FIN8202 S FINAL EXAM. Assume the following information is available for the United States and Europe:

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1 FIN8202 S FINAL EXAM Question 1 (10 marks) Assume the following information is available for the United States and Europe: US Europe Nominal Interest rate 4% 6% Expected Inflation 2% 5% Spot rate $1.13 One-year forward rate $1.10 a) Does IRP hold? b) According to IFE, what is the expected spot rate of the Euro in one-year? c) According to PPP, what is the expected spot rate of the Euro in one-year? d) Reconcile your answers to parts b) and c). (2.5 marks) (2.5 marks) (2.5 marks) (2.5 marks) a) Difference in interest rates = 2% Forward premium = [( ) /0.9091] x 100 = -2.65% IRP doesn t hold. b) Approximate formula ( S2)/S2 = S2 = /$ or $1.1525/ Accurate formula: ( S2)/S2 = ( )/1.06 S2 = /$ or $1.1513/ c) S2 = S1 (1.05/1.02) = /$ or $1.0977/ d) Nominal interest rates do not follow real rate + inflation; Future spot rates implied by IFE and PPP do not match. Possibly due to intervention by central bank to fix interest rates. Question 2 (12 marks) On 29 January 2008, the quoted price on the March day bank bill futures contract was Penny believed that interest rates would fall over the next week. Suppose that she bought 5 contracts on 29 January 2008 and closed out her position on 5 February 2008 at a price of Ignoring transaction costs, how much has Penny made or lost?

2 The purchase, on 29 January 2008, is at a quoted price of This provides an annual yield of = 7.33%. Using Equation 18.10, the contract price is: $ (0.0733)(90 / 365) $ The closing out, on 5 February 2008, is at a quoted price of This provides an annual yield of = 7.45%. The contract price is: $ (0.0745)(90 / 365) $ Penny will make a loss of $ $ = $ on each contract. On 5 contracts she will lose $ = $ Question 3 (10 marks) Determine the expected share price of the following companies using the dividend growth model. Assume that a cost of equity of 10% is applicable. (a) (b) (c) ABC Ltd has current earnings of $4 per share. It does not reinvest any of its funds and therefore is not expected to show any earnings growth in the foreseeable future. DEF Ltd is a fast-growing company with current earnings of 90 cents per share. These earnings have been growing at a rate of 6% p.a. but only 30% of earnings are paid out as a dividend. GHI Ltd has current earnings of $1 per share and a dividend payout ratio of 50%. It is expected that earnings will grow at the rate of 6% p.a. for the next three years and then level off (i.e. revert to zero growth). (a) d P t r e $40.00

3 (b) Next year s EPS (EPS1) is found using the growth rate (g). EPS EPS 1 g 1 0 Next year s dividend (d1) is equal to EPS1 multiplied by the payout ratio. d 1 EPS1 We can use these equations to modify the equation for the value of a share under the constantdividend growth model. g d EPS Pt $7.16 r g r g e e (c) After three years the dividends settle down to a perpetuity, and we can use the constant-dividend model. The first three dividends are not part of the perpetuity and must be treated separately. The price of the share will be the present value of each of the first three dividends, plus the present value of the perpetuity that begins with the fourth dividend. These dividends can be represented using the following diagram. PV? d1 d2 d3 d First three dividends to be treated separately Perpetuity that begins with d 4 Note that d4 is the first cash flow of the perpetuity. Since payments under a perpetuity occur at the end of each period, the first period of the perpetuity goes from year 3 to year 4. Year 3 is the beginning of the perpetuity. Hence, the perpetuity is deferred by 3 periods, and the present value of the perpetuity must be discounted by 3 periods to year 0. Another way of looking at this is to consider that if a perpetuity is not deferred, the first payment is at period 1. Since in this case the first payment of the perpetuity is at period 4, instead of period 1, the perpetuity is deferred by 3 periods. We need to calculate the values of d0 (using the current EPS and the payout ratio), and then d1, d2, d3 and d4 (using the applicable growth rates). Note that we need d0 in order to calculate subsequent dividends, but d0 is not a future cash flow and therefore is not part of the value of the share. d EPS $ d d 1 g $0.53 d d 1 g $ d d 1 g $ d d $0.5955

4 d 4 Note that represents the present value of the perpetuity as at the beginning of the re g perpetuity period Period 3. That s why is must be discounted by 3 periods to year 0. PV d d d d re re re re g re $ PV? First three dividends to be treated separately Perpetuity that begins with d 4

5 Question 4 (12 marks) In late March, the owner of a small manufacturing business has decided to expand operations. It is decided that the business needs to borrow about $3 million in late June to fund the initial expansion. It is further decided that this initial borrowing will be for a period of about three months, and will be in the form of a draw-down of bank-accepted bills. Given the risk associated with expansion, it is critical that borrowing costs are minimised. With this in mind, it is decided that the future borrowing should be hedged. Current market rates have been identified as: (physical) 90-day bank bills 7.5%; June BAB futures 92.2; September BAB futures What hedge transaction should be opened now (late March)? What is the overall borrowing cost (in % p.a.) if the hedge position is held until late June, when the draw-down of bills occurs? Assume that, in June, market rates are: (physical) 90-day bank bills 6.25%; June BAB futures 93.7; September BAB futures The appropriate hedge is a short position in three June BAB futures contract. We require a short position because we are concerned about increases in interest rates. If interest rates increase, the value of bank bills (and BAB futures contracts) will fall, enabling the short position to be closed out at a cheaper price, and resulting in a profit in the futures market that will offset the loss in the physical market. We require June contracts because that is when the borrowing will be undertaken. It is June interest rates that will determine the cost of borrowing (in the absence of hedging). We require three contacts because the size of each contract is $3m. If less than $3m is ultimately borrowed, there will be some residual risk associated with the difference between the size of the contracts and the amount borrowed. However, this is sometimes unavoidable due to the standardisation of futures contracts.

6 If bank bills with a face value of $3 million are issued in June, at an interest rate of 6.25%, the proceeds of the loan are given by: 3,000,000 Value of opening position $2, 954, The gain or loss from the futures position is the difference between the value of the contracts at the beginning of the hedge (March) and when the position is closed out (June). The value of the futures position in March is based on the quoted price of the June futures contract in March, which is This implies a yield of 7.8%. 3,000,000 Value of opening position $2, 943, ,000,000 Value of closing position $2, 954, Loss $2,954,110 $2,943,390 $10,720 This result needs to be subtracted from the proceeds of the loan. Hence the net proceeds are $2,954,469 $10,720 = $2,943,749. The borrowing cost in dollar terms (the difference between the net proceeds of the loan in June and the amount that needs to be repaid in September) is $3,000,000 $2,943,749 = $56,251. The borrowing cost as a percentage over the 3-month borrowing period is equal to the borrowing cost in dollar terms divided by the amount that is borrowed - i.e. the net proceeds of the loan: $56, 251 $2,943, % The borrowing cost as a percentage per annum is found by annualising the 3-month borrowing cost. This is achieved by dividing by 90 and multiplying by 365: % 7.75% 90 The hedge has locked in a borrowing cost that is approximately equal to the bank bill rate in March. Although the owner of the business was concerned about interest rates increasing, they have in fact fallen. The resulting profit in the physical market is offset by a loss in the futures market. The ultimate borrowing cost is not precisely the same as the bank rate in March because futures contracts don't necessarily move by exactly the same amount as the underlying physical rate. Any variation results in a small amount of residual risk, which is called basis risk.

7 Question 5 (10 marks) (a) How is minimum capital requirements of a bank computed according to the framework of Basel II? (b) Explain with an example the term operational risk in the context of a bank. (a) Banks are supervised and regulated by APRA and are subject to stringent regulation. They need to hold capital against credit, market and operational risk exposures. Minimum capital requirements in Australia follow the guidelines of the Basel II Capital Adequacy Accord. Banks need to hold capital based on their credit risk, operational risk and market risk. In Australia, the regulatory authority, APRA, financial institutions that seek to use the advanced internal ratings approach use advanced measurement approach for assessing operational risk. The soundness and validity of these models needs to be validated by APRA. (b) Operational risk is defined by the Basel committee as the risk of loss resulting from inadequate or failed internal processes. Example: Mr. Jérôme Kerviel, a rogue trader from the French Bank Société Générale conducted a series of high-risk trades and managed to conceal them from his managers. He racked up a total loss of $7.6 billion. This is an example of operational risk losses arising from failed or inadequate internal control processes. Question 6 (12 marks) Using the supply-and demand framework for bonds framework, explain the impact of the following events on interest rates: a) decrease in the volatility of gold prices b) increase in people s expectations of future real estate prices c) increase in overall riskiness of corporate bonds

8 Solution: a) Gold can be considered to be an alternate investment to bonds. When gold prices are less volatile, they appear less risky to investors compared to bonds. So, the demand for bonds fall, the demand curve shifting to the left. Bond prices fall, implying higher interest rates. b) Real estate can be considered to be an alternate investment to bonds. When real estate is more attractive to investors compared to bonds, the demand for bonds fall. The demand curve shifts to the left. Bond prices fall, implying higher interest rates. c) When corporate bonds become more risky compared to alternate assets, the demand for these bonds will fall in the equilibrium. The demand curve shifts to the left. Bond prices fall, implying higher interest rates in the corporate bond sector. Treasury bonds will now look safer, their demand will increase resulting in lower risk-free rates. Question 7 (10 marks) Suppose the 90-day bank bill reference rate is 6.35%. BNZ bank accepted a company s 90-day bills with a face value of $20 million and charged fees of $ Calculate the borrower s interest rate. Solution: The borrower s interest rate is the difference between the redemption payment and the net proceeds expressed as an annual rate of simple interest, calculated as follows: $20 m P $19,691, * $20m 365 r % $19,691,677 52, Question 8 (12 marks) What is meant by the following terms? (a) Agency costs (b) Information asymmetry (c) Adverse selection During the recent global financial crisis, explain the role played by agency conflicts, adverse selection, and information asymmetry.

9 i) Credit rating agencies consulted with firms on structuring products to achieve the highest rating. They also rated the firm s products, creating a clear conflict. Thus investors faced information asymmetry with respect to the credit quality of instruments they were purchasing. ii) During the financial crisis fewer banks operate. Information about the creditworthiness of several firms disappears. This results in a severe adverse selection problem. Existing banks are wary of lending to firms further exacerbating the crisis. iii) Agency problems in mortgage markets was a major factor in the US subprime lending markets: Mortgage originators did not hold the actual mortgage, but sold the note in the secondary market Mortgage originators earned fees from the volume of the loans produced, not the quality In the extreme, unqualified borrowers bought houses they could not afford through either creative mortgage products or outright fraud (such as inflated income) End of Examination