Question (1): Assume a two-stock portfolio with $70,000 invested in Du Telecom C
ID: 2788698 • Letter: Q
Question
Question (1):
Assume a two-stock portfolio with $70,000 invested in Du Telecom Company and $30,000 invested in Etisalat Company.
Estimated Return
Economy
Probability
Du Telecom (ri)
Etisalat (ri)
Portfolio(ri)
Strong
0.40
44%
20%
35 %
Normal
0.40
14%
30%
25 %
Weak
0.20
-16%
-20%
-9 %
Total
1.00
a) Calculate the expected rate of return for Etisalat stock (RE).
b) Assume the expected rate of return for Du Telecom (RD) is 20%; calculate the expected rate of return for the portfolio (sp).
c) Calculate the standard deviation (sE) for Etisalat stock.
d) Calculate the standard deviation (sp) of returns for the portfolio.
e) Assumes the standard deviation (sD) for Du Telecom is 22.45%, is it less risky to invest in the previous portfolio rather than investing in each stock separately? Explain
Question (2):
2.1) Calculate the present value of an annuity stream that pays $15,000 every year for 5 years on the last day of each year if your investment pays 20% compounded quarterly?
2.2) Calculate the future value of $19,000 invested today for 6 years if your investment pays 4% compounded annually
2.3) Calculate the future value of an annuity stream that pays $3,000 every year for 5 years onthe last day of each year if your investment pays 10% compounded semi annually?
Question (3):
AL-Futtaim Corporation has issued bonds that have 8% coupon rate, payable annually. The bonds mature in 7 years, have a par value of $1,500 and a yield to maturity of 12%. Calculate the price of the bonds.
Estimated Return
Economy
Probability
Du Telecom (ri)
Etisalat (ri)
Portfolio(ri)
Strong
0.40
44%
20%
35 %
Normal
0.40
14%
30%
25 %
Weak
0.20
-16%
-20%
-9 %
Total
1.00
Explanation / Answer
Question 2.1) Solution :- Present value of annuity stream = 15000 / (1 + 0.20 / 4)5 * 4
= 15000 / (1 + 0.05)20
= 15000 / (1.05)20
= 15000 / 2.6533
= $ 5653.34 (approx).
Conclusion :- Present value of an annuity stream = $ 5653.34 (approx).
Question 2.2) Solution :- Future value = 19000 * (1 + 0.04)6
= 19000 * (1.04)6
= 19000 * 1.2653
= $ 24040.70 (Rounded off to $ 24041)
Conclusion :- Future value = $ 24041 (approx).
Question 2.3) Solution :- Future value = 3000 * [ (1 + 0.10 * 6 / 12)5 * 12 / 6 - 1 ] / (0.10 * 6 / 12)
= 3000 * [ (1 + 0.05)10 - 1 ] / 0.05
= 3000 * [ (1.05)10 - 1 ] / 0.05
= 3000 * (1.6289 - 1) / 0.05
= 3000 * 0.6289 / 0.05
= 3000 * 12.578
= $ 37734 (approx).
Conclusion :- Future value = $ 37734 (approx).
Question 3). Solution :- Price of bond = 1500 * 8 % * [ 1 - (1.12)-7 ] / 0.12 + 1500 / (1.12)7
= 120 * [ 1 - 0.4523 ] / 0.12 + 1500 / 2.2107
= 120 * 0.5477 / 0.12 + 678.52
= 547.70 + 678.52
= $ 1226.22 (approx).
Conclusion :- Price of bond = $ 1226.22 (approx).