Problems and Solution

1. 
   Verbrugge Company has a level-coupon bond outstanding that pays coupon interest of $120 per year and has 10 years to maturity.  The face value of the bond is $1,000. If the yield for similar bonds is currently 14%, what is the bond's current market value? [Ans: $ 895.68]
   

2. 
   For the Verbrugge Company bond described in Problem 1, find the bond's value if the yield for similar bonds decreases to 12%. [Ans: $ 1,000]
   

3. 
   For the Verbrugge Company bond described in Problem 1, find the bond's value if the yield for similar bonds decreases to 9%. [Ans: 1192.53]
   

4. 
   What conclusions can you draw out of the solutions of the problems 1, 2 and 3 ?
   

5. 
   Suppose the Verbrugge bond paid interest semiannually. What would its value be if the yield is 14%? [Ans: $ 894.06]
   

6. 
   Sasha Company has a level-coupon bond with a 9% coupon rate; interest is paid annually. The bond has 20 years to maturity and a face value of $1,000; similar bonds currently yield 7%. By prior agreement the company will skip the coupon interest payments in years 8, 9, and 10. These payments will be repaid, without interest, at maturity. What is the bond's value? [Ans: $ 1134.56]
   

7. 
   The market price of a Rs 1,000 par value bond carrying a coupon rate of 14 % and maturing after 5 years is Rs 1,050. What is the yield to maturity on this bond ? What is the approximate YTM ? [Ans: 12.60 %, 12.62 %]
   

8. 
   A firm issues a bond today with a $1,000 face value, an 8% coupon interest rate, and 25-year maturity. An investor purchases the bond for $1,000. What is the yield to maturity (YTM)? [Ans: 8%]
   

9. 
   Suppose the investor bought the bond described in the previous problem for $900. What is the YTM? [Ans: 9.0197]
   

10. 
    Suppose the bond described in the previous two problems has a price of $1,100 five years after it is issued. What is the YTM at that time? [Ans: 7.0522]
    

11. 
    If the real rate is 4% and the inflation rate is 10%, what is the nominal return for a one-year T-bill? [Ans: 14.4 %]
    

12. 
    If the one-year T-bill rate is 8% and the expected inflation rate is 3% during the next year, what real rate of return does the investor expect? [Ans: 4.854]
    

13. 
    Suppose the investor described in the previous problem purchases the one-year T-bill, then finds that after one year, the actual inflation rate was 10%. What real return did the investor earn during the year? [Ans: investor has lost almost 2% on the Treasury bill investment]
    

14. 
    The equity stock of Rax Limited is currently selling for Rs 30 per share. The dividend expected next year is Rs 2.00. The investors’ required rate of return on this stock is 15 %. If the constant growth model applies to Rax Limited, what is the expected growth rate ? [Ans: 8.3 %]
    

15. 
    XYZ limited’s earnings and dividends have been growing at a rate of 18 % per annum. This growth rate is expected to continue for 4 years. After that the growth rate will fall to 12 % for the next 4 years. Thereafter, the growth rate is expected to be 6 % forever. If the last dividend per share was Rs 2.00 and the investors’ required rate of return on XYZ’s equity is 15 %, what is the intrinsic value per share? [Ans: Rs 40.32]
    

16. 
    The current dividend on an equity share of Pioneer Technology is Rs 3.00. Pioneer is expected to enjoy an above-normal growth rate of 40 % for 5 years. Thereafter, the growth rate will fall and stabilize at 12%. Equity investors require a return of 18% from Pioneer’s stock. What is the intrinsic value of the equity share of Pioneer? [Ans: Rs 157.39]
    

17. 
    A security analyst has forecast the dividends of Hodges Enterprises for the next three years. His forecast is: D₁ = $1.50; D₂ = $1.75; D₃ = $2.20. He has also forecast a price in three years of $48.50. The rate of return for similar-risk common stock is 14%. What is the value of Hodges common stock? [Ans: 36.88]
    

18. 
    TTK Corp. preferred stock pays a $10 annual dividend per share. What is the price of a share of TTK preferred if similar-risk preferred yields 8%? If the price of comparable preferred yields 11%? [Ans: $ 90.91]
    

19. 
    A share of preferred stock with a $12 annual dividend is selling for $75. What is the required rate of return for the preferred stock? [Ans: 16 %]
    

20. 
    The current price of a stock (P₀) is $20 and last year's price (P_-1) was $18.87. The latest dividend (D₀) is $2. Assume a constant growth rate (g) in dividends and stock price. What is the stock's return for the coming year? [Ans: 16.6 %]
    

21. 
    The current year's dividend (D₀) for a share of common stock is $2 and the current price (P₀) of the stock is $30. Dividends are expected to grow at 5% forever. What is the rate of return for this stock? [Ans: 12 %]
    

22. 
    A company pays a current dividend (D₀) of $1.20 per share on its common stock. The annual dividend will increase by 3%, 4% and 5%, respectively, over the next three years, and by 6% per year thereafter. The appropriate discount rate is 12%. What is P₀? [Ans: $ 20.08]
    

23. 
    Six years ago, the Singleton Compnay sold a 20 year bond issue with a 14% annual coupon rate and a 9% call premium. Today, Singleton called the bonds. The bonds were originally sold at their face value of Rs 1,000. Compute the realized rate of return for investors who purchased the bonds when they were issued and surrender then today in exchange of call price. [Ans: 15.03%]
    

Approximate YTM:

Use the same formula with annual coupon and n as no. of years even if the coupon payment is semiannual. (To find out approx YTM)

Alternative formulae for approximate YTM:

Find the exact YTM by doing trial and error and using method of linear interpolation linear interpolation.