Finance 2017 eksamen PDF

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RUC Corporate Finance Re-Exam Fall 2016

4 hours written exam Open Book

Remarks: 1) It is not allowed to connect the internet during the exam. 2) The exam consists of 4 questions. A percentage is given to each question, which is a guidance concerning their weights on the total points. 3) If you need to supply further assumptions, please make clear what you assume. Good Luck!

Problem 1 (25%) - Suppose you are 25 years old and start thinking about your pension fund. You plan to go in pension when completing 65 years old. The idea you have is that the earlier you start contributing to your fund, the less you will need to pay monthly in order to receive a pension monthly income of 25,000 DKK, the minimum you believe is needed for surviving. If the discount rate on pension funds equals 5% per year compounded monthly and your life expectancy is 85 years, answer the following questions (ignore taxes to ease calculations): a) What is the monthly effective rate for this problem? r=5%/12 =0.4166% b) How much money do you need to have in your fund the day you go in pension in order to receive the 25,000 DKK per month until you die? C 1 C C 1  C r PV C     t   t  r r r r r r r r )t    (1 ) (1 ) (1   C 25, 000 C 25, 000 r 0.004167  PV    PV 3, 788,132 PV   r (1  r ) t 0.004167 (1  0.004167) 20*12

c) If you make equal payments every month, how much will your monthly contribution need to be in order to achieve the amount you calculated in “b”?  (1  r ) t 1  C C    (1 r )t  FV of Annuity C  r r r  r 40*12  (1  0.004167)  1 3, 788,132 C     C  2, 482DKK 0.004167 0.004167  

d) Suppose now that you expect to receive a gift from your company in your 55 years old birthday of 500,000 DKK, which when received will be invested in the pension fund immediately. What would the new fixed value for your monthly contribution be in this case? 10 years invested in the fund 500,000 * (1.004167)^120 = 823,504.75 So, you will need to contribute with monthly payments in order to pay the rest: 3,788,132-823,504.75=2,964,628.08

 (1  r ) t 1  C C    (1 r )t  FV of Annuity C  r r r  r  (1  0.004167)40*12  1  2,964,628.08 C    C 1942.72DKK 0.004167 0.004167  

e) Reflect upon the beauty of compounded interest, explain the concept of time value of money and show how they are important in this exercise.

Problem 2 (25%) - Luthor Enterprises consider the implementation of an uncertain investment with duration of one year. The table below gives 3 possible cash flows for the uncertain investment according to the states of the economy. Suppose that the investment has an implementation cost of DKK 100,000,000 and that WACC is 10% per year. State

State Probability

Cash Flow (in DKK) in the end of the year -200,000,000

Recessio 0,20 n Normal 0,50 400,000,000 Boom 0,30 500,000,000 Assume that the investor is risk neutral, which implies that you can perform calculations of risky cash flows in expected values without taking into consideration any risk aversion measurements. a) Calculate the expected cash flow of this investment in the end of the year. Expected cash flow after 1 year: 0,2*(-200,000,000) + 0,5*400,000,000 + 0,3*500,000,000 = 310,000,000

b) Calculate the NPV of this investment using the WACC as discount rate. Present Value of 310,000,000 = 310,000,000/1,1 = 281,818,181 NPV = 281,818,181 – 100,000,000 = 181,818,181

c) Would you recommend the firm to make this investment? Explain your answer with your own words.

d) Immediately after implementing the investment, Mr. Fox, representing the Wayne Enterprises contacts you and says that his company is interested in buying 20% of this investment. How much is the minimum price you would consider for selling 20% of this investment to Mr. Fox? 20% * 181,818,181 = 36,363,636

e) Is it recommendable to use the overall WACC to discount the cash flows of this investment? Explain the problems associated to this decision. Problem 3 (25%) - Your friend asks you to give him a piece of advice related to which of the two stocks he should buy to save for his pension. The table below summarizes the information concerning these two stocks. Dividend just paid Stock 1 Stock 2

DKK 5.00 DKK 5.00

Expected annual growth forever 0 1%

a) What should be the “fair” price of stock 1 if the investor’s required return in this type of stocks is 10%.

P1 

5 D1  50 R 0.10

b) Calculate the fair price for stock 2 using the same required return you used in “a”.

P2 

D1 51.01  56.1111 R  g 0.10  0.01

c) In the market, stocks 1 and 2 are being sold for the same price of 52DKK each. Would you buy any of these stocks? d) You find out that the table above is not fully correct, since stock 2 is actually expected to grow 5% in the first 2 years and only afterwards 1% forever. Calculate in this case the “fair” price for stock 2. Would you buy stock 2 according to this new scenario? Explain.

First Way: P0 

D0 1  g1  D0 1  g1  D0 1  g2  (1  g1)t t 1 1   1  g 1 t R g –    R – g1   R – g1  1  R t 1  R  2

5  1.05  5  1.05  1 5 1.01 (1.05) 1    1.05 2  10% – 5%  10% – 5%  1.10  2  10% – 1%  1.10 2

P0 

2

P3 60.4545 Second Way: D D2 P3t 2 P3t 0  1  2  2 1  R  1  R  1  R 5 1.052 1.01 61.8625  10% 1% 5 1.05 5 1.05 2 61.8625    60.4545 P3t 0  2 2 1.10  1.10  1.10 t 2

P3

e) Supposing that your friend wants to use all his money to buy one of these stocks, what concepts related to systematic and unsystematic risk that you learned at RUC should you explain to him? Please explain with your own words the connection between risk, systematic risk, unsystematic risk and required rate of return as discussed in class.

Problem 4 (25%) - You are willing to make a valuation of Novo Nordisk. Answers the following questions according to the table below: Observed D/E 40% Long term D/E 50% Rd 5% t 30% EBIT 10,000,000,000 forever Rf 1% Rm 5% Beta 2 “D” is the market value of debt, “E” is the market value of equity, “Rd” is the cost of debt before taxes,” t” is tax rate, “EBIT” is earnings before interest and taxes, “Rf” is the risk free rate, “Rm” is the market return of the stock index and “Beta” is a measurement of systematic risk of the company. Assume that both depreciation and net-investment (replacement) are zero, the company has no current assets and no current liabilities and that it will add nothing to retained earnings in the future. All net income is paid out as dividends. a) What beta value should you use in order to calculate the cost of equity capital of Novo Nordisk? Explain with your own words your calculations.

 2   u  1.5625 u   1  1 t  D / E   1  0.7 0.4   u * 1  1  t  * D / E     1.5625 * 1  0.7  *0.5  2.1093

b) Calculate the cost of equity capital “Re” of Novo Nordisk.

R e R f    R m  R f  R e 1%  2.1093  5%  1%  9.4375% c) Calculate the weighted average cost of capital (WACC) of Novo Nordisk.

D D E 1 2 50%     E D E 3 D E 3 E D WACC  * Re  * R D 1  t  DE D E 2 1 WACC  *9.4375%  *5% 1 0.3  7.4583% 3 3 d) What is the total value of the company? What is the value of debt? What is the value of equity?

EBIT (1 t ) 10, 000, 000, 000(1 0.3)  93,864,135,017DKK WACC 7.4583% E 93,864,135,017*2 / 3 62,576,090,011

V

D 93,864,135,017 *1/ 3 31, 288, 045, 006 e) What would be the total value of Novo Nordisk if its entire capital were only financed by equity? V = VU + t D 93,864,135,017 = VU + 0.3(31,288,045,006)  Vu = 84,477,721,515

f)

Does the choice of capital structure influence the total value of the company in the presence of taxes? What can you observe in this exercise? Explain with your own words. Hint: You can answer this question without the answers of the prior ones....