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valina [46]
3 years ago
8

Davita Spencer is a manager at Half Dome Asset Management. She can generate an alpha of 2% a year up to $100 million. After that

her skills are spread too thin, so she cannot add value, and her alpha is zero. Half Dome charges a fee of 1% per year on the total amount of money under management (at the beginning of each year). Assume that there are always investors looking for positive alpha and no investor would invest in a fund with a negative alpha. In equilibrium, that is, when no investor either takes out money or wishes to invest new money, a.What alpha do investors in Davita’s fund expect to receive? b.How much money will Davita have under management? c.How much money will Half Dome generate in fee income?
Business
1 answer:
Dmitriy789 [7]3 years ago
6 0

Answer:

a.  Zero

b. $200 million

c. $2 million

Explanation:

a. The investor invest regular in portfolio with the positive alpha until the portfolio size has driven alpha to zero.

 

b. Davita return 2% of $100 million = $2 million

1% fee \times X million total under management.

Than, X = $200 million

c. $200 million \times 1% fee given = $2 million

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The present value of a prospective sum of money or cash flow stream given a specified return rate is known as its present value (PV). The present value of future cash flows is reduced by the discount rate, and the higher coupon rate, the lower the present value of future cash flows. The key to correctly valuing future cash flows, whether they are earnings or debt obligations, is determining the appropriate discount rate. The concept of present value states that a quantity of funds today is worth greater than the same amount in the long term. In other words, money gained in the long term is not as valuable as money received today.

The present value of a deferred perpetuity that pays $141 annually with the first payment occurring at year 5 is $1,938.89. This can be calculated by taking the present value of an ordinary annuity formula, which is PV = A / (1 + r)^n, and adding 5 to n. This gives the equation PV = A / (1 + r)^(n + 5), which can be simplified to PV = A / (1 + r)^n * (1 + r)^5. Thus, the present value is $141 / (1 + 0.06)^10 * (1 + 0.06)^5, which equals $1,938.89.

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