d: Discuss the diffulties
of estimating the expected cash flows for some types of bonds and identify the bonds for which
estimating the expected cash flows is difficult.
Normally, estimating the cash flow stream of a high-quality option-free bond is relatively
straight forward, as the amount and timing of the coupons and principal payments are known
with a high degree of certainty. Remove that certainty, and difficulties will arise in estimating
the cash flow stream of a bond. Aside from normal credit risks, the following three conditions
could lead to difficulties in forecasting the future cash flow stream of even high-quality issues:
•
The presence of embedded options, such as call features and sinking fund provisions
- in which case, the length of the cash flow stream (life of the bond) cannot be
determined with certainty.
•
The use of a variable, rather than a fixed, coupon rate - in which case, the future
annual or semi-annual coupon payments cannot be determined with certainty.
•
The presence of a conversion or exchange privilege, so you're dealing with a
convertible (or exchangeable) bond, rather than a straight bond - in which case, it's
difficult to know how long it will be before the bond is converted into stock.
e: Compute the value of a bond, given the expected cash flows and the appropriate discount rates.
Example: Annual coupons. Suppose that we have a 10-year, $1,000 par value, 6% annual
coupon bond. The cash value of each coupon is: CPN= ($1,000 * 0.06)/1 = $60. The value of
the bond with a yield to maturity (interest rate) of 8% appears below. On your financial
calculator, N = 10, PMT = 60, FV = 1000, I/Y = 8; CPT PV = 865.80. This value would
typically be quoted as 86.58, meaning 86.58% of par value, or $865.80.
Bond value = [60 / (1.08)
1
] + [60 / (1.08)
2
] + [60 + 100 / (1.08)
3
] = $865.80
Example:
Semiannual coupons. Suppose that we have a 10-year, $1,000 par value, 6%
semiannual coupon bond. The cash value of each coupon is: CPN = ($1,000 * 0.06)/2 = $30.
The value of the bond with a yield to maturity (interest rate) of 8% appears below. On your
financial calculator, N = 20, PMT = 30, FV = 1000, I/Y = 4; CPT PV = 864.10. Note that the
coupons constitute an annuity.
Bond Value=
n*m
Σ
t=1
30
(1 + 0.08/2)t
+
1000
(1 + 0.08/2)
n*m
= 864.10
f: Explain how the value of a bond changes if the discount rate increases or decreases and
compute the change in value that is attributable to the rate change.
The required yield to maturity can change dramatically during the life of a bond. These
changes can be market wide (i.e., the general level of interest rates in the economy) or
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