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# Chapter 4 – Support

Chapter 4 – Support. The Valuation of Long-Term Securities. Remember? Coupon Bond Example. 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 ? Where V = \$811 (rounded answer).

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## Chapter 4 – Support

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1. Chapter 4 – Support The Valuation of Long-Term Securities

2. Remember? Coupon Bond Example 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 thecoupon bond? Where V = \$811 (rounded answer). 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.

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

4. Remember? Zero-Coupon Bond 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 thezero-coupon bond? … V = \$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. Refer to ‘VW13E-04.xlsx’ on the ‘Bond Valuation’ tab.

5. Zero-Coupon Bond Example 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)’. Refer to ‘VW13E-04.xlsx’ on the ‘Bond Valuation’ tab.

6. Remember? Semiannual Compounding (1) Divide kd by 2 (2) Multiply n by 2 (3) Divide I by 2 Most bonds in the US pay interest twice a year (1/2 of the annual coupon). Adjustments needed:

7. Semiannual Coupon Bond 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?

8. Semiannual Coupon Bond 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)’. Refer to ‘VW13E-04.xlsx’ on the ‘Bond Valuation’ tab.

9. Remember? Preferred Stock Example Stock PS has an 8%, \$100 par value issue outstanding. The appropriate discount rate is 10%. What is the value of the preferred 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.

10. Preferred Stock 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(.1,3000,8)’ or simple ‘=8/.1’ Refer to ‘VW13E-04.xlsx’ on the ‘Bond Valuation’ tab.

11. Remember? Growth Phases 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?

12. Common 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.

13. Common Stock Example • 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.

14. Common Stock Example • 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. • Refer to ‘VW13E-04.xlsx’ on the ‘Growth Phases’ tab.

15. Common Stock Example • 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. • Refer to ‘VW13E-04.xlsx’ on the ‘Growth Phases’ tab.

16. Redo! Growth Phases Model 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?

17. Common Stock Example • 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! • Refer to ‘VW13E-04.xlsx’ on the ‘Growth Phases’ tab.

18. Redo!Redo! Growth Phases Model Example • NOW ASSUME: Stock GP3 has an expected growth rate of 8% for the first 3 years, 10% for the next 6 years and 12%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?

19. Common Stock 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! • Refer to ‘VW13E-04.xlsx’ on the ‘Growth Phases’ tab.

20. Remember? Determining 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. We can find the YTM in Excel also!

21. Bond 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.

22. Remember? Determining Semiannual 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. What is the YTM? [ 1 + (.0852514 / 2)2 ] -1 = 0.0871 or 8.71% (same result!)

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

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