Introduction
In fulfilling the duties of the position, a Chief Financial Officer (CFO) must ensure that when a firm issues debt securities such as bonds, it receives
the highest possible prices from investors for those bonds. That will lead to the lowest cost of debt. The CFO must also ensure that when a firm
invests in a revenuegenerating project, it is investing only in projects that will make the firm more valuable to equity investors. This is achieved
through sound project evaluation practices, part of the capital budgeting process.
This sample module will show how to compute the market value of a bond and perform a Net Present Value analysis of a revenuegenerating project.
Bond Valuation
A bond is a longterm debt instrument characterized by the payment at regular intervals of a fixed interest amount over the life of the bond and the
payment of the bond principal at its maturity. You can read the details of the qualitative characteristics of bonds in your textbook.
The key thing to understand about a bond is that it is two forms of cashflow over time. One form is an interest annuity, the regular interest payments, and the
other form is an amount, the payment of the bond principal or face value at maturity. The market value of a bond is the amount of money an investor is willing to pay
today, in the present, for the right to receive cashflows in the future.
If you have taken the Principles of Finance module, (the prerequisite to this module), you should recognize the bond valuation scenario as one
involving present value. Bond valuation is an application of present value.
There are two types of present value computation in determining the market value of a bond; annuity and amount. One finds the market value of a bond
by finding the present values of the interest annuity and the principal repayment and summing the two. As you learned in the prerequisite module,
computing present value requires a discount rate, a time period, and an amount or annuity. In the case of bond, we have both an amount and an annuity.
The amount is the bond principal to be received at maturity. By convention this is $1,000. The interest annuity is the bond coupon rate times
its principal amount or face value. For example, if a bond coupon rate is 5% paid annually, then the annual interest annuity is 0.05 * 1,000 = $50. The
time period is the length of time over which the bond will make interest payments. That is also the length of time until the principal amount is paid.
That length of time is called the bond maturity. The discount rate to be used is the current market annual interest rate.
A bond that matures in 10 years and has a coupon rate of 6%, paid annually, will pay $60 at the end of each year for 10 years and pay $1,000 at the
end of 10 years. Say the current market annual interest rate is 8%. To determine the present value of the interest annuity, we use the appropriate
financial calculator to find the present value interest factor for an annuity of 10 years at 8% annual interest. The calculator yields a present
value interest factor for an annuity of 6.7101 which when multiplied by the annuity payment of $60 results in the interest annuity having a present
value of $402.61. To determine the present value of the principal amount, we use the appropriate financial calculator to find the present value
interest factor for an amount at 8% annual interest and 10 years. The calculator yields a present value interest factor for an amount of 0.4632 which
when multiplied by the $1,000 principal amount results in the principal amount having a present value of $463.20. The market value of the bond is the
sum of these two values yielding $402.61 + $463.20 = $865.81. So, a bond with a coupon rate of 6% paid annually that matures in 10 years will have a
market value of $865.81 when the current market annual interest rate is 8%.
Example 1.
A bond with a 5% coupon rate, paid annually, matures in 8 years. If the current market annual interest rate is 4%, what is the market value
of the bond?
The interest annuity payment is 0.05 * 1,000 = $50 at the end of each year. The present value interest factor for an annuity at 4% and 8 years is
PVIFA(4%, 8 yrs) = 6.733. The present value of the interest annuity is $50 * 6.733 = $336.65. The present value interest factor for an amount at 4%
and 8 years is PVIF(4%, 8 yrs) = 0.7307. The present value of the principal amount is $1,000 * 0.7307 = $730.70. The market value of the bond is
$336.65 + $730.70 = $1,067.35 when the current market annual interest rate is 4%.
Example 2.
A bond with a 5% coupon rate, paid annually, matures in 8 years. If the current market annual interest rate is 5%, what is the market value
of the bond?
The interest annuity payment is 0.05 * 1,000 = $50 at the end of each year. The present value interest factor for an annuity at 5% and 8 years is
PVIFA(5%, 8 yrs) = 6.4663. The present value of the interest annuity is $50 * 6.4663 = $323.32. The present value interest factor for an amount at 5%
and 8 years if PVIF(5%, 8yrs) = 0.6768. The present value of the principal amount is $1,000 * 0.6768 = $676.80. The market value of the bond is $323.32 +
$676.80 = $1,000.12 when the current market annual interest rate is 5%.
In the above examples, the interest was paid at the end of each year. That means the discounting period is one year. Interest can be paid every six
months yielding a semiannual discounting period, or every 3 months yielding a quarterly discounting period. As you should remember from the prerequisite
module, when the discounting period is not one year, the annual interest rate and the maturity period in years must be adjusted to match the
discounting period.
A bond that matures in 10 years and has a coupon rate of 6%, paid semiannually, will pay $30 at the end of each 6month period for 10 years and pay $1,000 at the
end of 10 years. Say the current market annual interest rate is 8%. To determine the present value of the interest annuity, we use the appropriate
financial calculator to find the present value interest factor for an annuity of 20 6month periods at 4% interest per 6month period. The calculator
yields a present value interest factor for an annuity of 13.5903 which when multiplied by the annuity payment of $30 results in the interest annuity having a present
value of $407.71. To determine the present value of the principal amount, we use the appropriate financial calculator to find the present value
interst factor for an amount at 8% annual interest and 10 years. The calculator yields a present value interest factor for an amount of 0.4564 which
when multiplied by the $1,000 principal amount results in the principal amount having a present value of $456.40. The market value of the bond is the
sum of these two values yielding $407.71 + $456.40 = $864.11. So, a bond with a coupon rate of 6% paid annually that matures in 10 years will have a
market value of $864.11 when the current market annual interest rate is 8%.
Example 3.
A bond with a 5% coupon rate, paid semiannually, matures in 8 years. If the current market annual interest rate is 4%, what is the market value
of the bond?
The interest annuity payment is 0.025 * 1,000 = $25 at the end of each 6month period. The present value interest factor for an annuity at 2% per
6month period and 16 6month periods is PVIFA(2%, 16 per) = 13.5777. The present value of the interest annuity is $25 * 13.5777 = $339.44. The present
value interest factor for an amount at 2% per 6month and 16 6month periods is PVIF(2%, 16 per) = 0.7285. The present value of the principal amount
is $1,000 * 0.7285 = $728.50. The market value of the bond is $339.44 + $728.50 = $1,067.94 when the current market annual interest rate is 4%.
Example 4.
A bond with a 5% coupon rate, paid semiannually, matures in 8 years. If the current market annual interest rate is 6%, what is the market value
of the bond?
The interest annuity payment is 0.025 * 1,000 = $25 at the end of each 6month period. The present value interest factor for an annuity at 3% per
6month period and 16 6month periods is PVIFA(3%, 16 per) = 12.5611. The present value of the interest annuity is $25 * 12.5611 = $314.03. The present
value interest factor for an amount at 3% per 6month and 16 6month periods is PVIF(3%, 16 per) = 0.6232. The present value of the principal amount
is $1,000 * 0.6232 = $623.20. The market value of the bond is $314.03 + $623.20 = $937.23 when the current market annual interest rate is 6%.
You should notice that the market value of a bond is greater than its face value of $1,000 when the market interest rate is less than the bond coupon
rate, less than its face value of $1,000 when the market interest rate is greater than the bond coupon rate, and equal to its face value of $1,000
when the market interest rate is equal to the bond coupon rate. A bond whose market value is greater than its face value is said to sell at a premium.
A bond whose market value is less than its face value is said to sell at a discount. A bond whose market value is equal to its face value is said
to sell at par.
Sample Questions about Bond Valuation.
Net Present Value
As you learned in the Principles of Finance module, financial decision making emphasizes cashflow, in contrast to accounting based decision making
which emphasizes profit. The Net Present Value method of project valuation finds the excess of the present
value of a project's cash inflows during the life of the project over the project's cash outflow at its inception. The decison rule is that if a
project's Net Present Value (NPV) is greater than or equal to zero then the project will add value to the firm and it should be accepted and financed.
If a project's NPV is less than zero then the project will take value from the firm and it should not be accepted.
The cash outflow at the inception of a project is a straightforward matter. It is the initial cost of launching the project. There is no time value
because the cash outlay is made in the present day. The cash inflow over the life of the project must be discounted to account for the time value.
The time period over which the cashflows are discounted is the life of the project. The discount rate at which the cashflows are discounted is the
cost of capital of the project. The discounting period (ie. annually, semiannually, quarterly, etc.) is determined by the frequency of the payments
generated by the project. The general formula is NPV = [PVIF(i%, 1 yr) * CF_{1} + PVIF(i%, 2 yrs) * CF_{2} + PVIF(i%, 3 yrs) *
CF_{3}+ PVIF(i%, 4 yrs) * CF_{4} + ... + PVIF(i%, n yrs) * CF_{n}]  IO, where IO is the project's initial cash outlay, i is the
discount rate, CF is the cash inflow during the year, and n is the project's life in years.
As you learned in the prerequisite module, cashflows can be treated as individual amounts or as annuities. An annuity is cashflows made or paid in
equal amounts at regular time intervals. In the case where all the project's cashflows are the same amount and received at regular time intervals,
one can use the present value interest factor for an annuity.
Say a project has a life of 4 years and an initial cost of $50,000. It generates cash inflow of $10,000 in the first year of operations, $15,000 in
the second year of operations, and $20,000 and $25,000 in the third and fourth years respectively. The discount rate is 5%. In this scenario, the
cash inflows must be treated as individual amounts. NPV = PVIF(5%, 1 yr) * 10,000 + PVIF(5%, 2 yrs) * 15,000 + PVIF(5%, 3 yrs) * 20,000 + PVIF(5%, 4 yrs)
* 25,000  50,000 = 9,524 + 13,605 + 17,277 + 20,568  50,000 = $10,974. Because the NPV is greater than or equal to zero, the best decision for the firm
is to accept the project and pay the $50,000 outlay for the project's cost.
Say a project has a life of 6 years and an initial cost of $60,000. It generates cash inflow of $10,000 in each and every year of operations. The
discount rate is 5%. In this scenario, the cash inflows can be treated as an annuity. NPV = PVIFA(5%, 6 yrs) * 10,000  60,000 = 50,757  60,000 =
$9,243. Because the NPV is less than zero, the best decision for the firm is to reject the project and
not pay the $60,000 outlay for the project's cost.
Example 1.
A project with a 3 year life and a cost of $45,000 generates cashflow of $20,000 in its first year of operations, $18,000 in its second year, and $15,000
in its third and last year. The discount rate is 6%. Should the project be accepted or rejected?
The NPV = PVIF(6%, 1 yr) * 20,000 + PVIF(6%, 2 yrs) * 18,000 + PVIF(6%, 3 yrs) * 15,000  45,000 = 18,868 + 16,020 + 12,594  45,000 = $2,482.
Because the NPV is greater than or equal to zero, the best decision for the firm is to accept the project and pay the $45,000 outlay for the project's
cost.
Example 2.
A project with a 3 year life and a cost of $45,000 generates cashflow of $20,000 in its first year of operations, $18,000 in its second year, and $15,000
in its third and last year. The discount rate is 12%. Should the project be accepted or rejected?
The NPV = PVIF(12%, 1 yr) * 20,000 + PVIF(12%, 2 yrs) * 18,000 + PVIF(12%, 3 yrs) * 15,000  45,000 = 17,857 + 14,349 + 10,677  45,000 =
$2,117. Because the NPV is less than zero, the best decision for the firm is to reject the project and
not pay the $45,000 outlay for the project's cost.
Example 3.
A project with a 8 year life and a cost of $110,000 generates cashflow of $20,000 in each and every year of operations. The discount rate is 6%.
Should the project be accepted or rejected?
The NPV = PVIFA(6%, 8 yrs) * 20,000  110,000 = 124,196  100,000 = $14,196.
Because the NPV is greater than or equal to zero, the best decision for the firm is to accept the project and pay the $100,000 outlay for the project's
cost.
Example 4.
A project with a 8 year life and a cost of $110,000 generates cashflow of $20,000 in each and every year of operations. The discount rate is 12%.
Should the project be accepted or rejected?
The NPV = PVIFA(6%, 12 yrs) * 20,000  110,000 = 99,353  110,000 = $10,647. Because the NPV is less than zero,
the best decision for the firm is to reject the project and not pay the $110,000 outlay for the project's cost.
Sample Questions about Net Present Value.
This module is a prerequisite for the Corporate Financial Management II and Investment Analysis modules.
