MMock Exam

Question 1

On January 8, 2019, the price of an ASML share was €138; At that time, a three-month ASML call option with an exercise price of € 140 could be purchased for € 6.70. The risk-free interest rate at that time was 1% on an annual basis.

Based on the put-call parity, what would be the price for an ASML put option with the same strike price and term as the call option? (You can assume that ASML does not pay a dividend).

Answer 1

1. value call + PV (exc.price) = value put + value share
   6.70 + 140/1,010.25 = value put + 138
   Value put = 8.35

Question 2

On January 8, 2019, the price of an ASML share was €138; At that time, a three-month ASML call option with an exercise price of € 140 could be purchased for € 6.70. The risk-free interest rate at that time was 1% on an annual basis.

Suppose someone buys this call option ASML on January 8, 2019. At what price ASML on the expiration date does this investment yield neither profit nor loss?

Answer 2

2. 146.70. At this price, the investment of 140 (exercise price plus 6.70 for the purchase of the call) is equal to the value of the share.

Question 3

On January 8, 2019, the price of an ASML share was €138; At that time, a three-month ASML call option with an exercise price of € 140 could be purchased for € 6.70. The risk-free interest rate at that time was 1% on an annual basis.

What will happen to the price of the ASML call option if
a. the risk-free return falls?

Answer 3

3a. falls, because investing in options becomes less interesting compared to the purchase of the shares themselves, because of the smaller interest advantage.

Question 4

On January 8, 2019, the price of an ASML share was €138; At that time, a three-month ASML call option with an exercise price of € 140 could be purchased for € 6.70. The risk-free interest rate at that time was 1% on an annual basis.

What will happen to the price of the ASML call option if
b. the ASML share price falls?

Answer 4

3b. falls, because the right to buy something for a certain price decreases in value if the underlying asset becomes cheaper).

Question 5

On January 8, 2019, the price of an ASML share was €138; At that time, a three-month ASML call option with an exercise price of € 140 could be purchased for € 6.70. The risk-free interest rate at that time was 1% on an annual basis.

What will happen to the price of the ASML call option if

c. the volatility of the ASML stock price increases?

Answer 5

3c. rises, because the probability that the underlying value increases is greater.

Question 6

On January 8, 2019, the price of an ASML share was €138; At that time, a three-month ASML call option with an exercise price of € 140 could be purchased for € 6.70. The risk-free interest rate at that time was 1% on an annual basis.

Someone owns 100 ASML shares and decides to write a call option on his shares.

4. Why would anyone choose such a strategy?

Answer 6

4. With this strategy you have secured (in case of rising or constant prices) a certain fixed return (minimum 138 + 6.70 is 144.70 per share). With falling prices you will of course lose on your shares, but you earned the premium of 6.70 per share (because the option will not be excercised).

Question 7

Suppose you buy a 4% bond with a face value of €1,000.
The remaining term for this bond is exactly one year (maturing in one year)
The price for this bond is €900.
Assume that the one-year risk-free rate of return is 4%.
Suppose there is a chance that at the end of the year, only 50% of the promised interest and principal will be paid. This chance is 10%.

1. What is the promised yield to maturity for this bond?

Answer 7

1. 900 = 1040/1 +IRR
   IRR = (1040/900) -1 = 0.155556 (= 15.56%).

Question 8

Suppose you buy a 4% bond with a face value of €1,000.
The remaining term for this bond is exactly one year (maturing in one year)
The price for this bond is €900.
Assume that the one-year risk-free rate of return is 4%.
Suppose there is a chance that at the end of the year, only 50% of the promised interest and principal will be paid. This chance is 10%.

2. What is the expected return for this bond?

Answer 8

2. expected return (payoff) = 0.9 x 1040 + 0.1 (0.5 x 1040) = 988
   900 = 988/1+IRR
   IRR = (988/900) – 1 = 0.097777778 (= 9.78%).

Question 9

Suppose you want to insure yourself against non-payment or incomplete payment of the debtor (insure against default).

3. How much will this insurance cost you?

Answer 9

3. Spread (difference between the promised yield and the risk-free return) is 0.15555556 – 0.040000 = 0.115555556
   Insurance premium is: 0.11555555556 x 900 = 104.

Question 10

Suppose you want to insure yourself against non-payment or incomplete payment of the debtor (insure against default).

4. Show that the guaranteed rate of return is exactly equal to the risk-free return after you have taken out the insurance.

Answer 10

4. Total yield is promised bond yield minus insurance costs = 1050 – 104 = 936
   Guaranteed Return = (936/900) – 1 = 0.04 (4%) which is exactly the one-year risk-free return.

Question 11

Suppose you buy a 3-month future on the AEX in January for 495.20. At that time, the AEX index is trading at 497.80. The multiplier for the AEX future is 200, ie with the purchase of one future contract you buy 200 x the index. Assume that the dividend yield on the index is 0.

1. What can you say about the 3-month risk-free rate based on the information given above ?

Answer 11

1. Based on the formula: Ft = S0(1+ rf-y)t you can deduce that if y =o the interest rate rf must be negative. In that case, Ft is lower than S0.

Question 12

Suppose you buy a 3-month future on the AEX in January for 495.20. At that time, the AEX index is trading at 497.80. The multiplier for the AEX future is 200, ie with the purchase of one future contract you buy 200 x the index. Assume that the dividend yield on the index is 0.

Now, suppose the AEX 3-month future falls to 470 in the next 3 months.

2. What is the profit or loss on the AEX future contract?

Answer 12

2. You buy 200 x the index for 495.20 x 200 = 99,040.
   The value of 200 x the future is 470 x 200 = 94,000 after 3 months.
   Loss is 99,040 – 94,000 = 5,040.

Question 13

The following information is known about the futures market for Brent oil:

Current price (spot price) January 2018: $61.35 per barrel
Future price (January 2018) for a 1-year contract: $61.05 per barrel
The 1-year interest rate is – 0.12%.
The storage costs for oil are 0.5% per barrel on an annual basis.

3. Calculate the convenience yield for Brent oil using the formula for the commodity price of futures.

Answer 13

3. Ft =S0(1+rf + (storage costs – convenience yield))t
   61.05 = 61.35(1-0.0012+ 0.005 - convenience yield)1
   1-0.0012 + 0.005 - convenience yield = 61.05/61.35 = 0.99511
   1.0038 - convenience yield = 0.99511
   Convenience yield = 1.0038 - 0.99511 = 0.00869 ( = 0.869%).

Question 14

The following information is known about the futures market for Brent oil:

Current price (spot price) January 2018: $61.35 per barrel
Future price (January 2018) for a 1-year contract: $61.05 per barrel
The 1-year interest rate is – 0.12%.
The storage costs for oil are 0.5% per barrel on an annual basis.

4. What will happen to the convenience yield, other things being equal, if there is a major oil shortage? Explain this in words. Consider what this means for the future price compared to the spot price?

Answer 14

4. The convenience yield will increase, because of the increasing scarcity of oil (Having oil at your disposal now rather than in the future has now become more attractive). The futures price will become even lower compared to the spot price.

Question 15

On March 1, the following spot and forward rates are known for the exchange rate of the US dollar (USD) in Indian Rupia (INR):
Spot rate: 1USD = 60 INR
The six-month forward rate is: 1USD = 65 INR.
The six-month interest rate in the US is 2% (on an annual basis) on March 1.

1. Is there a forward discount or premium for the Indian Rupia against the US dollar on March 1, 2018? How much is this premium or discount on an annual basis?

Answer 15

1. There is a forward discount (Rupia forward price is lower than the spot price).
   2x (60/65 – 1) = -0.1538 (= -15.38%)

Question 16

On March 1, the following spot and forward rates are known for the exchange rate of the US dollar (USD) in Indian Rupia (INR):
Spot rate: 1USD = 60 INR
The six-month forward rate is: 1USD = 65 INR.
The six-month interest rate in the US is 2% (on an annual basis) on March 1.

2. Calculate (based on the interest rate parity theory) the six-month (annualized) interest rate in India on March 1, 2018.

Answer 16

2. 1+Rrupia(6/12)/1+Rdollar(6/12) = forward rate rupia/spot rate rupia
   1+X (6/12)/1+0.02 (6/12) = 65/60. 1+X (6/12)= 1.01x1.0833 = 1.0942
   X(6/12) = 0.0942. X = 0.0942 x 2 = 0.1883; The six-month rate in India is 18.83% (on an annual basis).

Question 17

On March 1, the following spot and forward rates are known for the exchange rate of the US dollar (USD) in Indian Rupia (INR):
Spot rate: 1USD = 60 INR
The six-month forward rate is: 1USD = 65 INR.
The six-month interest rate in the US is 2% (on an annual
basis) on march 1.

3a. Assuming that the real exchange rate of the Indian Rupia against the US dollar remains constant, what is the expected difference between the six-month inflation in India and the US based on purchasing power theory?

Answer 17

3a. Assuming that the real exchange rate remains constant, the expected difference in inflation will be: 65/60 -1 = 0.0833 (= 8.33%). Inflation in India will be 8.33% higher than in the US over the next six months.

Question 18

On March 1, the following spot and forward rates are known for the exchange rate of the US dollar (USD) in Indian Rupia (INR):
Spot rate: 1USD = 60 INR
The six-month forward rate is: 1USD = 65 INR.
The six-month interest rate in the US is 2% (on an annual basis) on March 1.

3b. If the actual exchange rate on September 1, 2018 is not 1 USD = 65 INR, but 1 USD = 75 INR, what is the change in the real exchange rate of the Indian Rupia? Has the real value of the Rupia increased or decreased?

Answer 18

3b. The real value of the rupiah has decreased by 65/75 – 1 = -0.13333 ( -13.33%)

Question 19

Suppose that you, as an entrepreneur, submitted a quote on 1 March for the delivery of a consignment of goods to an American customer. If the quote is accepted, you will receive $2 million over 6 months. To hedge the currency risk, you buy a 6 month option to sell dollars; the exercise price is € 0.87.
The dollar’s spot rate on March 1 is $1 = €0.83

4a. Calculate the revenue (payoff) for the entrepreneur on September 1 if the offer has been accepted and the dollar has been appreciated to $1 = € 0.90 on September 1.

Answer 19

4a. If the offer is accepted, then in 6 months, i.e. on September 1, $2 million will be received. The strike price of the option is then less favorable than the spot price on 1 September. You don’t exercise the option: the payoff is $2 million x 0.90 = $1,800,000.

Question 20

Suppose that you, as an entrepreneur, submitted a quote on 1 March for the delivery of a consignment of goods to an American customer. If the quote is accepted, you will receive $2 million over 6 months. To hedge the currency risk, you buy a 6 month option to sell dollars; the exercise price is € 0.87.
The dollar’s spot rate on March 1 is $1 = €0.83

4b. Calculate the payoff for the entrepreneur on September 1 if the offer is not accepted and the dollar is appreciated to $1 = € 0.90 on September.

Answer 20

4b. If the quote is not accepted, then no dollars will come in. The option also has no value, because you would rather sell the dollar at the spot price than at the strike price of the option. Payoff is 0.

Question 21

On April 1th, a company wants to hedge the interest rate risk on an existing loan of € 5 million based on 6-month EURIBOR + 0.5 for the next 6-month interest period with an FRA. The new interest period starts on July 1th.

To do this, the company purchases one of the following FRA’s from a bank (prices as of April 1th)

FRA Contract rate (%)

3 x 9 1.35
3 x 6 1.20

On July 1, the 6-month EURIBOR is 1.2%.

1. What amount is settled between the company and the bank on 1 July (the next settlement date) based on the FRA? Who will receive that amount?

Answer 21

6/12 x (0.15% van 5,000,000)/ 1.006 = 3,750/ 1.006 = 3,728.00.

The bank will receive this amount, because the contract rate (1.35%) is higher then the reference rate on July 1th (1.2%).

Question 22

A few years ago, a company took out a fixed-interest loan with an interest rate of 4% per year. The company wants to conclude an interest rate swap, which makes the interest rate on the combination of the swap and the loan variable. To do this the company can choose one of the following swaps, offered by its bank:

2. Which swap does the company conclude and what interest rate does the company pay on the combination of swap and loan?

Answer 22

2. The receivable swap. For the loan the company pays 4%. For the swap the company receives 1.7% and pays EURIBOR.
   On balance the company pays 4% - 1.7% + EURIBOR = EURIBOR + 2.3.

Question 23

On February 1th 2021, a Dutch exporter sells for $ 1,000,000 goods to an American customer. He will receive the amount 6 months later, on August 1th.
The following options will be available on the euro on February 1th via the exporter’s bank:

Type Duration Exercise price Premium
call 6 months $ 1.15 € 2.60
put 6 months $ 1.15 € 1.95

Contracts can be concluded for any amount. Exercise prices in pounds per euro, premium in euros per 100 euro.

The spot rate for the euro is $ 1.17 on February 1th, 2021.
At the time of settlement (August 1th 2021), the spot rate of the euro is:
1 € = $ 1.14.

Suppose the exporter chooses to hedge its currency risk by means of a currency option.

3. Which option should the exporter buy on February 1th, 2021?

Answer 23

3. Because the strike price is in dollars, these options give the right to buy or sell euros!
   Dollars will be received on August 1th. You want to sell it at a price that you agree on now. Selling dollars is buying euros, so a call option.

Question 24

On February 1th 2021, a Dutch exporter sells for $ 1,000,000 goods to an American customer. He will receive the amount 6 months later, on August 1th.
The following options will be available on the euro on February 1th via the exporter’s bank:

Type Duration Exercise price Premium
call 6 months $ 1.15 € 2.60
put 6 months $ 1.15 € 1.95

Contracts can be concluded for any amount. Exercise prices in pounds per euro, premium in euros per 100 euro.

The spot rate for the euro is $ 1.17 on February 1th, 2021.
At the time of settlement (August 1th 2021), the spot rate of the euro is:
1 € = $ 1.14.

Suppose the exporter chooses to hedge its currency risk by means of a currency option.

4.What is the cost for this option?

Answer 24

4. $ 1,000,000/1,15 = € 869.565/100 * 2.60 = € 22.609

Question 25

On February 1th 2021, a Dutch exporter sells for $ 1,000,000 goods to an American customer. He will receive the amount 6 months later, on August 1th.
The following options will be available on the euro on February 1th via the exporter’s bank:

Type Duration Exercise price Premium
call 6 months $ 1.15 € 2.60
put 6 months $ 1.15 € 1.95

Contracts can be concluded for any amount. Exercise prices in pounds per euro, premium in euros per 100 euro.

The spot rate for the euro is $ 1.17 on February 1th, 2021.
At the time of settlement (August 1th 2021), the spot rate of the euro is:
1 € = $ 1.14.

Suppose the exporter chooses to hedge its currency risk by means of a currency option.

5. How much are the net proceeds of the export transaction (in euros) on August 1th if the exporter hedges the exchange rate risk on this transaction on February 1th via a currency option?

Answer 25

5. $ 1,000,000/1.14 = € 877,193 – € 22,609 = € 854,584
   Exercise DOES NOT take place because the spot price on August 1th (1€ = $1.14) is more favorable than the exercise price at the time of settlement on August 1 (€1 = $ 1.15).
   Although you do not exercise, of course you already paid for the option, so you have to subtract these costs from you export proceeds.

Question 26

On January 1, 2021, company X has the following items on the balance sheet:

Inventory € 15 million
Receivables € 30 million
Payables € 10 million

In 2021, the company achieved a turnover (sales) of €165 million and the cost of goods sold were €130 million.

1. Explain in words what exactly is meant by the operating cycle of a company.

Answer 26

1. The total time (in days) between the purchase of raw materials and the final payment from the customer.

Question 27

On January 1, 2021, company X has the following items on the balance sheet:

Inventory € 15 million
Receivables € 30 million
Payables € 10 million

In 2021, the company achieved a turnover (sales) of €165 million and the cost of goods sold were €130 million.

2. Calculate the cash cycle for company X for 2021 (a year has 365 days).

Answer 27

2. cash cycle = inventory period + receivable period – payment period
   Cash cycle = 15/ (130/365) + 30/ (165/365) – 10/ (130/365) = 42.1 + 66.4 – 28.1 = 80.4 days.

Question 28

On January 1, 2021, company X has the following items on the balance sheet:

Inventory € 15 million
Receivables € 30 million
Payables € 10 million

In 2021, the company achieved a turnover (sales) of €165 million and the cost of goods sold were €130 million.

Company Y grants trade credit to its customers. The conditions are:

2/10 net 30.

A customer orders goods worth € 10,000

3. How much does the customer pay if he pays on day 10?

Answer 28

3. He gets a 2% discount ( = 200). He pays 9,800.

Question 29

On January 1, 2021, company X has the following items on the balance sheet:

Inventory € 15 million
Receivables € 30 million
Payables € 10 million

In 2021, the company achieved a turnover (sales) of €165 million and the cost of goods sold were €130 million.

Company Y grants trade credit to its customers. The conditions are:

2/10 net 30.

A customer orders goods worth € 10,000

4. What is the annual effective rate for the customer if he decides to make maximum use of his credit?

Answer 29

4. Rate = (full price – discount price) / discount price = (100 – 98)/ 98 = 0.020408
   Effective annual rate = (1+0.020408)365/20 - 1 = 1.02040818.25 -1= 0.4458 (= 44.58%).

Question 30

The company’s treasurer is not happy with the credit options the company offers. The current bad debt ratio (non-payment percentage) is currently 7%. By adopting a more stringent credit policy, the treasurer believes that the percentage of non-payment will be reduced to 5%, but that sales will fall by 5%. You can assume that the cost of good sold is 80% of the selling price.

5. Is it wise for the treasurer to implement the more stringent policy?

Answer 30

current policy more stringent policy
Sell 100 95
Non-payment 7 4.75
Cost 80 76
Profit 13 14.25

By pursuing a more stringent policy, the profit increases from 13 to 14.25, so a more stringent policy is recommended.

Question 31

Company Z has so far applied the principle of cash on delivery. The sales department called for granting trade credit to customers. The department believes this will attract additional customers, which will increase revenues.
The financial department examines whether it is desirable to provide the credit. It estimates that the extra income from granting credit amounts to € 14,000 and that the extra costs amount to € 11,000. The department also estimates that the customer’s chance of non-payment (default) will be 25%.

6. Show by means of a calculation whether it is wise to provide the credit, based on the assumptions of the finance department. You may assume that there is no possibility of repeat purchases by customers.

Answer 31

Credit is granted if the expected profit is greater than 0.

Expected profit = p(14,000 – 11,000) – 11,000 (1-p) = 0 (break even)
3,000p – 11,000 +11,000p = 0
14,000p = 11,000. p = 11,000/14,000 = 0.7857 (=78.57%).

So with a 78.57% probability of payment the profit is 0. If the probability of payment is higher then 78,57% the expected profit is greater than 0 and it is wise to grant the credit. If the probability of payment is lower then 78,57%, then a loss is expected. However, the probability of payment is 75% as expected by the finance department, so it is not wise to grant the credit.

Question 32

Company Z has so far applied the principle of cash on delivery. The sales department called for granting trade credit to customers. The department believes this will attract additional customers, which will increase revenues.
The financial department examines whether it is desirable to provide the credit. It estimates that the extra income from granting credit amounts to € 14,000 and that the extra costs amount to € 11,000. The department also estimates that the customer’s chance of non-payment (default) will be 25%.

7. To what extent will the decision made, based on the calculations in question 6, change if there is a chance of repeat purchases?

Answer 32

7. If there is a chance of repeat purchases, the decision to extend credit may well be made, because extending the credit can attract long-term, loyal customers, so that the extra revenue in the future may outweigh the extra costs .