Financial Reporting, Coursework #7

Financial Reporting Quiz

Scheduled: 5 Dec 2024 at 12:00 to 6 Dec 2024 at 17:00, GMT

#29-41

 

이제 끝을 달려가고 있다..ㅎ 화이팅!

 

Coursework Question 29

Juno plc is ungeared and has a β of 1.3 and the corporation tax rate is 20%
a) What would the β of the company's equity shares become if it issued an amount of debt equal to 64% of its market capitalisation and used the cash raised to repay existing equity shares?

 

β란 무엇인가?  CAPM을 활용할 경우 개별자산의 수익률은 β(주식 베타)에 의해 결정된다.βi(주식 i의 베타)는 마켓 포트폴리오 m이 변함에 따라 개별주식 i가 얼만큼 변동하는가를 나타낸다. 한마디로 주식 i의 변동성volatility이다.

 

what happens if a share has a zero β

Its expected return is the same as the risk free rate. This is the case even if it is very volatile if this volatility is uncorrelated to the market

What happens if a share has a negative β

Its expected return is less than the risk free rate. this means that the share price movements are negatively correlated to the market

 

 WACC란? The Weighted Average Cost of capital (WACC) 가중평균자본비용 지불하는 "평균 이자율" 남의 돈 빌릴 때, 내돈 쓸 때.

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WACC Summary

WACC=DD+E×rd+ED+E×re

Where:

rd = cost of debt (1-t)

re=r+βg× equity risk premium (CAPM)

βg=βu×(1+DE(1−t))

βg = geared beta βu = ungeared beta

N.B. Market values used where available

 

 

geared와 ungeared 란?

Ungeared: The company is financed entirely by equity, leading to lower risk and lower volatility for shareholders.

Geared: The company takes on debt (e.g., to repay equity), leading to higher financial risk and greater volatility in equity returns for the remaining shareholders.

 

t = tax rate

1.3 * (1+ 64/36(1-0.2)) = β = 3.14888889

 

 

Coursework Question 30

b) What would the β become if the debt was used to expand the business?

 

If Juno plc uses the debt to expand the business instead of repurchasing equity, the situation changes because the company’s capital structure and its total value increase without reducing the existing equity base.

이 경우, D = debt는 0에서 0.64로 늘어나고, E = equity 는 1로 그대로 있다. 총 자본은 1에서 1.64로 늘어나므로, D/E = 0.64

= 1.9656

β = 1.9656

 

Coursework Question 31

Minerva plc has a gearing ratio D:E of 4:4
The risk free rate is 2.9% and the yield on its own debt is 4.3%
The market equity risk premium is believed to be 3.1%
The β of the geared equity is 0.8 and the rate of corporation tax is 20%
a) Calculate the WACC

 

 

WACC example

X plc has a gearing ratio D:E of 1:1

The risk free rate is 4% and the yield on its own debt is 5%

The market equity risk premium is believed to be 6%

The β of the geared equity is 1.4 and the rate of corporation tax is 30%

i) Calculate the WACC

ii) If X plc were to repay all its debt, what would be the required return to the equity?

You may assume the debt is repaid by issuing selling equity (this could be new equity or equity already held by the company)

iii) If X plc does not repay all its debt but instead makes a rights issue to reduce its gearing, D/E to 1:3. Calculate its WACC after the rights issue

You may assume that the additional capital raised is invested in the same way as the rest of the business is invested

i)

 ungeared beta = geared beta / (1+(1-t)*D/E) = g.B/1.7 = 1.4/1.7 = 0.823529

WACC = D/(D+E)*r(d) + E/(D+E)*r(e) 

r(d) = cost of debt (1-t) = 0.05 * (1-0.3) = 0.035

r(e)  = r+β(g)× equity risk premium = 0.04 +1.4 * 0.06 = 0.124 then WACC = 1/2 * 0.035 + 1/2 * 0.124 = 0.0795

 

31의 경우도 이와 유사하게 r(d) = 0.043*(1-0.2) = 0.0344, r(e) = 0.029+0.8*0.031 = 0.0538.    

WACC = 1/2 * 0.0344 + 1/2*0.0538 = 0.0441

 

Answer: 4.41 % 

 

Coursework Question 32

b) If Minerva plc were to repay all its debt (having sold equities through a rights issue), what would be the required return to the equity?

Answer: 4.277764% 

 

 

"repay all its debt"  gear를 한 상태에서  ungear상태로 돌린다는 말, debt를 갚는다는 말. 그러면 1:1 비율에서  market capitalisation 은 equity 100% 가 된다. 먼저 example로 계산해보면 β(u) = β(g) / (1+(1/1)*(1-0.3) = β(g)/1.7 = 1.4/1.7 = 0.82353

new required equity = cost of equity = r(e) = 0.04+0.82353 * 0.06 =0.094118

 

다시 문제로 돌아와서, β(u) = β(g) / (1+(1/1)*(1-0.2) = 0.8/1.8 =. 0.4444444

new r(e) = risk free rate + β(u) * ERP = 0.029 + 0.44444* 0.031 

= 4.277764%

 

 

Coursework Question 33

c) If Minerva plc does not repay all its debt but instead simply makes a rights issue to reduce its gearing, D:E to 1:7. Calculate its WACC after the rights issue

 

Answer: 4.31083199% 

 

 일단 ungeared 상태에서, ratio가 바뀌었으니 다시 new β(g)를 구하도록 한다. 

 

β(g*) = β(u)*(1+D/E*(1-t)) = 0.444444*(1+1/7*0.8) =  0.4952376

r(e*) = 0.029 + 0.4952376 * 0.031 = 0.0443523656

r(d*) = r(d) = 0.0344

WACC = D/(D+E)*r(d) + E/(D+E)*r(e) = 1/8 * 0.0344 + 7/8 * 0.0443523656 = 0.0431083199

 

 

 

Coursework Question 34

A pension scheme has a liability of £463m which it has to meet in 21 years time. The trustees are concerned about their exposure to interest rate risk and are able to buy bond futures based on 5 year zero coupon bonds. Assume that interest rates are currently 6.7%. p.a.
a) What nominal value of bond futures would they need to hedge this risk. You should seek to calculate this as a pure delta hedge that is use as small a change in interest rates as possible.
Note:
The e-lecture shows this calculation with a 1% change in intererst rates. For this question you are being expressly asked to use the smallest change you can (0.001% works well here and will give you the right answer). 
If you do the question using a 1% change you will notice you get a similar answer (and for practical hedging purposes this is OK) but not exactly the same answer, that you need for the coursework.
Also the derivative being described here is a contract to buy a bond with one payment in 5 years. 
You should assume the contract is to buy the bond effectively immediately so that the value of the forward price is not sensitive to interest rates as it has a duration of t=0 and so it is just the value of the bond underlying the future that is sensitive to interest rates.
In practice this would be structured with, for example, 3 month forwards just being rolled over each time they expired so although there would be interest rate sensitivity in the future price it would not be material.
By nominal value we just mean the number of £1 underlying contracts that would be needed.

Answer: 

Coursework Question 35

b) How many bond futures, with immediate maturity, based on 2 year zero coupon bonds with nominal values of £100 would they need

Answer: 

 

Coursework Question 36

Company A wishes to borrow £170000 for 10 years at fixed rates. It finds it can borrow on the following terms in the market:

• Fixed rate for 10 years 4.9% pa
• Floating rate for 10 years 6 month LIBOR + 0.6%

Company B on the other hand wishes to borrow £170000 floating for 10 years and finds it can borrow on the following terms:

• Fixed rate for 10 years 4.2% pa
• Floating rate for 10 years 6 month LIBOR +2.5%

Assuming both companies will only enter into the swap if they can reduce the interest rate they pay on their preferred style of loan by 0.5%, what is the maximum annual profit the bank can make per year. An exam question would typically ask you the following as well: Show with the aid of a diagram how an investment bank could structure two swaps so that both companies A and B get the swap they want and the bank makes a profit (you cannot enter the diagram into the answer box)

Answer: £ 

Coursework Question 37

A hotelier takes out an interest only loan of £110000 for 7 years at a floating interest rate (LIBOR+1%) initially of 5% (i.e. assume that LIBOR is currently 4%). Given that he risks having to make increased payments under the loan if interest rates rise then he agrees to enter into an interest rate swap with a bank whereby he pays the bank the 5% on the nominal of the £110000 and the bank pays him the floating rate (LIBOR+1%) on the same nominal amount
The interest payments on the loan are due at the end of each year and the £110000 nominal is due at the end of the 7 years.
a) If LIBOR rises by 1% over the first year what is the hoteliers first repayment on the loan

Answer: £ 

Coursework Question 38

b) If LIBOR falls by 1% in the first year how much variation margin must the hotelier deposit with the bank offering the swap?. You should assume that the future swap payments are discounted at LIBOR.

Answer: £ 

Coursework Question 39

A wheat farmer will be able to sell 1500 tonnes of wheat is 6 months time. The current price of wheat is £103 per tonne and it has cost him £80 per tonne to produce the wheat. The 6 month future price of wheat is £101 and the cost of a 6 month put option on the price of wheat at a strike price of £100 is £11. Strategy A is to not hedge the price of wheat, strategy B is to hedge the price of wheat with a futures contract and strategy C is to hedge the price of wheat with an options contract. (You may assume interest rates are 0.
How much profit does the farmer make in 6 months time if he adopts strategy A and the price of wheat has become £93?

Answer: £ 

Coursework Question 40

How much profit does the farmer make in 6 months time if he adopts strategy B and the price of wheat has become £93?

Answer: £ 

Coursework Question 41

How much profit does the farmer make in 6 months time if he adopts strategy C and the price of wheat has become £93?

Answer: £