1 SOLVAY BUSINESS SCHOOL André Farber Mrs Xuan

Ms Xuan, the well known movie star, is confronted with financial problems that make her very nervous. She is about to meet her banker, M. Nguyên Tien in order to analyze the various solutions to the problems that worry her. Ms Xuan currently has $ 300,000 on her bank account at the FRBV (First Regional Bank of Vietnam). Her income for next year will be $ 220,000. She wonders how much she could afford to spend this year. In fact, she has recently realized (who knows how ?) that her preferences are correctly captured by the following utility function: U(Q0,Q1) = 2ln(Q0 )+ln(Q1) where Q0 and Q1 represent the amounts that she will spent this year (period 0) and next year (period 1). The current interest rate is 10% and M. Nguyên Tien has declared that his bank would be willing to lend her money at this rate. Several questions worry Mrs Xuan: 1. what budget constraint does Mrs Xuan face ? (provide the equation and the graphic) 2. if she decides to spend the same amount each year, how much will she consume? Is this a better plan than spending each year the total amounts available? 3. how much should she consume this year and next year ? (Hint: a relative of Ms Xuan, who studied economics, told her that in order to maximize her utility, she should choose Q0 = W/1.5 and Q1=Q0(1+r)/2) 4. what financial operations should she engage in, in order to achieve her optimal consumption pattern ? Mr Nguyên Tien has mentioned an investment proposal made by one of his clients. This person is willing to sell a building located downtown Hanoi for a price of $ 200,000. According to real estate experts, the value of this building will increase during the coming year and, in one year from now, it could be sold for $ 250,000. 5. what is the net present value of this proposition ? What should Mrs Xuan do ? 6. what would be the wealth of Mrs Xuan if she accepts this proposal ? 7. what would be the impact of the proposal on her pattern of consumption ? Will she be forced to restrict her current consumption in order to finance the purchase of the building ? In fact, M. Tien has suggested the creation of a company, Hanoi Estate, in order to purchase the building. The company would be liquidated after one year. A first solution would be to finance the company solely with shares. The capital of the company would be represented by 100,000 shares, each of them issued at $ 2. The shares will be listed on the Stock Exchange immediately after the purchase of the building. 8. at what price will the shares be quoted on the Stock Exchange ? 9. what will be the market value of the company ? 10. what will be the gain for the shareholders from this operation ? Another solution would consist in borrowing $ 100,000 and issuing 50,000 shares at $2 per share. 11. what dividend will shareholders receive in one year from now ? 12. at what price will the shares be quoted ?

Vietnam Xuan May 4, 2018 2 13. what are the market values of equity, of debt and of the company ? 14. what will be the gain for the shareholders from this operation ? As a matter of fact, just after the creation of the Hanoi Estate, Ms Xuan has been informed by a real estate agents that several buildings are for sale in Hanoi. He provided a list with the current purchase price and the resale value in one year.

Building Price today Value in 1 year A $ 100,000 $ 130,000 B $ 100,000 $ 115,000 C $ 100,000 $ 110,000 D $ 100,000 $105,000

15. What should Ms Xuan do?

Vietnam Xuan May 4, 2018