A mutual fund manager expects her portfolio to earn a rate of return of 14% this

Question

A mutual fund manager expects her portfolio to earn a rate of return of 14% this year. The beta of her portfolio is .9. Assume rate of return available on risk-free assets is 6% and you expect the rate of return on the market portfolio to be 16%.

1.Micro Spinoffs, Inc., issued 20-year debt a year ago at par value with a coupon rate of 9%, paid annually. Today, the debt is selling at $1,020. If the firm

Explanation / Answer

a) The expected rate of return would be a portfolio of the risk free asset and market portfolio that produces the same beta as the mutual fund (which has a beta of 0.9).

A portfolio of 10% risk free asset and 90% market portfolio would produce a beta of 0.9 (same as mutural fund).

0.1 * 0 beta for risk free + 0.9 * 1 beta of market = 0.9 beta

The return of this expected portfolio is 15%

0.1 * 6% risk free return + 0.9 * 16% market portfolio = 15%.

b) No, you should not invest in this portfolio. An investor can create a portfolio of 10% risk free and 90% market at the same risk (as measured by beta) and get a better return of 15% (better than 14%).

c) This question is essentially asking you to solve for the yield to maturity of the bond (which is the same as pre-tax cost of debt). The problem can be solved quickly with a financial calculator but the tricky part is identifying the right inputs.

Inputs for Financial Calculator:

Present value (PV) = -$1,020 (current price of bond, be sure to use negative sign! this is what you would pay if you had to buy bond today)

Future value (FV) = $1,000 (how much you get for bond at maturity)

Payments (PMT) = $90 per year (the annual coupon on the bond is 9% times face value of $1000)

Number of payments (n) = 19 (this is a 20 year bond and it was issued a year ago so there are 19 years left)

interest rate (i) = ? (this is the unknown you solve for)

If you punch the above into a financial calculator and solve for interest, you will find the yield is 8.78% (I won't go over how to use your financial calculator. I am just gonna assume you know).

This is the pre-tax cost of debt. To find the after-tax cost of debt, you have to multiple 8.78% by 0.7 = 6.15%. There is tax savings for debt. Becasue the firm's tax bracket is 30%, the firm saves 30 cents of tax on every dollar of interest they pay. Thus, they after tax cost of debt is 70% of pre-tax level (1 - 0.3). So after tax cost of debt is 6.15%

Hope this helps. Best luck!

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