Introduction to Corporate Finance

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).