million

Kd = 100/810.78 = 12.33%

Kd after tax= 12.33%*(1-30%) = 8.63%

**Cost of preference Share (Kp):**

No of shares = 15 million

Market Price = $3.20 each

Total Market Value = $48 million

Annual dividend = 30 cents per share = $0.30 per share

Kp = 0.30/3.20 = 0.09375 = 9.375%

**Cost of Equity (Ke) :**

No of shares = 21.5 million

Market Price, MP = $4 each

Total Market Value = $86 million

Dividend next year, D1= $0.75

Dividend growth rate, g = 3% constant

Ke = (D1 / MP) +g

= (0.75/4) + .03

= 0.2175

=21.75%

Weighted average cost of capital:

Type of capital | Total Market Value ($ million) | Weight in total capital | Cost of capital | Share in WACC |

Bonds /debt | $64.86 | 0.326 | 8.63% | 2.81% |

Preference Capital | $48.00 | 0.241 | 9.38% | 2.26% |

Equity Capital | $86.00 | 0.432 | 21.75% | 9.41% |

Total | $198.86 | $1.000 | | 14.48% |

The WACC = 14.48%

**Q5. Use the following option quotes to answer the questions below.**

** December****, 2019, Alibaba Ltd**

** Last sale price $16.00**

__ Calls – Last ____Puts - Last__

__Strike Price Jun July Aug Jun July Aug__

** $16.00 36 cents 48 cents 72 cents 24 cent 27 cents 32 cents**

**a. Suppose you buy 150 July $16.00 call contracts. How much will you pay, ignoring commissions?**

**Answer: **

The July call option is available at the premium of 48 cents. 150 call contract will be bought for 150*100*$.48= $7200.00 (1 contract is generally of 100 stocks)

**b. Suppose you buy 50 of August 2019 put contracts. What is your maximum net gain? **

**On the expiration date, Alibaba is selling for $14.00 per share. What are your options worth?**

**Answer:**

August put contracts are available for 32 cents each.

Cost of 50 contracts = 50*100*$.32 = $1600

The maximum net gain = strike price – premium paid

= 50 *100*16 – 1600 = 80,000 – 1600 = $78,400.

On expiration since the price of share has declined to $14 per share from $16, the gain on the stock =( $16 - $14)*50*100 = $10,000

The option is worth the difference between the gain on expiry less the premium paid

= $10,000 – 1600= $8,400

Cost of 1 put contract = 8,400/5000 = $1.68

**c. In part (b), suppose you sold your 50 August put contracts. What is your net gain or loss if Alibaba is selling for $13.00?**

**Answer:**

On expiration since the price of share has declined to $13 per share from $16, the gain on the stock =( $16 - $13)*50*100 = $15,000

The option is worth the difference between the gain on expiry less the premium paid

= $15,000 – 1600= $13,400

The net gain = $13,400

**Q6. You would like to invest in two shares A and B. The return on these shares over the next year depends on the state of economy, which will be described as “Boom”, “Normal”, “Slow” and “Recession”. The table below shows the probability of each of these states of economy, and the expected return on each share given each possible state of the economy. The correlation coefficient between shares A and B is 0.5.**

State of the economy | Probability | A Return | B Return |

Boom | 0.20 | 0.25 | 0.21 |

Normal | 0.40 | 0.16 | 0.12 |

Slow | 0.25 | 0.10 | 0.08 |

Recession | 0.15 | - 0.06 | 0.05 |

**a. What is the expected return on A and B shares?**

**Answer:**

State of the economy | Probability | A Return | Expected return A (Probability * return) | B Return | Expected return B (Probability * return) |

Boom | 0.20 | 0.25 | 0.05 | 0.21 | 0.04 |

Normal | 0.40 | 0.16 | 0.06 | 0.12 | 0.05 |

Slow | 0.25 | 0.10 | 0.03 | 0.08 | 0.02 |

Recession | 0.15 | -0.06 | -0.01 | 0.05 | 0.01 |

Expected Return | | | 0.1300 | | 0.1175 |

% age Return | | | 13.00% | | 11.75% |

**b. What is the standard deviation of A and B shares?**

**Answer:**

Standard deviation:

State of the economy | Probability | A Return | Expected return A (Probability * return) | [Return) - Ex return ]^2 for A | Prob * [Return) - Ex return ]^2 for A | B Return | Expected return B (Probability * return) | [Return) - Ex return]^2 for B | Prob* [Return) - Ex return]^2 for B |

Boom | 0.20 | 0.25 | 0.050 | 0.014 | 0.0029 | 0.21 | 0.042 | 0.009 | 0.0017 |

Normal | 0.40 | 0.16 | 0.064 | 0.001 | 0.0004 | 0.12 | 0.048 | 0.000 | 0.0000 |

Slow | 0.25 | 0.10 | 0.025 | 0.001 | 0.0002 | 0.08 | 0.020 | 0.001 | 0.0004 |

Recession | 0.15 | -0.06 | -0.009 | 0.036 | 0.0054 | 0.05 | 0.008 | 0.005 | 0.0007 |

Total Expected Return | | | 13.00% | | | | 11.75% | | |

Variance | | | | | 0.009 | | | | 0.003 |

Standard deviation | | | | | 0.094 | | | | 0.052 |

Standard deviation in % age | | | | | 9.42% | | | | 5.24% |

**c. What is the expected return on portfolio comprised of 55% invested in share A and the balance in share B?**

**Answer:**

Share | Weight | Expected return on Share | Expected return on portfolio |

A | 55% | 13.00% | 7.15% |

B | 45% | 11.75% | 5.29% |

Expected return | | | 12.44% |

**Expected Return on portfolio is 12.44%**

**d. What is the standard deviation on portfolio comprised of 55% invested in share A and 45% invested in share B?**

**Answer:**

Standard deviation for the portfolio is calculated using the following formula:

We need to calculate the correlation co-efficient between the two assets.

The correlation co-efficient of the two stocks is 0.92

[0.55^{2}*0.094^{2 }* + 0.45^{2}*0.052^{2 }+ 2*0.55*0.45*0.92*0.094*0.052]^(1/2)

= 0.1105

= 11.05%

SD of the portfolio is 11.05%

**Q7.**** ****The risky portfolio Q consists of 2,500 shares of Google and 7,500 shares of Yahoo. Assume that Google has a share price of $4, an expected return of 18 per cent, and a standard deviation of 25 per cent. Yahoo has a share price of $2, an expected return of 15 per cent, and a standard deviation of 20 per cent. The correlation between the two is 0.5, and the risk-free rate of interest is 2 per cent.**

**What fraction of your portfolio must you invest in risky portfolio of Q and risk-free to have a portfolio standard deviation of 12 per cent?**

Answer:

Risk Free rate = 2%

Share | No of shares | Market Price | Value of total shares | Weight in portfolio | Expected Return | Standard Deviation |

Google | 2500 | $4 | $10,000 | 0.40 | 18% | 25% |

Yahoo | 7500 | $2 | $15,000 | 0.60 | 15% | 20% |

Correlation between the two is 0.5

Standard deviation of the risky portfolio Q =

= [0.40^{2}*0.25^{2 }* + 0.60^{2}*0.20^{2 }+ 2*0.40*0.60*0.5*0.25*0.20]^(1/2)

= 0.2728

= 27.28%

SD of Q = 27.28%

Expected return of Q = 0.40 *18% + 0.60* 15% = 16.2%

Standard deviation of desired portfolio = 12%

Risk free rate = 2%

Risk free Standard deviation = 0

Desired weight:

Let the weight of Q = Wq and weight of Risk free = Wr

= [Wq^{2}*0.2728^{2} + Wr^{2}*0 + 0]^1/2 = 12%

= [Wq^{2}*0.2728^{2}]^1/2 = 12%

= Wq^{2}*0.2728^{2 }= 0.0144

Wq = 0.44

= 44%

The weight of Q should be 44% and risk free investment should be 56% in the new portfolio to give the SD of 12%

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