# Financial Modelling: Bond Valuation

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 Author: jordan_hs ID: 286315 Filename: Financial Modelling: Bond Valuation Updated: 2014-10-20 03:42:30 Tags: 125 220 M5 Bond Valuation Folders: Description: Show Answers:

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1. Choosing a Discount Rate
• The value of an asset is the present value of all future cashflows expected over the period the asset is held for.

• Where:
• • V0 = Value of asset at time 0
• • CFn = Cash flow expected at end of period n
• • r = Required rate of return
• • n = Relevant time period
2. Choosing a Discount Rate (undertake single project, two mutually exclusive projects)
• Choosing whether to undertake a single project:

• Comparing two mutually exclusive projects:
3. DISCOUNTING BASICS
Discounting: Cash flow vs Discount rate
• Cash flow
• · The numerator of the NPV is the cash flows--these can be either riskless or risky
• · The anticipated (expected) future cash flows

• Discount rate
• · The denominator of the NPV is the discount rate. The more risky the numerator, the higher the discount rate.
• · Discount rate appropriate to the risk of the cashflows (“RADR”=Risk‐Adjusted Discount Rate”)
4. Discount rate basics
• If cash flow numerator is riskless
•   • Discount rate = risk‐free rate, rf

• If cash flow numerator is risky
•   • Discount rate > risk‐free rate
•   • Discount rate = rf + risk premium
5. Cost of Capital Fundamentals
• • The terms, the cost of capital and the weighted average cost of capital (WACC) are used interchangeably and mean the same thing.
• ·The rate that a firm pays, on average, to its providers of capital, and therefore is the rate of return it must earn on its investment in order to maintain the market value of its shares.
• ·Minimum return to compensate suppliers of funds for time value of money & risk.
• ·The cost of capital provides a benchmark against which the potential rate of return on an investment is compared.
6. WACC formula

• where
• rE = firm's cost of equity (return required by firm's shareholders)
• rD = firms's cost of debt (return required by debtholders)
• E = market value of firm's equity
• D = market value of firm's debt
• TC = firm's tax rate
7. Determining the WACC components
• • E = market value of equity
•       = #shares × current market price/share
• • D=market value of debt
• • TC = Corporate tax rate
• • rD = Cost of debt = Corporate borrowing rate
• • rE = Cost of equity
8. (1‐TC)×rD as the cost of debt
rD is the rate charged by lenders to company

When lenders perceive that the company has higher risk, they demand a larger rD

• The after‐corporate‐tax cost of debt is
•           (1‐TC ) ×rD
• • The tax benefit from interest expense deductability must be included in the cost of funds.
• • This tax benefit reduces the effective cost of debt by a factor of the marginal tax rate.
9. rE as the cost of equity
• • rE is the return demanded (or expected) by shareholders
• • rE increases as the riskiness of the shareholder returns increases
• • The after‐corporate‐tax cost of equity is rE
10. The Cost of Equity (rs)
• 1. Constant Growth Valuation Model
• Where:
• D1 = Per-share dividend expected at end of yr 1
• P0 = Value of one ordinary share
• g = Constant rate of growth of dividends

• 2. CAPM
11. WACC example
• United Transport Inc. has 3 million shares outstanding; the current market price per share is \$10. The company’s cost of equity rE 20%.
• The company has also borrowed \$10 million from its banks at a rate of 8%; this is the company’s cost of debt, rD. United Transport has a tax rate of TC = 40%.

WACC = 16.20%
12. When is the WACC an appropriate discount rate?

• ‐ The investment decision (through NPV analysis) we have considered so far assume that the overall risk of the firm will be kept constant with the introduction of new project in a firm.
• ‐ In other words, the new project’s risk will be exactly the same as the risk of the firm.
• ‐ The above is the reason why we can simply use WACC as the discount rate in the NPV analysis.
13. CORPORATE NEW ISSUE OFFERINGS
• · Corporate bonds are fully taxable debt obligations issued by corporations in order to fund capital improvements, expansions, debt refinancing or acquisitions that require more capital than would ordinarily be available from a single lender, such as a bank
• · Investors in corporate bonds lend money to the issuing corporation in exchange for interest payments and repayment of the principal at a set maturity date
14. Bond terminology
• Par value: Principal or face value; typically \$1000
• • Coupon rate: Annual rate of interest paid.
• • Coupon: Regular interest payment received by holder per year.
• • Maturity date: Expiration date of bond when par value is paid back.
• • Yield to maturity: Expected rate of return, based on price of bond.
• • Current Yield = \$ Coupon/Price
15. Bond Valuation
• • The value of a bond is determined by discounting the bonds promised payments.
• • If a company has issued a bond which promises payments C1, C2, … CN, we value this bond by discounting the promised payments at an appropriate discount rate r:

16. Bond Valuation part 2
• • The yield to maturity (YTM) of the bond is the internal rate of return of the cash flows.
• • Suppose we observe the bond’s market price, P, and we know its stream of future promised payments C1, C2, … CN. Then the YTM is defined as follows:

17. YIELD function
YIELD(settlement, maturity, rate, pr, redemption,frequency, [basis])
18. YIELD function characteristics
Settlement The security's settlement date.

Maturity The security's maturity date

Rate The security's annual coupon rate.

Pr The security's price per \$100 face value.

Redemption The security's redemption value per \$100 face value.

• Frequency The number of coupon payments per year.
• • For annual payments, frequency = 1
• • for semiannual, frequency = 2
• • for quarterly, frequency = 4
19. YIELD function
- basis
Basis The type of day count basis to use.

• Basis⇒Day count basis:
• 0 or omitted⇒US (NASD) 30/360
• 1⇒Actual/actual
• 2⇒Actual/360
• 3⇒Actual/365
• 4⇒European 30/360
20. XIRR & YIELD
XIRR allows cash flows to happen at any time, at irregular intervals, and thus the timing of the cashflows is considered in the calculated result, and no adjustment (i.e., multiplying by 12) is required.

• • IRR: periodical rate
• • XIRR: effective annul rate
• • YIELD: annual percentage rate
21. PRICE Function
PRICE(settlement, maturity, rate, yld, redemption,frequency, [basis])

·Returns the price of a bond
22. PRICE Function characteristics
• = PRICE(A1, A2, .05, .08, 100, 2)
•               a    b     c     d     e    f

• Where:
• – a is the start date if the bond
• – b is the maturity date of the bond
• – c is the coupon rate
• – d is the bond’s yield to maturity
• – e is the redemption amount per \$100 of face value
• – f is the number coupon payments per yea

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