Final Exam Practice Problems
1. Firm ABC’s only outstanding debt is $100,000 worth of coupon bond (market value). Its yield to maturity is 8%. Given that its tax rate is 40%, what is its effective cost of debt? Effective cost of debt = cost of debt * (1-tax rate) =8%*(1-40%)=4.8% 2. Firm ABC has a stock currently traded at $20. The next year’s dividend will be $0.20. The dividend growth rate is forecasted to be 6% forever. Risk-free rate is 3%, and market risk premium is 4%. Assume that Constant Dividend Growth Model and CAPM give you the same estimate of the cost of capital for equity, what is the beta of its stock? By the Constant Dividend Growth Model:
Cost of Equity = D/P+g = 0.2/20+6%=7%
By CAPM, cost of equity = R(f)+ beta * market risk premium = 3% + beta* 4%, Set this to be equal to 7%, solve for beta: beta=1
3. Firm ABC has a cost of equity of 8%, a cost of debt of 5%. It stock is traded at $10/share, and has 10 million shares outstanding. Its debt value is $20 million. Tax rate is 40%. What is its after-tax WACC?
Equity Value = 10*10=$100 million, Debt Value=$20 million
So, equity weight = 100/120=83.3%, debt weight=20/120=16.7%
After-tax WACC= equity weight * cost of equity + debt weight * effective cost of debt =83.3%*8%+16.7%*5%*(1-40%) = 7.2%
4. Suppose you are the founder of a private company ABC. Initially you raised $500,000 from an angel investor from the first-round financing. As a result, both you and the angel investor hold 100,000 shares. Now in the second-found financing, you plan to raise another $1,000,000 from a venture capitalist. The venture capitalist will hold also 100,000 shares. What is your ownership before and after the second-round financing? Before the second-round financing, ownership = 100,000/200,000=50% After the second-round financing, ownership = 100,000/300,000=33%
5. What is the difference between a “firm commitment IPO” and an “auction IPO”?
Refer to the book for the answer.
6. In an auction IPO, your firm wants to sell 200,000 shares. The following is the demand from potential investors at different price levels: Price Demand
At what price should your firm set the IPO price?
Price should be $65. At this price, the cumulative demand = 40,000+40,000+70,000+50,000=200,000
7. Firm ABC plans to issue three types of a five-year coupon bond with coupon rate of 10%, and a face value of $1000. Bond A is a callable bond, which callable at par. Bond B is a plain-vanilla bond without any call or convertible feature. Bond C is a convertible bond with a conversion ratio of 10. If all three bonds are identical except the call and convertibility feature, can you make an inference regarding the prices of these three bonds?
Everything else being equal, call bond price < plain-vanilla bond price < convertible bond price. This is because the callable bond give the issuer the right to buy back the bond at the call price when the situation is favorable to the issuer, the convertible bond give the investor the right to convert the bond to stocks at the conversion ratio when the situation is favorable for to the investor. Apparently investors should be willing to pay less for callable bonds, but more for convertible bonds.
8. IBM has just issued a callable (at par) five-year, 8% coupon bond with annual coupon payments. The bond can be called at par in one year or anytime thereafter on a coupon payment date. It has a price of $103 per $100 face value, implying a yield to maturity of 7.26%. What is the bond’s yield to call? What is the yield to worst?
Please refer to the lecture slides in Lecture 8 for the solution.
9. Assume perfect capital markets and no taxes. The unlevered (all-equity) firm ABC has a firm value of $100 million, and cost of equity of 8%. If the firm decides to borrow debt, so that the new debt to equity ratio is 1 to...
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