1.Which will be the value of 100 rubles at the end of 2years if the APR is 4%?
𝐹𝑉 = 100 ⋅ (1 + 0.04)2 = 108.16
2. Estimate the Profitability Index of a project that last for 5 years, it IRR is 5%, its NPV is 1000
and the investment is 500.
𝑃𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝐼𝑛𝑑𝑒𝑥 =
𝑁𝑃𝑉
1000
=
=2
𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡
500
3.Consider a zero-coupon bond with a $1000 face value and ten years left until maturity. If the
bond is currently trading for $459, which is the yield to maturity on this bond?
$459 =
$1000
⇒ 𝑌𝑇𝑀 = 8.098%
(1 + 𝑌𝑇𝑀)10
4.If the stocks of Company Aaretradedat €3.60 per share today and is expected to sell them for
€4.00 one year from now, what is the expected return if the dividend one year from now is
forecasted to be €0.60? Which is the capital gain? Which is the dividend yield?
𝑃0 = €3.6, 𝑃1 = €4.00, 𝐷𝑖𝑣1 = €0.6
𝑟=
𝑃1 + 𝐷𝑖𝑣1 − 𝑃0
4 − 3.6
0.6
= 27.78%; 𝑌𝑐𝑎𝑝𝑖𝑡𝑎𝑙 =
= 11.11%; 𝑌𝑑𝑖𝑣 =
= 16.67%
𝑃0
3.6
3.6
5. Having a portfolio composed by securities A and B, distributed 20% in A and the rest in B. The
expected return for A is 10% and for B 15%. Knowing that the total risk of A is 10% and that of
B is 5%, and that the Covariance between A and B is 0.05, calculate the return and risk of the
Portfolio.
E(portfolio) = 1.1 ⋅ 0.2 + 1.15 ⋅ 0.8 = 1.14 ⇒ 14%
𝑅𝑖𝑠𝑘 = 𝜎(𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜) = √(0.22 ⋅ 0.12 + 2 ⋅ 0.8 ⋅ 0.2 ⋅ 0.05 + 0.82 ⋅ 0.052 ) = 13.42%
6. Write the expression of Markowitz model of portfolio theory.
7. Considering CAPM, which would be the expected return of the stocks of a company that its
covariance with the market is 0.5. The risk-free asset has a return of 2% and the market has an
expected return of 8% and a total risk of 0.4.
8. You estimate the Beta of MSFT for the period 2013-2017. The value of that beta is 1.0087. The
R2 of the regression is 0.2033.What is interpretation of the R2?
9. What is the underwriter in an initial public offering?
10. What does the Dividend Irrelevance Theory say?