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Find the first and second derivative of function f(x) at x=1.5 if:
Fewer than 10% of U.S. girls start to menstruate before 11 years of age, and 90% of all U.S. girls are menstruating by 13.8 years of age, with a median age of 12.4 years. This age at menarche is not much different (0.3 years earlier) than that reported for U.S. girls in 1973. Wikipedia
Assignment #01Marks =20
Risk, Return and Investment Decisions Investment decisions are supported by various factors including investor choice of risk appetite, return on investment and most important the market situation that is backed by supply and demand forces. The supply and demand impact is reflected in the market price of securities and guide investors to take a rational decision.Along with market forces, company specific information is also helpful in determining the fair price of an investment. Rational investor s consider both market and company specific information to choose among different investment options. Following information is available for the three stock and you have to choose the two from the three securities to construct a portfolio.
Required:Calculate required rate of return for three stock using SML Equation,if risk free rate of return is 10%.Calculate Fair value of three stocks using Gordon Growth Model.Based on fair price calculation, identify whether the stocks are undervalued or overvalued, justify your answer with reasoning.Considering the above calculations,if you want to construct the portfolio of two stock from the above mentioned three stock., which two stocks you will add in your portfolio and why?NOTE: Formula and complete working is mandatory in each part, provide complete calculations in order to avoid marks deduction.IMPORTANT NOTE: 24 hours extra / grace period after the due date is usually available to overcome uploading difficulties. This extra time should only be used to meet the emergencies and above mentioned due dates should always be treated as final to avoid any inconvenience.
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Required rate of Return of Stock A
r A = r RF + (r M – r RF ) β A
= 10% + (12% - 10%) 0.5
Required rate of Return of Stock B
r B = r RF + (r M – r RF ) β B
= 10% + (13% - 10%) 1.5
Required rate of Return of Stock C
r c = r RF + (r M – r RF ) β C
= 10% + (12.5%-10%) 1
Fair Price of Stock A
Po* = DIV1 / [(r RF + (r M – r RF) A) - g]
= 5/ [(10% + (12%-10%) 0.5)-4%]
5/7%=R s 71.43
Fair Price of Stock B
Po* = DIV1 / [(r RF + (r M – r RF) B) - g]
= 3/ [(10% + (13% - 10%) 1.5) – 6%
= 3/ 8.5%= R s 35.29
Fair Price of Stock C
Po* = DIV1 / [(r RF + (r M – r RF) C) - g]
= 6/ [10% + (12.5%-10%) 1) – 2%
= 6/10.5%= R s.57.14
Stock A is Undervalued as the fair price is more than the market price.
Stock B is Overvalued as the fair price is less than market price.
Stock C is Undervalued as the fair price is more than the market price.
The Stock A and Stock C should be used to construct the portfolio because of two reasons as the beta of Stock A and Stock C is less than Stock B. The required rate of return of Stock A is less than its market rate of return and required rate of return of Stock C is equal to its market rate of return while the required rate of return of Stock B is more than its market rate of return.
Binary Search Tree (BST) –
BST is a special type of binary tree in which left child of a node has value less than the parent and right child has value greater than parent. Consider the left skewed BST shown in Figure 2.
Searching: For searching element 1, we have to traverse all elements (in order 3, 2, 1). Therefore, searching in binary search tree has worst case complexity of O(n). In general, time complexity is O(h) where h is height of BST.
Insertion: For inserting element 0, it must be inserted as left child of 1. Therefore, we need to traverse all elements (in order 3, 2, 1) to insert 0 which has worst case complexity of O(n). In general, time complexity is O(h).
Deletion: For deletion of element 1, we have to traverse all elements to find 1 (in order 3, 2, 1). Therefore, deletion in binary tree has worst case complexity of O(n). In general, time complexity is O(h).