7.6 RATE OF RETURN OF A BOND INVESTMENT

SECTION 7.6
7.6
1
Rate of Return of a Bond Investment
RATE OF RETURN OF A BOND INVESTMENT
In Chapter 5 we learned the terminology of bonds and how to calculate the PW of a
bond investment. The cash flow series for a bond investment is conventional and has
one unique i*, which is best determined by solving a PW-based rate of return equation in the form of Equation [7.1]. Examples 7.8 and 7.9 illustrate the procedure.
EXAMPLE
Sec. 5.8
Bonds
7.8
Allied Materials needs $3 million in debt capital for expanded composites manufacturing.
It is offering small-denomination bonds at a discount price of $800 for a 4% $1000 bond
that matures in 20 years with interest payable semiannually. What nominal and effective
interest rates per year, compounded semiannually, will Allied Materials pay an investor?
Solution
The income that a purchaser will receive from the bond purchase is the bond interest
I $20 every 6 months plus the face value in 20 years. The PW-based equation for
calculating the rate of return
0 800 20(P兾A,i*,40) 1000(P兾F,i*,40)
Solve by computer (IRR function) or by hand to obtain i* 2.87% semiannually. The
nominal interest rate per year is computed by multiplying i* by 2.
Nominal i 2.87%(2) 5.74% per year, compounded semiannually
Sec.
Sec. 4.3
4.3
Using Equation [4.5], the effective annual rate is
ia (1.0287) 2 1 5.82%
EXAMPLE
Effective
Effective ii
7.9
Gerry bought a bond from a corporation that had defaulted on its interest payments. He
paid $4240 for an 8% $10,000 bond with interest payable quarterly. The bond paid no
interest for the first 3 years after Gerry bought it. If interest was paid for the next 7 years,
and then Gerry was able to resell the bond for $11,000, what rate of return did he make
on the investment? Assume the bond is scheduled to mature 18 years after he bought it.
Perform hand and computer analysis.
Solution by Hand
The bond interest received in years 4 through 10 was
I
(10, 000)(0.08)
$200 per quarter
4
The effective rate of return per quarter can be determined by solving the PW equation
developed on a per quarter basis, since this basis makes PP CP.
0 4240 200(P兾A,i* per quarter,28)(P兾F,i* per quarter,12)
11,000(P兾F,i* per quarter,40)
The equation is correct for i* 4.1% per quarter, which is a nominal 16.4% per year,
compounded quarterly.
Secs.
4.5 & 4.7
PP = CP
2
CHAPTER 7
E-SOLVE
Rate of Return Analysis: Single Alternative
Solution by Computer
The solution is shown in Figure 7–11. The spreadsheet is set up to directly calculate an
annual interest rate of 16.41% in cell E1. The quarterly bond interest receipts of $200 are
converted to equivalent annual receipts of $724.24 using the PV function in cell E6. A
quarterly rate could be determined initially on the spreadsheet, but this approach would
require four times as many entries of $200 each, compared to the six times $724.24 is
entered here. (A circular reference may be indicated by Excel between cells E1, E6, and
B6. However, clicking on OK will override and the solution i* 16.41% is displayed. A
circular reference is avoided if all 40 quarters of $0 and $200 are entered in column B
with necessary changes in the column E relations to find the quarterly rate.)
Rate of return i*
IRR(B2:B12)
Bond face value
Bond interest rate
E3*E4/4
E$6
11000E$6
Figure 7–11
Spreadsheet solution of i* for a bond investment, Example 7.9.
PV(E1/4,4,E5)
PROBLEMS
3
PROBLEMS
Bonds
7.35 A $10,000 mortgage bond with a bond in-
terest rate of 8% per year, payable quarterly,
was purchased for $9200. The bond was
kept until it was due, a total of 7 years. What
rate of return was made by the purchaser per
3 months and per year (nominal)?
7.36 A collateral bond with a face value of
$5000 was purchased by an investor for
$4100. The bond was due in 11 years, and
it had a bond interest rate of 4% per year,
payable semiannually. If the investor kept
the bond to maturity, what rate of return
per semiannual period did she make?
7.37 An engineer planning for his child’s
college education purchased a zero coupon corporate bond (i.e., a bond that has no
interest payments) for $9250. The bond
has a face value of $50,000 and is due in
18 years. If the bond is held to maturity,
what rate of return will the engineer make
on the investment?
7.38 Four years ago, Rogers Communications
Inc. issued $5 million worth of debenture bonds having a bond interest rate of
10% per year, payable semiannually.
Market interest rates dropped, and the
company called the bonds (i.e., paid them
off in advance) at a 10% premium on the
face value (i.e., paid $5.5 million to retire
the bonds). What semiannual rate of return
did an investor make if he purchased one
$5000 bond at face value 4 years ago and
held it until it was called 4 years later?
7.39 Five years ago, GSI, an oil services company, issued $10 million worth of 12%,
30-year bonds with interest payable quarterly. The interest rate in the marketplace
decreased enough that the company is considering calling the bonds. If the company
buys the bonds back now for $11 million,
(a) what rate of return per quarter will the
company make on the $11 million expenditure and (b) what nominal rate of return
per year will it make on the $11 million investment? Hint: By spending $11 million
now, the company will not have to make
the quarterly bond interest payments or
pay the face value of the bonds when they
come due 25 years from now.