4: Valuing Bonds
example
A few years ago, Mitchells & Butlers, Britain’s largest operator of pubs, entered into a sale–leaseback transaction
with real-estate management company Prupim. In this type of transaction, one party sells an asset to another and
agrees to lease the asset back from the buyer. In this transaction, Mitchells & Butlers sold eight pubs, agreeing
to lease them back from Prupim for £960,000 (or £120,000 per pub) per year for 25 years following the deal.
Suppose that Prupim’s required return on this deal is 10%. We can use Equation 4.1 to calculate the price Prupim
would be willing to pay today in exchange for lease payments over the next 25 years.^1
=
+
+
+
+...+
+
P =
£960,000
(1 0.10)
£960,000
(1 0.10)
£960,000
(1 0.10)
0 12 25 £8,713,^958
Remember that Equation 3.7, on page 90, provided a mathematical shortcut for solving a problem like this
one. The £960,000 annual payments represent an annuity, and Equation 3.7 says that the present value of an
ordinary annuity can be found as follows:
PV
PMT
r rn
=×−
+
(^1)
1
() 1
Substituting £960,000 for the annual payment (or cash flow), 10% for the interest rate, and 25 for the
number of years, we can calculate the present value (or price) of this stream of payments:
P
£960, 000
0.10
1
1
(1 0.10 )
£960, 000 1
1
10 .8347
0 =×− 25 £8,713,^958
+
=×−
=
The lease payments are worth more than £8.7 million to Prupim.
With this simple framework in hand, we turn to the problem of pricing bonds. Though bond-pricing
techniques can get very complex, we focus on ‘plain-vanilla’ bonds: those that promise a fixed stream of
cash payments over a finite time period. Among the largest issuers of such fixed income securities are
national governments and large, multinational corporations.
CONCEPT REVIEW QUESTIONS 4-1
1 Why is it important for corporate managers to understand how bonds and shares are priced?
2 Holding constant an asset’s future benefit stream, what happens to the asset’s price if its risk
increases?
3 Holding constant an asset’s risk, what happens to the asset’s price if its future benefit stream
increases?
4 Discuss how one might use Equation 4.1 to determine the price per hectare of rural land.
1 We can use Excel to solve for the present value of 25 annual lease payments by using the PV (present value) function. The correct syntax for
this example is = pv(0.10,25,-960,000,0,0).