Question

14) You are evaluating a closed-end mutual fund and see that its price is different from its net asset value (NAV).

The fund has an expense ratio (ε) of 4.95% and a dividend yield (δ) of 4.00%. The fund has experienced a risk-adjusted abnormal return (α) of 6.05%.

a)By what amount (premium or discount) is the fund likely to trade relative to its NAV?

Use the equation: (α−ϵ) / (δ + ϵ − α)

NewCorp stock has a required return of 10.00% and is expected to pay a dividend of $3.25 next year. Investors expect a growth rate of 5.55% on the dividends for the foreseeable future.

b. What is the current fair price for the stock?

c. Suppose the stock is selling at this price, but then investors revise their expectations. The new expectation for the growth rate is 5.20%. If investors are rational, what will be the new price for NewCorp stock?

Answer 1

a. By what amount (premium or discount) is the fund likely to trade relative to its NAV?

Premium/Discount relative to its NAV can simply be formulated as (Price-NAV)/NAV

In the given question, since price is not directly available, we determine using the following equation:

Premium or discount = (α−ϵ) / (δ + ϵ − α)

where (ε) = expense ratio of 4.95%

(δ) = dividend yield of 4.00%

(α) = risk-adjusted abnormal return of 6.05%.

= (6.05%-4.95%)/(4%+4.95%-6.05%) = 0.3793

Since the answer is positive, the mutual fund is trading at premium relative to its NAV.. This is primarily because the expense ratio is less than the risk adjusted normal return.

b. Fair price of the stock

Required return = 10%

Dividend next year = $3.25

Growth rate = 5.55%

Price of the stock = Dividend next year /(Required return - Growth rate) = $3.25/(10%-5.55%) = $73.03

Fair price of the stock is $73.03

c. Fair price of the stock with revised growth rate

Required return = 10%

Dividend next year = $3.25

Growth rate = 5.20%

Price of the stock = Dividend next year /(Required return - Growth rate) = $3.25/(10%-5.20%) = $67.71

New Fair Price of the stock is $67.71