FM for Actuaries

Rates of Return 145
4.50 Judy is considering whether she should buy a junk bond. The price of the
bond is $4,429 and the cash flows of the bond are shown in the table below.
Time (year) Cash flow ($)
0.5 500
1.0 500
1.5 5,500
(a) Calculate the annualized internal rate of return of the junk bond.
(b) Judy calculated the net present value of the junk bond using the annualized
3-month Treasury Bill rate, which is 4% per annum. Calculate
the NPV of this investment based on Judy’s assumption.
(c) Give two reasons why the price of the junk bond is so low when compared
with that in (b).
Advanced Problem
4.51 When you are bearish on a stock you may try to make profit by short selling.
When you are bullish on a stock you may borrow extra money from a broker
to buy more stocks in order to earn a higher return. This is called “buy
on margin.” However, just like short selling, in buy-on-margin you have to
maintain a margin level in your margin account, which is defined as
Equity in your account
Value of security you own .
In the definition above, the value of the security you own is the value of the
stock you purchase as your own investment plus the extra stock you own by
borrowing money from the broker. The equity in your account is the value
of the security you own minus the amount of money you borrow from the
broker. If the margin level falls below a margin maintenance requirement,
you will receive a broker’s call.
(a) Andrew is bullish on Orange Corporation whose current market price
is $40 per share, and he has $9,200 to invest. To leverage his position
Andrew borrows $4,000 from the broker at an interest rate of 5% per
year. After 1 year, the price of Orange Corporation pays $2 dividend
and the ex-dividend price has increased by 7%. Find the rate of return.
(b) How far can the price of the stock fall before Andrew receives a margin
call, supposing that the margin maintenance requirement is 40%? You
may ignore the interest incurred in the margin account.