Chengyuan H.

Tutor for two years in Math, Computer, Chemistry and Physics

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GMAT

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Question:

At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale? A 33 B 34 C 35 D 36 E 37

Chengyuan H.

Answer:

the highest price top: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,....... we have 14 items with higher price than price of radio the lowest price top: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,....... we have 19 items with lower price than price of radio the total number of items = 14 (higher price) + 1 (radio) + 19 (lower price) = 34

Calculus

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Question:

f(x)=3xe^(2x-10) at x=5 find a linear approximation to the function at the given point.

Chengyuan H.

Answer:

We’ll need the derivative first as well as a couple of function evaluations. f'(x)=3e^(2x-10)+6xe^(2x-10) x(5)=15 x'(5)=33 There really isn’t much to do at this point other than write down the linear approximation. L(x)=15+33(x-5)=33x-150

Corporate Finance

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Question:

Bill Clinton reportedly was paid $10 million to write his book My Way. The book took three years to write. In the time he spent writing, Clinton could have been paid to make speeches. Given his popularity, assume that he could earn $8 million per year (paid at the end of the year) speaking instead of writing. Assume his cost of capital is 10% per year. a. What is the NPV of agreeing to write the book (ignoring any royalty payments)? b. Assume that, once the book is finished, it is expected to generate royalties of $5 million in the first year (paid at the end of the year) and these royalties are expected to decrease at a rate of 30% per year in perpetuity. What is the NPV of the book with the royalty payments?

Chengyuan H.

Answer:

a) NPV=10-8/0.1[1-1/(1.1)^3]=-9.895 million b) First calculate the PV of the royalties at year 3. The royalties are a declining perpetuity: PV5=5/[0.1-(-0.3)]=5/0.4=12.5 million So the value today is PV=12.5/1.1^3=9.9391 Now add this to the NPV from part a), NPV= -9.895+9.391=-$503,381

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