Business Finance Chapter 7-9 PDF

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Notes for Chapters 7-9 + Homework questions from chapter 7 on Bonds...

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Business Finance Chapter 7 HW & Assignment

1. Today, a bond has a coupon rate of 10.8%, par value of $1000, 13 years to maturity, YTM of 9.6%, and semiannual coupons with the next one due in 6 months. One year ago, the price of the bond was $1075. What is the current yield of the bond today? Coupon Pmt = 108/2 = 54 semi annual Bond Value Today N = 13 x 2 = 26 I = 9.6/2 FV = 1000 PMT = 54 PV = 1088.06 Current Yield Today = Annual Coupon/Bond Value Today = 108/1088.06 = 0.0993 = 9.93

2. 6 years ago, Allen Corp issued bonds that pay annual coupons, have a face value of $1000, have an annual coupon rate of 8.6, and are schedule to mature in 4 years. One year ago, you bought one of the bonds for $998. The bond just paid a coupon. If the percentage return on your bond was 4.6% over the past year, what is the price of the bond today?

Percentage Return = (Coupon Payment + Capital Gain)/Initial Value 0.046 = (86 + CG)/998 CG = 0.046*998 - 86 CG = 45.91 - 86 CG = -40.09 Price Today = 998 + (-40.09) = 957.91 = 958

3. The coupon rate of Cafe bonds is less than the yield-to-maturity of these Cafe bonds. Which of the following assertions is most likely to be true?

The Cafe bonds sell at a discount in the primary market.

4. Bond XYZ and bond ABC both pay annual coupons, mature in seven years, have a face value of $1000, and have the same yield-to-maturity. Bond XYZ has a coupon rate of 8.5% and is priced at $1035.09. Bond ABC has a coupon rate of 6.4%. What is the price of bond ABC?

XYC N7 PV -1035.09 PMT 85 (8.5%) FV 1000

ABC 7 CPT 64 (6.4%) 1000

CPT I/Y 7.83

I/Y 7.83 PV = 925.12

1. Interpreting Bond Yields

Is the yield to maturity on a bond the same thing as the required return?

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For noncallable bonds, the yield to maturity and required rate of return are interchangeable terms.

Is the YTM the same thing as the coupon rate?

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The coupon rate is not a return used as the interest rate in bond cash flow valuation, but is a fixed percentage of par over the life of the bond used to set the coupon payment amount.

Suppose today a 10% coupon bond sells at par. Two years from now, the required return on the same bond is 8%. What is the coupon rate on the bond then? The YTM?

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The coupon rate is constant at 10% The YTM is 8%

3. Bond Prices Malahat Inc. has 7.5% coupon bonds on the market that have 10 years left to maturity. The bonds make annual payments. If the YTM on these bonds is 8.75%, what is the current bond price?

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N 10 I/Y 8.75% PMT 75 FV 1000 PV = 918.89

4. Bond Yields Leech town Co. 9% coupon bonds on the market with 9 years left to maturity. The bonds make annual payments. If the bond currently sells for $924, what is its YTM?

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N9 PV -924 PMT 90 FV 1000 I/Y = 10.34

5. Coupon Rates

Goldstream Enterprises has bonds on the market making annual payments, with 13 years to maturity, and selling for $1045. At this price, the bonds yield 7.5%. What must the coupon rate be on the bonds?

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N 13 I/Y 7.5 PV -1045 FV 1000 PMT = 80.54 = 8.054%

9. Calculating Real Rates of Return If Treasury bills are currently paying 7% and the inflation rate is 3.8%, what is the approximate real rate of interest? The exact real rate?

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Approx = 7 - 3.8 = 3.2 Fisher equation shows the exact relationship between nominal and real and inflation o (1 + R) = (1 + r) x (1 + h) o (1 + 0.07) = (1 + r) x (1 + 0.038) o Exact r = 1.07/1.038 - 1 o r = 0.031 or 3.1%

10. Inflation and Nominal Returns

Suppose the real rate is 3% and the inflation rate is 4.7%. What rate would you expect to see on a treasury bill? (1 + R) = (1 + 0.03) x (1 + 0.047) (1 + R) = 1.03 x 1.047 R = 1.078 - 1 = 0.078 or 7.8% 18. Interest Rate Risk

Both Bond Sam and Bond Dave have 9% coupons, make semiannual payments and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2%, what is the % change in the price of Bond Sam? Of Bond Dave?

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Bonds sold at par have YTM equal to the coupon rate PV is 1000 right now We are looking for PV with an increased rate Sam N 6 Dave N 40 I/Y = 11 Semi Annual Coupon 9% PMT = 45 FV 1000 Sam PV = 950.04 Dave PV 839.54 % Change o Sam -4.99%

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Dave -16.05%

If rates were to suddenly fall by 2% instead, what would the % change in the price of Bond Sam be then? Of Bond Dave?

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Sam N 6 Dave N 40 I/Y = 7 Semi Annual Coupon 9% PMT = 45 FV 1000 Sam PV = 1053.29 Dave PV 1213.55 % Change o Sam 5.33 Up o Dave 21.36 Up

24. Bond Prices vs. Yields o a. What is the relationship between the price of a bond and its YTM?  When interest rate rises, price goes down o b. Explain why some bonds sell at a premium over par value while other bonds sell at a discount. What do you know about the relationship between the coupon rate and the YTM for premium bonds? What about for discount bonds? For bonds selling at par value?  Coupon rates stay the same  If the coupon rate is higher than YTM, then bond will sell at premium  If the coupon rate is lower than YTM, then bond will sell at a discount o c. What is the relationship between the current yield and YTM for premium bonds? For discount bonds? For bonds selling at par value?  Current yield = annual coupon payment/current bond price  For premium bonds, current yield is less than YTM  For discount bonds, current yield is more than YTM  For bonds selling at par value, current yield is = YTM

26. Zero Coupon Bonds

Suppose your company needs to raise $30 million and you want to issue 30-year bonds for this purpose. Assume the required return on your bond issue will be 8%, and you’re evaluating two issue alternatives: an 8% annual coupon bond and a zero coupon bond. Your company’s tax rate is 35%.

a. How many of the coupon bonds would you need to issue to raise the $30 million? How many of the zeroes would you need to issue?

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30,000 Bonds 301880 Zero coupon bonds o N 30 o I/Y 8 o PV 30 000 000 o PMT 0 o FV = 301 879 706/1000 = 310 880

b. In 30 years, what will your company’s repayment be if you issue the coupon bonds? What if you issue the zeroes

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You will need 30 million to repay all bonds plus 30 000 x 80 = 2.4 million in final coupon payments 301 879 706 to repay zero coupon bonds

c. Based on your answer, why would you ever want to issue the zeroes? To answer, calculate the firm’s after-tax cash outflows for the first year under the two different scenarios.

Business Finance Chapter 7 Interest Rates and Bond Valuation

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7.1 Bonds and Bond Valuation  Bond - An interest-only loan, the borrower pays interest every period, principal repaid at the end of the loan  Coupon - Interest payments  Face/Par Value - Paid at the end of the loan  Coupon Rate - Annual coupon divided by the face value (%)  Maturity - Number of years until the face value is paid o Bond Values and Yields  When interest rates rise, the PV of the bond’s remaining cash flows declines, and the bond is worth less  When interest rates fall, the bond is worth more  To determine value of a bond on a particular date, we need to know :  Number of periods remaining until maturity  Face value  Coupon  Market interest rate

Yield to Maturity - The market interest rate that equates a bond’s PV of interest payments and principal repayment with its price  PV of bond = PV of cash flows + PV of Face Value  Rate = 5.6, 10 years, $1000 face value  PV of Bond = 420.09 + 579.91 = 1000  The bond sells for exactly its face value  Suppose in a year, market rate is 7.6. Find PV of 1000 paid in 9 years.  PV = 517.25 + 355.71 = 872.96  Bond sells for 873$ - discount bond  Will have a $127 gain at maturity, only because buyer gives up $20 worth of bond payments every year o Interest Rate Risk  Risk that arises for bond owners from fluctuating interest rates  Sensitivity depends on:  Time to Maturity  Coupon Rate  The longer the time/lower the coupon rate, the greater the interest rate risk o Finding the Yield to Maturity 7.2 More on Bond Features o Securities issued by corporations may be classified as equity/debt securities  Debt is not an ownership interest in the firm  Corporation’s payment of interest on debt is considered a cost of doing business and is tax deductible  Unpaid debt is a liability of the firm o Is it Debt or Equity?  Debt holders are paid before equity holders  Debt holders are limited to amount of loan, whereas there is no limit for reward of owning an equity interest o Long Term Debt Basics  Debt Securities are typically called notes/debentures/bonds o Indenture - Written agreement between the corporation (the borrower) and its creditors  Basic terms of bond  Face value (usually $1000)  Registered Form - Registrar of company records ownership of each bond; payment is made directly to the owner of record  Bearer Form - Bond issued without record of the owner’s name; payment is made to whoever holds the bond  Difficult to recover if lost  Company cannot notify bondholders of important events because it does not know who owns its bonds  Amount of bonds issued  Description of property used as security if bonds are secured  Security 

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Collateral - Pledged as security for payment of debt Mortgage Securities - Secured by a mortgage on the real property of the borrower  Debenture - Unsecured bond usually with a maturity 10 years or more  Note - Unsecured debt, usually with a maturity under 10 years  Seniority - Preference in position over other lenders  Repayment arrangements  Can be repaid at maturity or in part/entirety before maturity  Sinking Fund - Account managed by the bond trustee for early bond redemption  Call provision  Call Provision - Agreement giving the corporation the option to repurchase the bond at a specified price before maturity  Call Premium - Amount by which the call price exceeds the par value of the bond  Deferred Call - Call provision prohibiting the company from redeeming the bond before a certain date  Call Protected - Bond during period in which it cannot be redeemed by the issuer  Details of protective covenants  Protective Covenant - Part of the indenture limiting certain transactions that can be taken during the term of the loan, usually to protect the lender’s interest 7.3 Bond Ratings o Highest rating a firm can have is AAA (best quality and lowest degree of risk) 7.4 Different Types of Bonds o Financial Engineering  Stripped/Zero-Coupon Bond - A bond that makes no coupon payments, initially priced at a deep discount  Floating Rate Bonds  Income Bonds  Retractable Bond - Bond that may be sold back to the issuer at a respecified price before maturity 7.5 Bond Markets 7.6 Inflation and Interest Rates o Fisher Effect Interest rates and bond inverse relationship 10% Nominal = R + H Real rate is actual cost of lending money without any inflation risk R = 1 H? o 10 - 1 = 9% Fisher Effect o R = r+rh+h o = 0.01 + (0.01*0.09) + 0.09  

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= 0.1009 10.09% 7.7 Determinants of Bond Yields o Term Structure of Interest Rates - Relationship between nominal interest rates on default-free, pure discount securities and time to maturity; pure time value of money o o

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Business Finance Chapter 8 Stock Valuation

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8.1 Common Stock Valuation o More difficult to value a share of common stock than a bond 1. Promised cash flows are not known in advance 2. Life of the investment is essentially forever because common stock has no maturity 3. There is no way to easily observe the rate of return that the market requires o Common Stock Cash Flows 1. 2. 3. 4. 5. 6.

Ex. Stock will be worth $70 in one year (FV 70) (N 1) Stock will pay $10 dividend (PMT 10) You require 25% return (I/Y 25) What is the most you would pay for the stock? PV = 64 Price of Stock now  P0 = (D1 + P1)/(1 + r) 7. Price of stock in future  P0 = (D1/(1+r)^1) + (D2/(1+r)^2) + etc.. o Common Stock Valuation: Some Special Cases 1. Zero Growth  Value of Stock  P0 = D/r  Policy of $10/share dividend/year, what is value of a share of stock if required return is 20%?  = $10/0.2 = $50/share 2. Constant Growth  Dt = D0 x (1 + g)^t  Next Dividends = D1 = D0 x (1 + g)  Dividend in 2 periods = D2 = D1 x (1 + g) ^2  Ex. Dividend of $3/share. (PV 3)  Grows at 8%/year (I/Y 8)  What would the dividend be in 5 years? (N 5)  3 x (1.08)^5 = 4.41  or FV = 4.41  Dividend Growth Model -

 P0 = (D0 x (1 + g))/(r - g) = D1/(r - g) Stock price at any point in time:  Pt = (Dt x (1 + g))/(r - g) = Dt+1/(r - g) 3. Non Constant Growth  Ex. Company isn’t paying dividends currently  In 5 years, will pay a dividend of $0.5/share  Required return is 20%  What is price of stock today?  Find what it will be worth once dividend are paid. Then calculate PV of the future price  P4 = D5/(r - g)  = 0.5/(0.2 - 0.1)  = $5  PV of FV of 5  P0 = $5/(1.2)^4  = $2.41  N 4 I/Y 20 FV 5 PV = 2.41  If dividends are not equal, you have to calculate each on separately, add them all then find PV  8.2 Common Stock Features 

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Business Finance Chapter 9 Capital Budgeting

Approaches 1. 2. 3. 4. 5. 6.

Net Present Value (NPV) Payback Rule Discount Payback Rule Internal Rate of Return Profitability Index Mutually Exclusive Projects

Net Cash Flow EBIT + Depreciation - Tax PV = Rate Cost NPV = Year 0 = 165 000

1 = 63 120 2 = 70 800 3 = 91 080 Rate = 12% NPV = 21 627.41 = 0 Accept or reject = < 0 Reject because you’re spending money to work on project Invest 500 000 (Make Negative) 1 = 50 000 2 = -25 000 (Costs to maintain or close down) 3 = 125 000 4 = 175 000 5 = 450 000 6 = 100 000 7 = -25 000 Rate = 8% NPV = 107 414.22 Payback Rule Year 1 -165 000 + 63 120 = -101 880 Management 2.5 Invest + Get = Still need Year 2 -101 880 + 70 800 = -31 080 Year 3 -31 080 + 91 080 = 60 000 31 080 / 91 080 = 0.3412 In Reality Management will receive their money in 2.3412 year therefore we accept Invest Management 4 Years and 4.5 Months Year 1 -150 000 + 75 000 = -75 000 Year 2 -75 000 + -25 000 = -100 000 Year 3 -100 000 + 50 000 = -50 000 Year 4 -50 000 + 25 000 = -25 000 Year 5

- 25 000 + 65 000 = 40 000 25 000 / 65 000 = 0.385 x 12 = 4.62 months Will Receive in 4 Years and 4.62 Months Reject Discount Rule is the Same as NPV Year 1 = -165000 + 63 120/(1.12)^1 = -108642.86 Year 2 = -108642.86 + 70 800/(1.12)^2 = -52201.53 Year 3 = -52201.53 + 91 080/(1.12)^3 = 12627.41 52201.53 / 91 080/(1.12)^3 = 2.805 5 years and 295 days...