chapter 4 – support

4b.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Chapter 4 – Chapter 4 – SupportSupport

The Valuation of The Valuation of Long-Term SecuritiesLong-Term Securities

The Valuation of The Valuation of Long-Term SecuritiesLong-Term Securities


Bond C has a $1,000 face value and provides an 8% annual coupon for 30 years. The appropriate discount rate is 10%. What is the value of the coupon bond?

WhereWhere V V = $811 (rounded answer)$811 (rounded answer).

Bond C has a $1,000 face value and provides an 8% annual coupon for 30 years. The appropriate discount rate is 10%. What is the value of the coupon bond?

WhereWhere V V = $811 (rounded answer)$811 (rounded answer).

Remember?Remember? Coupon Coupon Bond ExampleBond ExampleRemember?Remember? Coupon Coupon Bond ExampleBond Example

Well, we can use our knowledge of TVM from Chapter 3. The value of a bond has been shown to be the

present value of the coupon payments (an annuity) and the future maturity value.

Refer to ‘VW13E-04.xlsx’ on the ‘Bond Valuation’ tab.

Well, we can use our knowledge of TVM from Chapter 3. The value of a bond has been shown to be the

present value of the coupon payments (an annuity) and the future maturity value.



Coupon Bond ExampleCoupon Bond ExampleCoupon Bond ExampleCoupon Bond Example

Students should notice that the valuation is exactly the same as other accurate methods to solve and can be solved in one step in Excel using ‘=pv(.1,30,80,1000)’.


Students should notice that the valuation is exactly the same as other accurate methods to solve and can be solved in one step in Excel using ‘=pv(.1,30,80,1000)’.


B C D E F

2 Explanations

3 10.00% 10% Reqd return per pd (yearly)

4 30 Number of periods (30 years here)

5 80.00$ $80 received per yr (positive)

6 1,000.00$ Assumed face amount of $1000

7 0 Ordinary Annuity

8

9 ($811.46) =PV(D3,D4,D5,D6,D7)This amount is "negative" as we assume the investorwill purchase the bond for that amount today.

fv:type:

Output - Bond ValuationBond Value today (pv)

Inputs for Bond Valuation!rate:

nper: pmt:


Remember?Remember? Zero-Coupon Zero-Coupon Bond ExampleBond ExampleRemember?Remember? Zero-Coupon Zero-Coupon Bond ExampleBond Example

Bond Z has a $1,000 face value and a 30 year life. The appropriate discount rate is 10%. What is the value of the zero-coupon bond?

… V V = $57.00 (rounded answer). $57.00 (rounded answer).

Bond Z has a $1,000 face value and a 30 year life. The appropriate discount rate is 10%. What is the value of the zero-coupon bond?

… V V = $57.00 (rounded answer). $57.00 (rounded answer).

This is the same type of problem once again, EXCEPT there is no annuity cash flow! It is simply a straight

PV-type problem of finding the PV of the maturity value. We can place a value of $0 in the payment cell.


This is the same type of problem once again, EXCEPT there is no annuity cash flow! It is simply a straight

PV-type problem of finding the PV of the maturity value. We can place a value of $0 in the payment cell.



Zero-Coupon Bond Zero-Coupon Bond ExampleExampleZero-Coupon Bond Zero-Coupon Bond ExampleExample

Students should notice that the valuation is again exactly the same as other accurate methods and can be solved in

one step using ‘= pv(.1,30,0,1000)’.


Students should notice that the valuation is again exactly the same as other accurate methods and can be solved in

one step using ‘= pv(.1,30,0,1000)’.


B C D E F

2 Explanations

3 10.00% 10% Reqd return per pd (yearly)

4 30 Number of periods (30 years here)

5 -$ $0 received per yr (positive)

6 1,000.00$ Assumed face amount of $1000


8

9 ($57.31) =PV(D3,D4,D5,D6,D7)This amount is "negative" as we assume the investorwill purchase the bond for that amount today.

fv:type:



nper: pmt:


Remember? Remember? Semiannual Semiannual CompoundingCompoundingRemember? Remember? Semiannual Semiannual CompoundingCompounding

(1) Divide kkdd by 22

(2) Multiply nn by 22

(3) Divide II by 22

(1) Divide kkdd by 22

(2) Multiply nn by 22

(3) Divide II by 22

Most bonds in the US pay interest twice a year (1/2 of the annual

coupon).Adjustments needed:

Most bonds in the US pay interest twice a year (1/2 of the annual

coupon).Adjustments needed:


Semiannual Coupon Semiannual Coupon Bond ExampleBond ExampleSemiannual Coupon Semiannual Coupon Bond ExampleBond Example

• Bond C was purchased on 12-31-2009 and will be redeemed on 12-31-2024. This is identical to the 15-year period we discussed for Bond C.

• It is an American-style and pays its annual coupon interest semiannually. The stated coupon rate is 7%.

• The US economy has recently been struggling and market interest rates have fallen to 5.5%.

• You expect to hold the bond to maturity to redeem the $1,000 face amount.

• What is the value of this bond?

• Bond C was purchased on 12-31-2009 and will be redeemed on 12-31-2024. This is identical to the 15-year period we discussed for Bond C.

• It is an American-style and pays its annual coupon interest semiannually. The stated coupon rate is 7%.

• The US economy has recently been struggling and market interest rates have fallen to 5.5%.

• You expect to hold the bond to maturity to redeem the $1,000 face amount.

• What is the value of this bond?


Semiannual Coupon Semiannual Coupon Bond ExampleBond ExampleSemiannual Coupon Semiannual Coupon Bond ExampleBond Example

Students should notice that we have adjusted the rate, nper and pmt values in the semiannual problem. Again, this can be solved

in one step using ‘= pv(.0275,30,35,1000)’.



in one step using ‘= pv(.0275,30,35,1000)’.


B C D E F

2 Explanations

3 2.75% 5.5% Reqd return annual (2.75/semi)

4 30 Number of periods (15 years x 2)

5 35.00$ 7% is $70/yr or $35 per semiannual

6 1,000.00$ Stated maturity amount of $1000


8

9 ($1,151.87) =PV(D3,D4,D5,D6,D7)This amount is "negative" as we assume the investorwill purchase the bond for that amount today.

fv:type:



nper: pmt:


Remember? Remember? Preferred Preferred Stock ExampleStock ExampleRemember? Remember? Preferred Preferred Stock ExampleStock Example

Stock PS has an 8%, $100 par value issue outstanding. The appropriate

discount rate is 10%. What is the value of the preferred stockpreferred stock? … V = $80.

Stock PS has an 8%, $100 par value issue outstanding. The appropriate

discount rate is 10%. What is the value of the preferred stockpreferred stock? … V = $80.

Students should recall that perpetuities such as preferred stock can be generally solved with a simple calculator solution (cash flow

divided by required rate of return). We will briefly review.

Refer to ‘VW13E-04.xlsx’ on the ‘PS Valuation’ tab.

Students should recall that perpetuities such as preferred stock can be generally solved with a simple calculator solution (cash flow

divided by required rate of return). We will briefly review.

Refer to ‘VW13E-04.xlsx’ on the ‘PS Valuation’ tab.


Preferred Stock ExamplePreferred Stock ExamplePreferred Stock ExamplePreferred Stock Example


in one step using ‘=pv(.1,3000,8)’ or simple ‘=8/.1’



in one step using ‘=pv(.1,3000,8)’ or simple ‘=8/.1’


B C D E F

2 Explanations

3 10.00% 10% Reqd return annual

4 3,000 Assume a large number of pds

5 8.00$ Dividend is 8% of $100 par value

6 -$ No cash flow as infinite life


8

9 ($80.00) =PV(D3,D4,D5,D6,D7)This amount is "negative" as we assume the investorwill purchase the preferred stock for that amount today.

Normal Calculation: 80.00$ =D5/D3

fv:type:



nper: pmt:


Remember?Remember? Growth Growth Phases Model ExamplePhases Model ExampleRemember?Remember? Growth Growth Phases Model ExamplePhases Model Example

Stock GP has an expected growth rate of 16% for the first 3 years and 8% thereafter. Each share of stock

just received an annual $3.24 dividend per share. The appropriate

discount rate is 15%. What is the value of the common stock under

this scenario?

Stock GP has an expected growth rate of 16% for the first 3 years and 8% thereafter. Each share of stock

just received an annual $3.24 dividend per share. The appropriate

discount rate is 15%. What is the value of the common stock under

this scenario?


Common Stock ExampleCommon Stock ExampleCommon Stock ExampleCommon Stock Example

The above information provides the inputs into the process. This may be confusing for this problem as the .xlsx file is designed to provide limited flexibility to the student in

valuing these types of problems. As such, since there is only two phases the third phase has the same growth rate as the second and will not alter the value.

Refer to ‘VW13E-04.xlsx’ on the ‘Growth Phases’ tab.

The above information provides the inputs into the process. This may be confusing for this problem as the .xlsx file is designed to provide limited flexibility to the student in

valuing these types of problems. As such, since there is only two phases the third phase has the same growth rate as the second and will not alter the value.

Refer to ‘VW13E-04.xlsx’ on the ‘Growth Phases’ tab.

B C D E F

2 Explanations

3 3.24$ Most recent 12-month dividend

4 16% Rate at which dividends grow

5 3 Length that they grow at rate g1



8 8% Rate at which dividends grow forever

9infinite

Will grow at the same rate forever after phase 2 ends.

10 15% Rate investors expect to earn

11

12 $61.19 =NPV(D10,D27:E35)

OutputsIntrinsic Value (t=0)

InputsDividend at t=0 (D0):

Growth in first phase (g1)

Length of first phase (n1)

Discount rate for cash flows:

Growth in second phase (g2)

Length of second phase (n2)

Growth in third phase (g3)

Length of third phase (n3)



• The first step is to calculate all of the forecasted dividends. You will need to calculate one more forecasted dividend than the sum of periods in the first two phases (cells D5 and D7). In this example, we will need to estimate 10 (3 + 6 + 1).

• While the reality of designing your own sheet would only require four (three from phase 1 plus the following dividend), you will see the flexibility momentarily.

• Refer to ‘VW13E-04.xlsx’ on the ‘Growth Phases’ tab.

• The first step is to calculate all of the forecasted dividends. You will need to calculate one more forecasted dividend than the sum of periods in the first two phases (cells D5 and D7). In this example, we will need to estimate 10 (3 + 6 + 1).

• While the reality of designing your own sheet would only require four (three from phase 1 plus the following dividend), you will see the flexibility momentarily.


B C D E F14 Step 1: Forecast Dividends15 Period16 117 218 319 420 521 622 723 824 925 10

A sequence of 'IF' statements are used to allow some flexibility in this model. It is

reasonable to assume that you generally would create an individually calculated

spreadsheet for the specific asset and its attributes. An example of the 'IF'

statement from cell D24 is: =IF(C24=1,($D$3*(1+$D$4)^C24),IF(C24>($D$5+$D$7),(D23*(1+$D$8)),IF(C24>$D$5,(D23*(1+$D$6)),($D$3*(1+$D$4)^C2

4))))$8.67

$5.90$6.37$6.88$7.43$8.03

Forecasted Dividends$3.76$4.36$5.06$5.46



• The second step is to calculate all of the forecasted cash flows. You will notice that this differs as the last cash flow represents an estimate of what you will sell the asset for at the end of the second phase.

• Since the stock is assumed to be growing at a constant rate forever after the second phase, we use the constant growth model to estimate that value. V9 = D10/(k-g3) = 8.66733/(.15-.08) = $123.81. The cash flow in period 9 is then $8.03+$123.81=$131.84.


• The second step is to calculate all of the forecasted cash flows. You will notice that this differs as the last cash flow represents an estimate of what you will sell the asset for at the end of the second phase.

• Since the stock is assumed to be growing at a constant rate forever after the second phase, we use the constant growth model to estimate that value. V9 = D10/(k-g3) = 8.66733/(.15-.08) = $123.81. The cash flow in period 9 is then $8.03+$123.81=$131.84.


B C D E F27 Step 2: Forecast Cash Flows28 Period29 130 231 332 433 534 635 736 837 93839 Step 3: Value using the NPV function! (see above in output)

$131.84 = $8.67 + PV of future cash flows in years 10 to infinity

$5.46$5.90$6.37$6.88$7.43

Forecasted Cash Flows$3.76$4.36$5.06



• Now use the NPV function to find the PV of the cash flows from periods 1 through 9.

• This is simple to use as is seen in the formula listed in cell F12 which refers to the cash flows in cells D27:E35 (merged cells were used for viewing only or it would be a simple array) and discounting at the 15% rate of cell D10.


• Now use the NPV function to find the PV of the cash flows from periods 1 through 9.

• This is simple to use as is seen in the formula listed in cell F12 which refers to the cash flows in cells D27:E35 (merged cells were used for viewing only or it would be a simple array) and discounting at the 15% rate of cell D10.


B C D E F

2 Explanations







9infinite



11

12 $61.19 =NPV(D10,D27:E35)











Redo!Redo! Growth Phases Growth Phases Model ExampleModel ExampleRedo!Redo! Growth Phases Growth Phases Model ExampleModel Example

• NOW ASSUME: Stock GP2 has an expected growth rate of 24% for the first 3 years, 16% for the next 6 years and 8% thereafter. Each share of stock just received an annual $3.24 dividend per share. The appropriate discount rate is still 15%. What is the value of the common stock under this scenario?

• So we are only increasing the growth rate in the first 9 years of an infinitely-lived asset.

• What impact does it have on valuation today?






• Now the stock GP2 is worth $102.45 rather than $61.19 for GP. That is an astounding 67.4% increase in the stock price because you assumed that dividends would grow at a rate that is only 8% higher for only the first nine years!

• Now we see why investors listen so closely to determine how earnings for a firm are growing or not right now!


• Now the stock GP2 is worth $102.45 rather than $61.19 for GP. That is an astounding 67.4% increase in the stock price because you assumed that dividends would grow at a rate that is only 8% higher for only the first nine years!

• Now we see why investors listen so closely to determine how earnings for a firm are growing or not right now!


B C D E F

2 Explanations







9infinite



11

12 $102.45 =NPV(D10,D27:E35)











Redo!Redo! Redo!Redo! Growth Growth Phases Model ExamplePhases Model ExampleRedo!Redo! Redo!Redo! Growth Growth Phases Model ExamplePhases Model Example









• Now the stock GP3 is worth $99.14 rather than $61.19 for GP and $102.45 for GP2. Yet this stock is not as highly valued as GP2 even though for years 10 through infinity it is growing 4% faster (from 8% to 12%)!

• So it is important to grow fast in the short-term as well as the long-term with a goal of MAXIMIZING SHAREHOLDER WEALTH!


• Now the stock GP3 is worth $99.14 rather than $61.19 for GP and $102.45 for GP2. Yet this stock is not as highly valued as GP2 even though for years 10 through infinity it is growing 4% faster (from 8% to 12%)!

• So it is important to grow fast in the short-term as well as the long-term with a goal of MAXIMIZING SHAREHOLDER WEALTH!


B C D E F

2 Explanations







9infinite



11

12 $99.14 =NPV(D10,D27:E35)











Remember? Remember? Determining the YTMDetermining the YTMRemember? Remember? Determining the YTMDetermining the YTM

Julie Miller want to determine the YTM for an issue of outstanding bonds at Basket Wonders (BW). BW has an issue of 10% annual coupon bonds with 15 years left to maturity. The

bonds have a current market value of $1,250$1,250.

We can find the YTM in Excel also!We can find the YTM in Excel also!

Julie Miller want to determine the YTM for an issue of outstanding bonds at Basket Wonders (BW). BW has an issue of 10% annual coupon bonds with 15 years left to maturity. The

bonds have a current market value of $1,250$1,250.

We can find the YTM in Excel also!We can find the YTM in Excel also!


Bond YTM ExampleBond YTM ExampleBond YTM ExampleBond YTM Example

• Similar to TVM, we will use the RATE function to solve this problem.

• A critical item is to note that your cash inflows and outflows must be signed properly. We are assuming here that you are an investor purchasing the bond

• The YTM is 7.22% which is the same answer as before. Since this rate is less than the coupon rate, it explains why this bond is selling at a premium.

• Refer to ‘VW13E-04.xlsx’ on the ‘YTM’ tab.

• Similar to TVM, we will use the RATE function to solve this problem.

• A critical item is to note that your cash inflows and outflows must be signed properly. We are assuming here that you are an investor purchasing the bond

• The YTM is 7.22% which is the same answer as before. Since this rate is less than the coupon rate, it explains why this bond is selling at a premium.


B C D E F

2 Explanations

3 (1,250.00)$ Purchase for $1,250 (negative)

4 15 Number of periods

5 100.00$ 10% x $1,000 face (maturity) value



8

9 7.22% =RATE(D4,D5,D3,D6,D7)

Output - Bond ValuationBond YTM per period

Inputs for Bond Valuation!pv

nper: pmt:

fv:type:


Remember?Remember? Determining Determining Semiannual YTMSemiannual YTMRemember?Remember? Determining Determining Semiannual YTMSemiannual YTM

Julie Miller want to determine the YTM for another issue of outstanding bonds. The firm

has an issue of 8% semiannual coupon bonds with 20 years left to maturity. The

bonds have a current market value of $950$950.What is the YTM?What is the YTM?

Julie Miller want to determine the YTM for another issue of outstanding bonds. The firm

has an issue of 8% semiannual coupon bonds with 20 years left to maturity. The

bonds have a current market value of $950$950.What is the YTM?What is the YTM?

[ 1 + (.0852514 / 2)2 ] -1 = 0.0871 or 8.71% (same result!)


Bond YTM ExampleBond YTM ExampleBond YTM ExampleBond YTM Example

• Just like the last problem, we calculate the YTM per period.

• We have one further step here and that is to annualize the answer for compunding (see cell F10 for the formula)

• The YTM is 8.71% which is the same answer as before. Since this rate exceeds the coupon rate, it explains why this bond is selling at a discount.


• Just like the last problem, we calculate the YTM per period.

• We have one further step here and that is to annualize the answer for compunding (see cell F10 for the formula)

• The YTM is 8.71% which is the same answer as before. Since this rate exceeds the coupon rate, it explains why this bond is selling at a discount.


B C D E F

12 Explanations

13 (950.00)$ Purchase for $950 (negative)

14 40 Number of periods = 20 yrs x 2

15 40.00$ 8%/2 x $1,000 face (maturity) value



18

19 4.26% =RATE(D4,D5,D3,D6,D7)

20 8.71% =(1+D19)^2-1

fv:

type:

Output - Bond ValuationBond YTM per period

Bond YTM Annualized

Inputs for Bond Valuation!pv

nper:

pmt:

chapter 4 – support

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