FINANCE 100 Corporate Finance

Transcription

1 FINNCE 100 Corporate Finance Professor Roberts Solutions to Sample Quiz # NME: SECTION: Question Maimum Student Score Question 1 50 Question 50 TOTL 100 Instructions: You may bring one inch sheet of paper to the eam with writing on both sides. Round all numbers to the 0.01 place. Show all work, but keep your answers brief. Please check that the eam contains 5 pages including cover. Good luck. 1

2 Question 1: (50 points) Consider the following information concerning the epected return and standard deviation of two stocks: Epected Return Standard Deviation Stock 8% 30% Stock 16% 0% a) Compute the epected return and standard deviation of a portfolio that is 70% invested in stock (and therefore, 30% invested in stock ) assuming the correlation between the asset returns is 0.3. (0 points) nswer: The epect return on the portfolio, E ( R P ), is: ( R ) E P, that is, 10.4%. The variance of the portfolio, V ( R ) P, is: ( 0.70 )( 0.30) + ( 0. ) ( 0. ) + ( 0.30)( 0.70)( 0.30)( 0.0)( 0.3) V ( ) The R P standard deviation is therefore by: ( ) SD, that is, 0.04%. R P b) What is the standard deviation of the global minimum variance portfolio and what are the corresponding portfolio weights? (0 points) nswer: We know that the weights in the global minimum variance portfolio are given by: σ ρ σ σ 1 σ + σ σ σ, ρ, ( 0.0) ( 0.30)( 0.30)( 0.0) ( 0.30) + ( 0.0) ( 0.30)( 0.30)( 0.0), Hence, we get: Therefore, the variance of the global minimum variance portfolio is: Var ( ) R MVP ( ) ( 0.0)( 0.30) 1 ( 0.3) ( 0.30) + ( 0.0) ( 0.0)( 0.30)( 0.3)

3 and the standard deviation is just: ( ) SD, that is, 14.04%. R MVP c) Sketch the mean-variance frontier, being sure to label both aes and identify the location of assets and. Eplain if there are gains to diversification, as defined in class? Please be brief! (10 points) nswer: Yes. There are gains to diversification. The MVP weights are both positive, implying a backward bending mean-variance frontier. Thus, it is possible to move from a low return asset (stock ) to a higher return, while decreasing risk (standard deviation). n Epected Retur sset sset Standard Deviation 3

4 Question : (50 points) You have recently been hired by Gold-in-Sacks, Inc. The job starts immediately and you will be paid monthly, with a starting salary of $7,000 per month (you receive your first payment eactly one month from today). You epect your salary to increase at the rate of 4% p.a. throughout your career, and you plan to retire in 30 years. Specifically, in your first year of employment you will receive 1 monthly payments of $7,000. In your second year, you will receive 1 monthly payments of $7,80 ($7, ), and so on. The appropriate discount rate is 1% p.a. compounding monthly. Compute the present value of your future income as of today. [HINT: Think of your annual salary as a 30-year growing annuity. egin by calculating the value, as of one year from today, of the first 1 monthly payments. Once you have computed that end-of-year value, consider it to be the first payment of an annual, growing annuity.] (50 points) a) Calculate the value, as of one year from today, of the first 1 monthly payments. (0 points) nswer: We begin by calculating the future value of the first 1 monthly salaries. This is done using the formula for the future value of an annuity. Recall that the PR is equal to 1% so that with monthly compounding we obtain and effective monthly rate equal to 1%. The future value is therefore equal to: 7,000 ( 1.01) 1 1 $88, b) Using your result from a), calculate the present value of your total projected future income. (30 points) nswer: Since we will consider the end-of-year salary values, we need to make sure that we have the appropriate discount rate that prevails over one year. Since the effective monthly rate is 1% we calculate the effective annual rate as follows: 4

5 1 ( 1.01) , that is, 1.685%. The easiest way to obtain the present value of the 30-year growing annuity is to first calculate the present value as if it etends forever and then deduct from it the portion of salaries beyond year 30. Hence, the present value of the annual salaries that last forever is given by the constant growth formula: P 88,777, , forever 1,0, Since we need to deduct from this present value the salaries beyond year 30 we need to determine the value of these additional salaries. The future value of the monthly salaries 30 for the 31 st year is given by:,777.5( 1.04) 87, value, in year 30, of those salaries that are never earned is: P 87, , forever The present value of P, forever 88. Consequently, the present 3,316, is 3,316, , ( ) Finally, the correct present value that does not include the salaries beyond year 30 is: 1,0, ,38.1 5