The University of Hong Kong
Faculty of Business and Economics
FINA2312—Advanced Corporate Finance
Assignment 3
Due: November 10, 2022
1. Suppose that the current market value of a firm is 150. The firm lasts for two periods.
The rate of return on the assets of the firm, over one period, is either 20% or −20%
with equal probabilities. The riskless rate of interest is 5% in each period. If any
cash payout, coupon and/or dividend, is made at the end of the first period, then the
ex-payout firm value will change by either 20% or −20% over the second period.
(a) Consider a callable bond with the coupon rate of 6.56% and the face value of 100.
The call price on an ex-coupon basis is 100. What is the price of this callable
bond? The firm pays no dividends on the stock at the end of the first period.
(b) What is the price of the callable bond in part (a) if the firm pays dividends of 5
on the stock at the end of the first period?
(c) What is the price of the callable bond in part (a) if the call premium follows
a declining call schedule on an ex-coupon basis? The call price is 102 at the
beginning of the first period, 101 at the end of the first period, and 100 at the
end of the second period. The firm pays no dividends on the stock at the end of
the first period.
2. Consider a firm which is currently worth $400,000. There is a 62% chance that the
ex-coupon firm value will increase by 35% and a 38% chance that it will decrease by
26%. Two corporate securities are outstanding: 150 shares of stock, and 100 callable,
convertible bonds that mature two year later. Each bond has a face value of $1,000
and pays annual coupon at a rate of 10%. If bondholders decide to convert, they can
convert at a ratio of half-a-share per bond and receive no accrued interest. Anytime
before maturity, stockholders can call the bonds for a fixed call price of $1,200 plus
the accrued interest. The firm pays no dividends. The risk-free rate of interest is
constant at 8% per year. When the bonds are called, bondholders have the choice to
convert the bonds into the stocks.
(a) What is the current market price per unit of the callable, convertible bonds?
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(b) What is the option value of the convertibility provision per bond if the bonds
are not callable?
(c) What is the option value of the call provision per bond if the the bonds are not
convertible?
(d) What can you conclude from parts (a), (b), and (c)?
3. Acme Industries is considering building a plant. After an initial investment of $100
million, the plant will be completed in one year and then have the series of annual
cash flows. After a year of start-up procedures, next year’s cash flow will be $20
million, but a perpetual annual cash flow stream of either $15 million or $2.5 million
will occur each year thereafter, depending on whether the economy is good or bad
one year from now.
Acme’s managers can decide to immediately invest the $100 million, or they can wait
until next year to decide whether to build or not. Assume that the risk-free interest
rate is 5% per year and that $1 invested in the market portfolio today will be worth
either $1.3 (if the economy is good) or $0.8 (if the economy does poorly). Compute
the NPV of the project and decide whether or not it pays to wait. What if the next
year’s cash flow is $40 million and not $20 million?
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