Financial Management

Please help me with the highlighted questions!

>Model 2/

12 Chapter

. Mini Case Situation Sam Strother and Shawna Tibbs are vice

–

presidents of Mutual of Seattle Insurance Company and co-direct

s of the company’s pension fund management division. A major new client, the

orthwestern Municipal Alliance, has requested that Mutual of Seattle present an investment seminar to the mayors of the represented cities, and Strother and Tibbs, who will make the actual presentation, have asked you to help them by answering the following questions. Because the Boeing Company operates in one of the league’s cities, you are to work Boeing into the presentation.

a. What are the key features of a bond? The key features of a bond are, Par or face value,

Coupon rate

Maturity

Issue date

and default risk

b. What are call provisions and sinking fund provisions? Do these provisions make bonds more or less risky? A call provision is a provision in a bond contract that gives the issuing corporation the right to redeem the bonds under specified terms prior to the normal maturity date. A sinking fund provision is a provision in a bond contract that requires the issuer to retire a portion of the bond issue each year. A sinking fund provision facilitates the orderly retirement of the bond issue. The call provisions is potentially detrimental to the investor especially if the bonds were issued in a period when interest rates were cyclically high so therefore, bonds with a call provision are riskier than those without a call provision . Call Provisions and Sinking Funds A call provision that allows the issuer to redeem the bond at a specified time before the maturity date. If interest rates fall, the issuer can refund the bonds and issue new bonds at a lower rate. Because of this, borrowers are willing to pay more and lenders require more on callable bonds. In a sinking fund provision, the issuer pays off the loan over its life rather than all at the maturity date. A sinking fund reduces the risk to the investor and shortens the maturity. This is not good for investors if rates fall after issuance. c. How is the value of any asset whose value is based on expected future cash flows determined? The value of an asset is just the present value of its expected future cash flows. d. How is the value of a bond determined? What is the value of a

-year,

$1,000

par value bond with a

percent annual coupon if its required rate of return is 10 percent? Finding the “Fair Value” of a Bond First, we list the key features of the bond as “model inputs”: Years to

Mat:

10
Coupon rate: 1

0% Annual Pmt: $

100 Par value

= FV:

$1,000
Going rate, r

d: 10% The easiest way to solve this problem is to use Excel’s PV function. Click fx, then financial, then PV. Then fill in the menu items as shown in our snapshot in the screen shown just below. Value of bond = $

1,000.00 Thus, this bond sells at its par value. That situation always exists if the going rate is equal to the coupon rate. The PV function can only be used if the payments are constant, but that is normally the case for bonds. e. (1.) What would be the value of the bond described in Part d if, just after it had been issued, the expected inflation rate rose by

percentage points, causing investors to require a

percent return? Would we now have a discount or a premium bond? We could simply go to the input data section shown above, change the value for r from 10% to

13%

. You can set up a data table to show the bond’s value at a range of rates, i.e., to show the bond’s sensitivity to changes in interest rates. This is done below. To make the data table, first type the headings, then type the rates in cells in the left column. Since the input values are listed down a column, type the formula in the row above the first value and one cell to the right of the column of values (this is B

3; note that the formula in B73 actually just refers to the bond pricing formula above in B

0). Select the range of cells that contains the formulas and values you want to substitute (A73:B7

). Then click Data, What-If-Analysis, and then Data Table to get the menu. The input data are in a column, so put the cursor on “column input cell” and enter the cell with the value for r (B37), then Click OK to complete the operation and get the table. Bond Value Going rate, r:

$1,000
0%

$2,000.00 7% $1,

0.71 10%

$1,000.00 13%

$837

.21 20

% $

80.75 We can use the data table to construct a graph that shows the bond’s sensitivity to changing rates. Put B37 here. (2.) What would happen to the value of the 10-year bond over time if the required rate of return remained at 13 percent, or if it remained at 7 percent? Would we now have a premium or a discount bond in either situation? You pick a rate. Value of Bond in Given Year: N 7% 10% 13%
0

$1,2

$1,000 $837
1

$1,1

$1,000

$846 2

$1,

$1,000

$856 3

$1,

$1,000

$867 4

$1,

$1,000

$880 5

$1,1

$1,000

$894 6

$1,102

$1,000

$911 7

$1,079

$1,000

29 8

$1,054

$1,000

$950 9

$1,0

$1,000

$973 10 $1,000 $1,000 $1,000
You pick the rate for a bond: Your choice: 20%
Resulting bond prices $581 $597 $616 $640 $667 $701 $741 $789 $847 $917 $1,000
If rates fall, the bond goes to a premium, but it moves towards par as maturity approaches. The reverse hold if rates rise and the bond sells at a discount. If the going rate remains equal to the coupon rate, the bond will continue to sell at par. Note that the above graph assumes that interest rates stay constant after the initial change. That is most unlikely–interest rates fluctuate, and so do the prices of outstanding bonds. Yield

to Maturity (

YTM

)

f. (1.) What is the yield to maturity on a 10-year, 9 percent annual coupon, $1,000 par value bond that sells for

$887.00

? That sells for $1,134.20? What does the fact that a bond sells at a discount or at a premium tell you about the relationship between rd and the bond’s coupon rate? What is the yield-to-maturity of the bond? Use the

Rate

function to solve the problem.

Years to Mat: 10

Coupon rate:

9% Annual Pmt:

$90.00 Going rate, r =

YTM: 10.91% See RATE function at right. Current price:

$887.00
Par value = FV:

$1,000.00
(2.) What are the total return, the current yield, and the capital gains yield for the discount bond? (Assume the bond is held to maturity and the company does not default on the bond.) Current and

Capital Gains Yield

s The current yield is the annual interest payment divided by the bond’s current price. The current yield provides information regarding the amount of cash income that a bond will generate in a given year. However, it does not account for any capital gains or losses that will be realized if the bond is held to maturity or call. Simply divide the annual interest payment by the price of the bond. Even if the bond made semiannual payments, we would still use the annual interest. Par value $1,000.00
Coupon rate: 9%

Current Yield

= 10.1

5% Annual Pmt: $90.00

Current price: $887.00

YTM: 10.91%
The current yield provides information on a bond’s cash return, but it gives no indication of the bond’s total return. To see this, consider a zero coupon bond. Since zeros pay no coupon, the current yield is zero because there is no interest income. However, the zero appreciates through time, and its total return clearly exceeds zero. YTM =

Current Yield

Capital Gains Yield
Capital Gains Yield =

YTM

–

Current Yield
Capital Gains Yield = 10.91% – 10.

%
Capital Gains Yield =

0.7

6% g. How does the equation for valuing a bond change if semiannual payments are made? Find the value of a 10-year, semiannual payment, 10 percent coupon bond if nominal rd = 13%. Bonds with Semiannual Coupons Since most bonds pay interest semiannually, we now look at the valuation of semiannual bonds. We must make three modifications to our original valuation model: (1) divide the coupon payment by 2, (2) multiply the years to maturity by 2, and (3) divide the nominal interest rate by 2. Use the Rate function with adjusted data to solve the problem. Periods to maturity = 10*2 = 20
Christopher Buzzard: N=20, because of semi-annual compounding (10*2 =

). Coupon rate: 10%
Semiannual pmt = $100/2 = $50.00

Bart Kreps: PMT=$50, because of semiannual payments
(100 ÷ 2) = 50 PV = $834.72 Future Value:

$1,000.00
Periodic rate = 13%/2 = 6.5%
Christopher Buzzard: I=6.5%, because of semi-annual compounding (13%/2 = 6.5%). Note that the bond is now more valuable, because interest payments come in faster. Excel Bond Functions Supose today’s date is January 1, 2013, and the bond matures on December 31, 20

22 Settlement (today) 1/1/13 Maturity

12/31/22 Coupon rate

0.00% Going rate, r

3.00% Redemption (par value)

100
Frequency (for semiannual)

2
Basis (360 or 365 day year)

0
Value of bond = $83.4737

$834.74 Notice that you could choose a current date that is between coupon payments, and the PRICE function will calculate the correct price. See the example below. Settlement (today)

/13

Maturity 12/31/22
Coupon rate 10.00%
Going rate, r 13.00%
Redemption (par value) 100
Frequency (for semiannual) 2
Basis (360 or 365 day year) 0

Value of bond =

$83.6307

$836.31 This is the value of the bond, but it does not include the accrued interest you would pay. The ACCRINT function will calculate accrued interest, as shown below. Issue date 1/1/13
First interest date 6/30/13

Settlement (today) 3/25/13
Maturity 12/31/22
Coupon rate 10.00%
Going rate, r 13.00%
Redemption (par value) 100
Frequency (for semiannual) 2
Basis (360 or 365 day year) 0

Accrued interest = $2.3333

$23.33 Suppose the bond’s price is $1,150. You can also calculate the yield using the YIELD function, as shown below. Curent price $ 1,150.00

Settlement (today) 1/1/13
Maturity 12/31/22
Coupon rate 10.00%
Redemption (par value) 100
Frequency (for semiannual) 2
Basis (360 or 365 day year) 0

Yield

7.81% h. Suppose a 10-year, 10 percent, semiannual coupon bond with a par value of $1,000 is currently selling for

$1,135.90

, producing a nominal yield to maturity of 8 percent. However, the bond can be called after 5 years for a price of $1,050. (1.) What is the bond’s nominal yield to call (YTC)? (2.) If you bought this bond, do you think you would be more likely to earn the YTM or the YTC? Why? Yield to Call The yield to call is the rate of return investors will receive if their bonds are called. If the issuer has the right to call the bonds, and if interest rates fall, then it would be logical for the issuer to call the bonds and replace them with new bonds that carry a lower coupon. The yield to call (YTC) is found similarly to the YTM. The same formula is used, but years to maturity is replaced with years to call, and the maturity value is replaced with the call price.

Use the Rate function to solve the problem.

Number of semiannual periods to call:

10
Seminannual coupon rate:

Semiannual Rate = I = YTC = 3.77% Seminannual Pmt:

$50.00

Annual nominal rate = 7.53% Current price: $1,135.90
Call price = FV $1,050.00 Par value $1,000.00
i. Write a general expression for the yield on any debt security (rd) and define these terms: real risk-free rate of interest (r*), inflation premium (IP), default risk premium (DRP), liquidity premium (LP), and maturity risk premium (MRP). j. Define the nominal risk-free rate (rRF). What security can be used as an estimate of rRF? k. Describe a way to estimate the inflation premium (IP) for a T-Year bond. l. What is a bond spread and how is it related to the default risk premium? How are bond ratings related to default risk? What factors affect a company’s bond rating? m. What is interest rate (or price) risk? Which bond has more interest rate risk, an annual payment 1-year bond or a 30-year bond? Why?

Interest Rate

Risk is the risk of a decline in a bond’s price due to an increase in interest rates.

Price

sensitivity to interest rates is greater (1) the longer the maturity and (2) the smaller the coupon payment. Thus, if two bonds have the same coupon, the bond with the longer maturity will have more interest rate sensitivity, and if two bonds have the same maturity, the one with the smaller coupon payment will have more interest rate sensitivity.

Your Choice of Maturity 10-Yr Maturity 1-Yr Maturity Years to Mat: 10 Rate Price Rate Price Rate Price
Coupon rate: 9%

$929.60 $887.63 $982.87 Annual Pmt: $90.00

5.0% 1,173.

5.0%

$1,308.87

5.0%

$1,038.10 Current price: $887.63

7.0% 1,082.00

7.0%

$1,140.47

7.0%

$1,018.69 Par value = FV: $1,000.00

9.0%

1,000.00 9.0% $1,000.00 9.0% $1,000.00
YTM =

10.9% 11.0% 9

.08

11.0%

$882.22

11.0%

$981.98 13.0% 859.31

13.0%

$782.95

13.0%

$964.60 Years to Mat: 1

Scratch sheet for Your Choice Coupon rate: 9% Years to Mat: 5
Annual Pmt: $90.00 Coupon rate: 9%
Current price: $982.87 Annual Pmt: $90.00
Par value = FV: $1,000.00 Current price: $929.60
YTM = 10.9% Par value = FV: $1,000.00
YTM = 10.9%
Enter your choice for years to maturity: 5
n. What is reinvestment rate risk? Which has more reinvestment rate risk, a 1-year bond or a 10-year bond? o. How are interest rate risk and reinvestment rate risk related to the maturity risk premium? p. What is the term structure of interest rates? What is a yield curve? The term structure describes the relationship between long-term and short-term interest rates. Graphically, this relationship can be shown in what is known as the yield curve. See the hypothetical curve below. Hypothetical Inputs See to right for actual date used in graph. Suppose most investors expect the inflation rate to be 5 percent next year, 6 percent the following year, and 8 percent

thereafter.

The real risk-free rate is 3 percent. The maturity risk premium is zero for securities that mature in 1 year or less, 0.1 percent for 2-year securities, and then the MRP increases by 0.1 percent per year thereafter for 20 years, after which it is stable. What is the interest rate on 1-year, 10-year, and 20-year

Treasury

securities? Draw a yield curve with these data. What factors can explain why this constructed yield curve is upward sloping? Real risk free rate

3.00%
Expected inflation of

for the next

years. Expected inflation of 6% for the next 1 years.
Expected inflation of

thereafter.
Now, we want to set up a table that encompasses all of the information for our yield curve. INPUT DATA Real risk free rate 3.00%
Expected inflation of 5% for the next 1 years.
Expected inflation of 6% for the next 1 years.
Expected inflation of 8% thereafter.
Years to

Real risk-free Inflation Maturity Risk

Treasury
Maturity

rate (r*) Premium (IP) Premium (MRP)

Yield
1 3.00%

5.00%

0.00%

8.00% 2 3.00%

5.50% 0.10% 8.60% 3 3.00%

6.33% 0.20% 9.53% 4 3.00%

6.75% 0.30% 10.05% 5 3.00%

7.00% 0.40% 10.40% 6 3.00%

7.17% 0.50% 10.67% 7 3.00%

7.29% 0.60% 10.89% 8 3.00%

7.38% 0.70% 11.08% 9 3.00%

7.44% 0.80% 11.

% 10 3.00%

7.50% 0.90% 1

1.40% 11 3.00%

7.55% 1.00% 11.55% 12 3.00%

7.58% 1.10% 11.68% 13 3.00%

7.62% 1.20% 11.82% The yield is upward sloping due to increasing expected inflation and an increasing maturity risk premium

14 3.00%

7.64% 1.30% 11.94% 15 3.00%

7.67%

1.40%

12.07% 16 3.00%

7.69% 1.50% 12.

% q. Briefly describe bankruptcy law. If a firm were to default on the bonds, would the company be immediately liquidated? Would the bondholders be assured of receiving all of their promised payments?

17 3.00%

7.71% 1.60% 12.31% 18 3.00%

7.72% 1.70% 12.42% 19 3.00%

7.74% 1.80% 12.54% 20 3.00%

7.75% 1.90% 12.65% 21 3.00%

7.76% 2.00% 12.76% 22 3.00%

7.77% 2.10% 12.87% 23 3.00%

7.78% 2.20% 12.98% 24 3.00%

7.79% 2.30% 13.09% 25 3.00%

7.80% 2.40% 13.20% 26 3.00% 7.81%

2.50% 13.31% 27

3.00% 7.81%

2.60% 13.41% 28 3.00%

7.82% 2.70% 13.52% 29 3.00%

7.83% 2.80% 13.63% 30 3.00% 7.83%

2.90% 13.73% The table above gives us all of the components for our Treasury yield curve. Recall, we have said that Treasury securities are subject to two kinds of risk premiums, the inflation premium and the maturity risk premium. Just as we “built” Treasury yields in the table, we can “build” a yield curve based upon these expectations.

Interest Rate Sensitivity of a 10-Year Bond

0 7.0000000000000007E-2 0.1 0.13 0.2 2000 1210.7074462279782 1000.0000000000001 837.21269572141352 580.75279144492288

Value of the bond over time

Rates fall to 7% 1210.7074462279782 1195.4569674639365 1179.138955186412 1161.6786820494608 1142.9961897929231 1123.0059230784277 1101.6163376939176 1078.729481332492 1054.2405450257663 1028.0373831775701 1000 Rates stay the same 1000.0000000000001 999.99999999999989 1000 1000 1000 1000.0000000000001 1000 1000 1000 999.99999999999989 1000 Rates increase to 13% 837.21269572141352 846.05034616519731 856.03689116667294 867.32168701834041 880.07350633072463 894.48306215371883 910.76586023370237 929.16542206408371 949.95692693241449 973.45132743362842 1000 Your choice 580.75279144492288 596.90334973390736 616.28401968068897 639.54082361682674 667.44898834019205 700.93878600823041 741.12654320987656 789.35185185185185 847.22222222222229 916.66666666666674 1000

Years to maturity

Price

10 Yr. versus 1 Yr.

0.05 7.0000000000000007E-2 0.09 0.11 0.13 1038.0952380952381 1018.6915887850466 999.99999999999989 981.9819819819819 964.60176991150456 0.05 7.0000000000000007E-2 0.09 0.11 0.13 1308.8693971673924 1140.4716308186521 999.99999999999989 882.21535977717576 782.95026096188474 Your Choice 1173.1790668252329 1082.0039487189517 1000.0000000000001 926.08205964701062 859.31074953829182 YTM

Hypothetical Treasury Yield Curve

Real Risk Free Rate 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 Inflation Premium 0.05 5.5E-2 6.3333333333333339E-2 6.7500000000000004E-2 6.9999999999999993E-2 7.166666666666667E-2 7.2857142857142856E-2 7.3749999999999996E-2 7.4444444444444452E-2 7.4999999999999997E-2 7.5454545454545455E-2 7.5833333333333336E-2 7.6153846153846155E-2 7.6428571428571429E-2 7.66 66666666666675E-2 7.6875000000000013E-2 7.7058823529411763E-2 7.7222222222222234E-2 7.7368421052631586E-2 7.7499999999999999E-2 Maturity Risk Premium 0 1E-3 2E-3 3.0000000000000001E-3 4.0000000000000001E-3 5.0000000000000001E-3 6.0000000000000001E-3 7.0000000000000001E-3 8.0000000000000002E-3 9.0000000000000011E-3 0.01 1.0999999999999999E-2 1.2E-2 1.3000000000000001E-2 1.4E-2 1.4999999999999999E-2 1.6E-2 1.7000000000000001E-2 1.8000000000000002E-2 1.9E-2 Maturity
Interest Rate

Value at 7%

Value at 13%

td><

>Mini

Case 1

/6/1

Chap

er 8 Mini Case

Situation

Your employer

a mid

–

sized human resources mana

ement company, is considering expansion into related fields, including the acquisition of Temp Force Company, an employment agency that supplies word processor

erators and computer programmers to businesses with temporary heavy workloads. Your employer is also considering the purchase of a Biggerstaff & McDonald

(

B&M

)

, a privately held company owned by two friends, each with 5 million shares of stock. B&M currently has free cash flow of $2

million, which is expected to grow at a constant rate of

. B&M’s financial statements report marketable securities of $1

0 million, debt of $200 million, and preferred stock of $50 million. B&M’s weighted average cost of capital (

WACC

) is

11%

. Answer the following questions.

a. Describe briefly the legal rights and privileges of common stockholders. Features of Common Stock

1. Common Stock represents ownership. 2. Ownership implies control.

. Stockholders elect directors. 4. Directors hire management who attempt to maximize stock price.

Classified Stock Classified Stock carries special provisions. For example, shares could be classified as founders’ shares which come with voting rights but dividend restrictions.

b. What is free cash flow (

FCF

)? What is the weighted average cost of capital? What is the free cash flow valuation model?

c. Use a pie chart to illustrate the sources that comprise a hypothetical company’s total value. Using another pie chart, show the claims on a company’s value. How is equity a residual claim? Data for charts Column1 10 Mkt. Sec.

Claims on

alue

Pref. Stk.

1
Debt

3
7

d. Suppose the free cash flow at Time 1 is expected to grow at a constant rate of g

forever. If

< WACC, what is a formula for the present value of expected free cash flows when discounted at the WACC? If the most recent free cash flow is expected to grow at a constant rate of gL

forever (and gL < WACC), what is a formula for the present value of expected free cash flows when discounted at the WACC? If constant growth begins at Time 1: If constant growth begins at Time 0: e. Use B&M’s data and the free cash flow valuation model to answer the following questions. INPUT DATA SECTION: Data used for valuation (in millions) Free cash flow $24.0 WACC 11%
Growth

5%
Short-term investments $100.0 Debt

$200.0 Preferred stock $50.0 Number of shares of stock 10.0 (1) What is its estimated value of operations?

Vop

FCF1

= FCF0 (1

gL)

(WACC-gL) (WACC-gL)
Vop = $25.2 0.06 Vop =

$420.0

0 (2) What is its estimated total corporate value? Value of Operation

$420.0
Plus Value of Non-operating Assets

$100.0
Total Corporate Value $520.0 (3) What is its estimated intrinsic value of equity? Debt holders have the first claim on corporate value. Preferred stockholders have the next claim and the remaining is left to common stockholders.

Total Corporate Value $520.0

Minus Value of Debt

$200.0
Minus Value of Preferred Stock

$50.0

Intrinsic Value of

Equity

$270.0 (4) What is its estimated intrinsic stock price per share? Intrinsic Value of Equity

$270.0
Divided by number of shares

10.0
Intrinsic price per share $27.00 Estimating the Value of R&R’s Stock Price (Millions, Except for Per Share Data) INPUTS: Value of operations = $420.00 Value of nonoperating assets = $

100.00 All debt = $

200.00 Preferred stock = $

50.00 Number of shares of common stock = 10.00 ESTIMATING PRICE PER SHARE Value of operations $420.00
+ Value of nonoperating assets

100.00
Total estimated value of firm $520.00 − Debt

200.00
− Preferred stock

50.00
Estimated value of equity $270.00 ÷

Number of shares

10.00
Estimated stock price per share =

$27.00
f. You have just learned that B&M has undertaken a major expansion that will change its expected free cash flows to −$10 million in 1 year, $20 million in 2 years, and $35 million in 3 years. After 3 years, free cash flow will grow at a rate of 5%. No new debt or preferred stock were added, the investment was financed by equity from the owners. Assume the WACC is unchanged at 11% and it that there are still has 10 million shares of stock outstanding. (1.) What is its horizon value (i.e., its value of operations at year three)? What is its current value of operations (i.e., at time zero)? Explicit forecast: Year

0 1 2 3
FCF

FCF1

FCF2 FCF3 Constant growth from Year 3 and afterwards: Year 0 1 2 3 4 5

… t FCF FCF1 FCF2 FCF3

FCF3(1+gL) FCF4(1+gL) FCFt(1+gL) Explicit forecast ends at Year 3, so make the horizon date Year 3, too. (Note: it is possible to make the horizon date Year 2 because FCF3 is known and grows at a constant rate, but it is easy to make mistakes if horizon year is not set equal to end of explicit forecast.)

3 = Vop,3 = PV of FCF4 and beyond discounted back to Year 3

Year 0 1 2 3 4 5 … t

FCF FCF3(1+gL) FCF4(1+gL) FCFt(1+gL)
HV3 ←↵

←↵ ←↵
Because free cash flows are constant from Year 4 and beyond, we can apply the constant growth model at Year 3: The general horizon value formula is: R&R’s explicit forecast:

Year 0 1 2 3

FCF

−$10.00 $20.00 $35.00 After Year 3,

gL =

5%
WACC =

11%
R&R’s horizon value: HV3 = Vop,3 = FCF0 (1+gL)

(WACC-gL)

HV3 = Vop,3 =

$36.75

0 6% HV3 = Vop,3 =

$612.50 After estimating the horizon value, you can estimate the current value of operations by following these steps: (1) Find the present value of the FCFs from the explicit forecast, discounted back to Time 0 at the WACC; (2) find the present value of the horizon value, discounted back to Time 0 at the WACC; and (3) sum the PV of the FCFs and the PV of the horizon value. This sum is the present value of all future

FCF

from Time 0 to infinity, discounted back to Time 0. Therefore, this sum is the current value of operations, Vop,0.

Year 0 1 2 3 4 5 … t
FCF FCF1 FCF2 FCF3

PV of FCF in explicit forecast

←↵ ←↵ ←↵

FCF3(1+gL) FCF4(1+gL) FCFt(1+gL)
HV3 ←↵ ←↵ ←↵

PV of HV

is the PV of FCF beyond the explicit forecast

←↵ ←↵ ←↵

B&M’s

Value of Operations

(Millions of Dollars)
INPUTS:

gL = 5.00% WACC =

11.00% Projections Year 0 1 2 3 4

FCF −$10.00 $20.00 $35.00

↓

FCF1 FCF2 FCF3

──────

────── ──────
(1+WACC)1 (1+WACC)2 (1+WACC)3 HV = Vop,3 FCF3(1+gL) PVs of FCFs −$9.009 ───────── $16.232 (WACC− gL) $25.592 PV of HV

$447.85

$612.50 $36.75
= ────── = ──── Vop = $480.67

(1+WACC)3

6.00% (2.) What is its value of equity on a price per share basis? Estimating the Value of B&M’s Stock Price (Millions, Except for Per Share Data)

INPUTS:

Value of operations =

$480.67

Value of nonoperating assets =

$100.00

All debt =

$200.00

Preferred stock =

$50.00

Number of shares of common stock = 10.00
ESTIMATING PRICE PER SHARE

Value of operations $480.67

+ Value of nonoperating assets 100.00

Total estimated value of firm

$580.67

− Debt 200.00
− Preferred stock 50.00

Estimated value of equity

$330.67

÷ Number of shares 10.00

Estimated stock price per share =

$33.07 g. If B&M undertakes the expansion, what percent of B&M’s value of operations at Year 0 is due to cash flows from Years 4 and beyond? Hint: use the horizon value at t = 3 to help answer this question.

INPUTS:

Vop,0

$480.67
HV3 =

$612.50
First, calculate the present value of the horizon value. Then divide the Year 0 value of operations by the present value of the horizon value. This will show what percent of value is due to cash flows occurring 4 or more years in the future. PV of HV3

= HV3 / (1+WACC)3 PV of HV3 = $447.85
Percent of value
due to cash flows beyond Year 3

PV of HV3
=
Vop,0
Percent of value
due to cash flows beyond Year 3
=

93% h. Based on your answer to the previous question, what are two reasons why managers often emphasize short-term earnings? i. Your employer also is considering the acquistion of Hatfield Medical Supplies. You have gathered the following data regarding Hatfield, with all dollars reported in millions: (1) most recent sales of

$2,000

; (2) most recent total net operating capital,

OpCap

$1,120

; (3) most recent operating profitability ratio,

NOPAT

Sales

4.5%

; and (4) most recent capital requirement ratio,

= OpCap/Sales = 56%. You estimate that the growth rate in sales from Year 0 to Year 1 will be

10%

, from Year 1 to Year 2 will be

, from Year 2 to Year 3 will be 5%, and from Year 3 to Year 4 will be 5%. You also estimate that the long-term growth rate beyond Year 4 will be 5%. Assume the operating profitability and capital requirement ratios will not change. Use this information to forecast Hatfield’s sales, net operating profit after taxes (NOPAT), OpCap, free cash flow, and return on invested capital (

ROIC

) for Years 1 through 4. Also estimate the annual growth in free cash flow for Years 2 through 4. The weighted average cost of capital (WACC) is

. How does the ROIC in Year 4 compare with the WACC? No Change Actual Forecast

Year 0 1 2 3 4

Inputs WACC

9.0% Sales $2,000
OpCap $1,120
Sales growth rate

10% 8% 5% 5%
NOPAT/Sales

4.5% 4.5% 4.5% 4.5% 4.5%
OpCAP/Sales 56.0%

56.0% 56.0% 56.0% 56.0%

Forecast

Sales $2,000

$2,200 $2,376 $2,495 $2,620 NOPAT

$99 $107 $112 $117.879 OpCap $1,120

$1,232 $1,331 $1,397.088 $1,466.942 FCF

−$13.00 $8.360 $45.738 $48.025 Growth in FCF -164% 447.1% 5.0% ROIC

8.0%

8.0% 8.0% 8.0%
j. What is the horizon value at Year 4? What is the value of operations at Year 4? Which is larger, and what can explain the difference? What is the value of operations at Year 0? How does the value of operations compare with the current total net operating capital? Horizon Value: =

$1,260.65 Value of Operations: Present value of HV $893.08 + Present value of FCF $64.450 Value of operations ≈ $958 The value of operations is less than the total net operating capital because the ROIC is too low when compared to the WACC. ROIC must be greater than WACC/(1+gL) before the horizon value exceeds the total net operating capital. ROIC needed to make HV greater than Vop at horizon: ROIC

= WACC/(1+gL) ROIC at horizon = 8.04%

< 8.57%

= WACC/(1+gL)
Horizon value ≈ $1,261

< $1,467 = OpCap at horizon Current value of operations

≈

$958 < $1,120 = OpCap at horizon k. What are value drivers? What happens to the ROIC and current value of operations if expected growth increases by 1 percentage point relative to the original growth rates (including the long-term growth rate)? What can explain this? Hint: Use

Scenario

Manager. Value drivers are the inputs to the free cash flow valuation model that managers are able to influence: sales growth rates, operating profitability, capital requirements, and the cost of capital. Using the Scenario Manager, the new ROIC and value of operations are: Scenario No Change

Improve Growth g0,1

10% 11%
g1,2

8% 9%
g2,3

5% 6%
g3,4

5% 6%
gL 5% 6%
OP 4.5% 4.5%
CR 56.0% 56.0%
ROIC 8.0% 8.0%
Current value of operations $958

$933 WACC

9.00%

9.00%
WACC/(1+WACC) 8.26%

8.26%
Growth hurts value because the ROIC is too low. Growth will only help value if ROIC>WACC/(1+WACC). l. Assume growth rates are at their original levels. What happens to the ROIC and current value of operations if the operating profitability ratio increases to

5.5%

? Now assume growth rates and operating profitability ratios are at their original levels. What happens to the ROIC and current value of operations if the capital requirement ratio decreases to 51%? Assume growth rates are at their original levels. What is the impact of simultaneous improvements in operating profitability and capital requirements? What is the impact of simultaneous improvements in the growth rates, operating profitability, and capital requirements? Hint: Use Scenario Manager. Using the Scenario Manager and improving operating profitability, the new ROIC and value of operations are: Scenario No Change

Improve OP g0,1 10% 10%
g1,2 8% 8%
g2,3 5% 5%
g3,4 5% 5%
gL 5% 5%
OP 4.5% 5.5%

CR 56.0% 56.0%

ROIC 8.0%

9.8% Current value of operations $958

$1,523

WACC 9.00% 9.00%
WACC/(1+WACC) 8.26% 8.26%

Using the Scenario Manager and improving capital requirements, the new ROIC and value of operations are: Scenario No Change

Improve CR

g0,1 10% 10%
g1,2 8% 8%
g2,3 5% 5%
g3,4 5% 5%
gL 5% 5%
OP 4.5% 4.5%

CR 56.0%

51.0% ROIC 8.0%

8.8% Current value of operations $958

$1,191

WACC 9.00% 9.00%
WACC/(1+WACC) 8.26% 8.26%

Using the Scenario Manager and improving operating profitability and capital requirements, the new ROIC and value of operations are: Scenario No Change

Improve OP and CR

g0,1 10% 10%
g1,2 8% 8%
g2,3 5% 5%
g3,4 5% 5%
gL 5% 5%
OP 4.5% 5.5%
CR 56.0% 51.0%

ROIC 8.0%

10.8% Current value of operations $958

$1,756

WACC 9.00% 9.00%
WACC/(1+WACC) 8.26% 8.26%

Using the Scenario Manager and improving growth rates, operating profitability, and capital requirements, the new ROIC and value of operations are: Scenario No Change

Improve All

g0,1 10% 11%
g1,2 8% 9%
g2,3 5% 6%
g3,4 5% 6%
gL 5% 6%
OP 4.5% 5.5%
CR 56.0% 51.0%
ROIC 8.0% 10.8%

Current value of operations $958

$2,008

WACC 9.00% 9.00%
WACC/(1+WACC) 8.26% 8.26%

m. What insight does the free cash flow valuation model give provide us about possible reasons for market volatility? Hint: Look at the value of operations for the combinations of ROIC and gL in the previous questions. ROIC
gL 8.0% 8.8% 9.8% 10.8%
5% $958 $1,191 $1,523 $1,756
6% $933 $2,008
Notice that small changes in ROIC and growth cause large changes in value. b. (1.) Write out a formula that can be used to value any dividend-paying stock, regardless of its dividend pattern. The value of any financial asset is equal to the present value of future cash flows provided by the asset. When an investor buys a share of stock, he or she typically expects to receive cash in the form of dividends and then, eventually, to sell the stock and to receive cash from the sale. Moreover, the price any investor receives is dependent upon the dividends the next investor expects to earn, and so on for different generations of investors. Thus, the stock’s value ultimately depends on the cash dividends the company is expected to provide and the discount rate used to find the present value of those dividends. Here is the basic dividend valuation equation: D1

. . . . DN ( 1

rs ) ( 1 + rs ) 2 ( 1 + rs ) N The dividend stream theoretically extends on out forever, i.e., n = infinity. Obviously, it would not be feasible to deal with an infinite stream of dividends, but fortunately, an equation has been developed that can be used to find the PV of the dividend stream, provided it is growing at a constant rate. Naturally, trying to estimate an infinite series of dividends and interest rates forever would be a tremendously difficult task. Now, we are charged with the purpose of finding a valuation model that is easier to predict and construct. That simplification comes in the form of valuing stocks on the premise that they have a constant growth rate. (2.) What is a constant growth stock? How are constant growth stocks valued? In this stock valuation model, we first assume that the dividend and stock will grow forever at a constant growth rate. Naturally, assuming a constant growth rate for the rest of eternity is a rather bold statement. However, considering the implications of imperfect information, information asymmetry, and general uncertainty, perhaps our assumption of constant growth is reasonable. It is reasonable to guess that a given firm will experience ups and downs throughout its life. By assuming constant growth, we are trying to find the average of the good times and the bad times, and we assume that we will see both scenarios over the firm’s life. In addition to assuming a constant growth rate, we will be estimating a long-term required return for the stock. By assuming these variables are constant, our price equation for common stock simplifies to the following expression: D1
( rs – gL ) In this equation, the long-run growth rate (g) can be approximated by multiplying the firm’s return on assets by the retention ratio. Generally speaking, the long-run growth rate of a firm is likely to fall between 5% and 8% a year. (c.) What happens if a company has a constant gL which exceeds rs? Will many stocks have expected growth greater than the required rate of return in the short run (i.e., for the next few years)? In the long run (i.e., forever)? o. Assume that Temp Force has a beta coefficient of 1.2, that the risk-free rate (the yield on T-bonds) is 7.0%, and that the market risk premium is 5%. What is the required rate of return on the firm’s stock? CAPM = rRF + b (rRF – rM) 7% + 1.2(5%) =

13% p. Assume that Temp Force is a constant growth company whose last dividend (D0, which was paid yesterday) was

$2.00

and whose dividend is expected to grow indefinitely at a 6% rate. (1.) What is the firm’s current stock price? (2.) What is the stock’s expected value 1 year from now? (3.) What are the expected dividend yield, the capital gains yield, and the total return during the first year? Constant Growth Model:

INPUTS:

D0 =

$2.00
gL = 6%
rs = 13.0% D1 =

D0 (1 + g) ( rs – gL ) ( rs – gL )
D1 = D0 (1 + gL) = $2.12 P0

D1 = $2.12
( rs – gL )

0.07 $30.29 Stock Price 1 year from now: P1 =

( rs – gL )

D2 = D1 (1+gL) = $2.2472 P1 =

$2.2472

0.07

P1 =

$32.10 Dividend

Yield

CG Yield = P1 – P0 P0

P0
Dividend Yield =

$2.12 CG Yield =

$1.82 $30.29 $30.29
Dividend Yield =

7.00%

CG Yield =

6.00%
Bart Kreps: For a constant growth stock, the capital gains yield equals the growth rate. Total Yield =

Dividend Yield

+ CG
Yield Total Yield =

13.00% q. Now assume that the stock is currently selling at $30.29. What is its expected rate of return? Rearrange to rate of return formula D1 + gL

$2.12 + 0.06

$30.29

13%
r. Now assume that Temp Force’s dividend is expected to experience nonconstant growth of

30%

from Year 0 to Year 1,

25%

from Year 1 to Year 2, and

15%

from Year 2 to Year 3. After Year 3, dividends will grow at a constant rate of 6%. What is the stock’s intrinsic value under these conditions? What are the expected dividend yield and capital gains yield during the first year? What are the expected dividend yield and capital gains yield during the fourth year (from Year 3 to Year 4)? For many companies, it is unreasonable to assume that it grows at a constant growth rate. Hence, valuation for these companies proves a little more complicated. The valuation process, in this case, requires us to estimate the short-run non-constant growth rate and predict future dividends. Then, we must estimate a constant long-term growth rate at which the firm is expected to grow. Generally, we assume that after a certain point of time, all firms begin to grow at a rather constant rate. Of course, the difficulty in this framework is estimating the short-term growth rate, how long the short-term growth will hold, and the long-term growth rate. Specifically, we will predict as many future dividends as we can and discount them back to the present. Then we will treat all dividends to be received after the convention of constant growth rate with the Gordon constant growth model described above. The point in time when the dividend begins to grow at a constant rate is called the horizon date. When we calculate the constant growth dividends, we solve for a horizon value (also called the terminal value or continuing value) as of the horizon date. We can then find the present value of the dividends in the forecast period and the present value of the horizon value, which gives the current estimated stock price. Process for Finding the Value of a Nonconstant Growth Stock

INPUTS:

D0 = $2.00

Last dividend the company paid. rs = 13.0%

Stockholders’ required return. g0,1 =

30%

Growth rate

for Year 1 only. g1,2 =

25%

Growth rate for Year 2 only. g2,3 =

15%

Growth rate for Year 3 only. gL = 6%

Constant long-run growth rate for all years after Year 3. Growth rate 30% 25% 15% 6% 6%

Year 0 1 2 3 4

Dividends $2.6000 $3.2500 $3.7375

↓ ↓ ↓

D1 D2

D3 D4 ────── ────── ──────

──── = (1+rs)1 (1+rs)2 (1+rs)3 (rs− gL)

↓

D3 (1+gL) PVs of dividends $2.301 ────── = $2.545

(rs− gL)
$2.590

↓
PV of HV3 $39.224 $56.596 $3.962 = ───────

$56.596

= ────

=
$46.661

(1+rs)3 7.00%
Expected Dividend and CG Yields at t = 0 Dividend Yield =

5.6% CG Yield =

7.4% Total Return =

13.0%
Expected Dividend and CG Yields at t = 3 Dividend Yield =

0.0% CG Yield = 13.0%

Total Return = 13.0%

s. Compare and contrast the free cash flow valuation model and the dividend growth model. t. What is market multiple analysis? u. What is preferred stock? Suppose a share of preferred stock pays a dividend of

$2.10

and investors require a return of 7%. What is the estimated value of the preferred stock? The dividend stream would be a perpetuity. Vps =

Dividend ÷

rps Vps = $2.10 ÷ 7.00%
Vps =

$30.00

Value of Operations
Column1

Mkt. Sec. 10 1

Equity

Claims on Value

Pref. Stk. Debt 1 3 7

Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
Value of Operations
Column1
Mkt. Sec. 10 1
Equity
Claims on Value
Pref. Stk. Debt 1 3 7
L
L
t
t
,
op
t
g
WACC
)
g
1
(
FCF
V
HV
–
+
=
=
L

t,opt

gWACC

)g1(FCF

VHV







L
1
0
,
op
g
WACC
FCF
V
–
=
L
L
0
0
,
op
g
WACC
)
g
1
(
FCF
V
–
+
=
L
L
3
3
,
op
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WACC
)
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1
(
FCF
V
HV
–
+
=
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3,op3

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

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