Practice Set and Solutions #3

Transcription

1 /Bo Sjö Practice Set and Solutions #3 What to do with this practice set? Practice sets are handed out to help students master the material of the course and prepare for the final exam. These sets contain worked-out problems in corporate finance and investments, with a bias toward quantitative problems. These sets are not graded, and there is no need to hand-in the solutions. Students are strongly encouraged to solve them, discuss the solutions with other course participants, and discuss any problems with their teacher. Some questions in the final exam might resemble the problems given here. Question 1 Suppose that the Danish krona against the USD is quoted in American terms as What would the rate of the DKK against the USD in European terms? (Give four decimals, and write out both quotations in full.) Solution 1 If the American quote is USD /DKK the corresponding European quote is DKK5.7527/USD. Question 2 Suppose you have a direct quote for the Euro in Paris as a) What is the corresponding outright direct bid and ask quotes, and mid-prices in Paris and New York? (Write it out in full) b) Compute the percentage bid-ask spread in New York. (Hint use the ask as the base) Solution 2 a) The outright direct quote in Paris is the number of Euros it takes to sell or purchase one euro: Bid: EUR0.7710/USD Ask: EUR /USD In NY Bid: USD1.2953/EUR Ask: EUR /EUR. In NY you take the inverse of the Paris quotations and the bid becomes the ask and vice versa. The mid price in Paris is EUR0.7715/USD and in NY USD1.2915/EUR. b) The percentage bid ask spread in Paris is [( )/0.7720]*100 = %. In NY the spread is [( /1.2970)]*100 = % Question 3 The 3-month interest rate in Denmark is currently about 3.5%. Meanwhile, the equivalent interest rate in England is about 6.5%. All rates are annualized. What should be the 1

2 annualized 3-month forward discount or premium at which the Danish krone will sell against the pound? Solution 3 From covered interest rate parity (CIP), we know that the Danish krone (DKK) should sell at a premium against the pound approximately equal to the interest rate differential between the two countries, i.e., the krone should be trading at a premium of about 3% to offset the lower interest rate in Denmark. Precisely, let F and S stand for the GDP spot and T-day forward prices of 1DKK, respectively. Thus, GBP is the home currency in our example. Transform the simple yearly interest rates to effective 90 day rates. Without any further details use 30/360 convention. UK : r = 0.065/4 = DEN: r* = 0.035/4 = Then, the percentage forward premium is equal to: F S S = = => % In annualized terms we have 2.974%. We can also calculate the forward premium (forward discount due to the sign change) 1 1 F S 1 S = = 0.738% we say that the GBP would be trading at a forward discount against the Danish krona. Annualised the discount is * (360/90) = 2.952%. Question 4 The direct spot quote for the Canadian dollar in New York is $0.86 and the 180-day forward rate is $0.82. What accounts for the difference between the 2 rates? Explain. Solution 4 2

3 From IRP, we know that a country s currency (here, the USD is the home currency) will sell at a forward discount (F-S) < 0 when interest rates in that country are lower than in the other country (here, Canada). In this question, you need less USD to buy forward Canadian dollars than you do spot: thus, it must be that interest rates are lower in the US than in Canada. Question 5 Alpha and Beta Companies can borrow at the following rates. Alpha Beta Moody s credit rating ALPHA Beta Diff/Spread Credit rating (Moody s) Aa Baa Fixed rate 10.5% 12.0% 1.5% Floating LIBOR LIBOR+1% 1% Spread? a) Calculate the Quality Spread Differential QSD. b) Develop an interest rate swap in which both Alpha and Beta have an equal cost savings in their borrowing costs. Assume Alpha desires floating-rate debt and Beta desires fixed-rate debt. Solution 5 a) The QSD = (12.0% %) minus (LIBOR + 1% - LIBOR) = 0.5%, meaning they have 0.5% to split. In this 50/50 meaning 0.25% each. b) Each firm should borrow where they have their comparative advantage. Alpha needs to issue fixed-rate debt at 10.5% and Beta needs to issue floating rate-debt at LIBOR +1%. Alpha needs to pay LIBOR to Beta. Beta needs to pay 10.75% to Alpha. If this is done, Alpha s floating-rate all-in-cost is: 10.5% + LIBOR % = LIBOR -.25%, a.25% savings over issuing floating-rate debt on its own. Alpha borrows fixed at 10.5 hands over the loan/costs to Beta and charges fixed interest. At the same time they borrow the same amount floating => add up the net costs for Alpha. Beta s fixed-rate all-in-cost is: (LIBOR+ 1%) % - LIBOR = 11.75%, a.25% savings over issuing fixed-rate debt. Beta Borrows floating at LIBOR+1, and hand over the loan to Alpha and charges LIBOR from Beta 3

4 Question 6 Explain the difference between government bond yield and corporate bond yields. Solution 6 The difference is made up by a default risk premiums, such that the yield is higher for risky bonds than for default-free bonds. Question 7 Identify the two most important factors behind the credit risk ratings of bonds, and how they are used to give bond risk ratings. Solution 7 The two most important factors are the debt/equity ratio and interest payments/ EBIT (operating cash flow). Given these two and estimated probabilities of default from historical data leads to rating in terms of AAA, AA A, BBB etc, where each step along this ladder leads to an increase in the risk premium. Question 8 Förklara varför två på varandra följande 1-åriga obligationer borde ge samma totala avkastning som en 2-årig obligation. Solution 8 Utgå från lagen om ett pris (förväntningshypotesen). Givet att båda alternativen omfattar samma risk kommer rationella investerare att enbart välja det ena alternativet framför det andra om avkastningen skiljer sig åt för en löptid på två år. Utbud och efterfrågan kommer då att justera priset på obligationerna och därmed avkastningen så att alternativen blir lika attraktiva genom att ge samma totala avkastning. Question 9 You are given the following values from the spot yield curve. Use them to calculate the forward yield curve: - 1-year YTM (y1) 9 % - 2-year YTM (y2) 10 % - 3-year YTM (y3) 10,5 % 4

5 Calculate the implicit future value for the one-year interest rate one year from now. Solution 9 Let f2 be the implied forward rate, which equal to the expected future one-year short rate expected one-year in the future. Solve for f2 = implicit forward rate. Then, (1+y2) 2 = (1+r1) (1+f2) = > 1+y2 = [(1+r1) (1+f2)] 0.5 Since r1=9% och y2 = 10% we can solve for f2 = eller %. For the third year we have the implicit forward r3 as one-year (1+y3) 3 = (1+y2) 2 (1+f3) Giving f3 = (1.105) 3 /(1.10) 2 = /1.21 = => 11.50% The forward yield curve is therefore f1 = 9.00%, f2 = 11.01%, f3 = 11.50% If the expectations hypothesis holds these are also the expected future short rates. Question 10 What is exposure? How can operating exposure be measured? Discuss the determinants of operating exposure. What can you do about operating exposure Question 11 Discuss the implications of purchasing power parity for operating exposure. Solution 11 If the exchange rate changes are matched by the inflation rate differential between countries, firms competitive positions will not be altered by exchange rate changes. Firms are not subject to operating exposure. Question 12 General Motors exports cars to Spain but the strong dollar against the peseta hurts sales of GM cars in Spain. In the Spanish market, GM faces competition from the Italian and French car makers, such as Fiat and Renault, whose currencies remain stable relative to the peseta. What kind of measures would you recommend so that GM can maintain its market share in Spain. Solution 12 5

6 Answer: Possible measures that GM can take include: (1) diversify the market; try to market the cars not just in Spain and other European countries but also in, say, Asia; (2) locate production facilities in Spain and source inputs locally; (3) locate production facilities, say, in Mexico where production costs are low and export to Spain from Mexico. Question 13 What are the advantages and disadvantages of financial hedging of the firm s operating exposure visa-vis operational hedges (such as relocating manufacturing site)? Solution 13 Financial hedging can be implemented quickly with relatively low costs, but it is difficult to hedge against long-term, real exposure with financial contracts. On the other hand, operational hedges are costly, time-consuming, and not easily reversible. 6