bachelors of commerce accounting PDF

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chapter 10...

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Lance Whittingham IV specializes in buying deep discount bonds. These represent bonds that are trading at well below par value. He has his eye on a bond issued by the Leisure Time Corporation. The $1,000 par value bond with semiannual payments has 6 percent annual interest and has 15 years remaining to maturity. The current yield to maturity on similar bonds is 14 percent. (Round "PV Factor" to 3 decimal places. Do not round intermediate calculations. Round the final answers to 2 decimal places.) a. What is the current price of the bonds? Use Appendix B and Appendix D. Current price

$ 503.27 ± 0.1

b. By what percent will the price of the bonds increase between now and maturity? Price increases by

98.70 ± .1 %

c. What is the annual compound rate of growth in the value of the bonds? (Use Appendix A) Annual compound rate

4.68 ± 0.1 %

Explanation a. Current price of the bonds

Present value of interest payments

PVA = A × PVIFA (N = 15 × 2 = 30, %I/Y = 14%/2 = 7) (Appendix D) PVA = $30 × 12.409 = $372.27 Present value of principal payments at maturity

PV = FV × PVIF (N = 30, %I/Y = 7) PV = $1,000 × 0.131 = $131.00

Total present value

(Appendix B)

Present value of interest payments

$372.27

Present value of principal payment

131.00

Total present value or price of the bond $503.27

b. Percent increase at maturity

Maturity value $1,000.00 Current price –503.27 Dollar increase

Percent increase

=

$496.73

$496.73 = 0.987 = 98.70% $503.27

c. Compound rate of growth The bond will grow by 98.70 percent over 15 years. Using Appendix A, the future value of $1, we see the growth rate is between 4 and 5 percent (4.68 percent based on interpolation)

Applied Software has a $1,000 par value bond outstanding that pays 13 percent interest with annual payments. The current yield to maturity on such bonds in the market is 10 percent. Use Appendix B and Appendix D. Compute the price of the bonds for these maturity dates: (Round "PV Factor" to 3 decimal places. Do not round intermediate calculations. Round the final answers to 2 decimal places.) Price of the bond a. 30 years $ 1,282.51 b. 20 years $ 1,255.82 c. 2 years $ 1,051.68 Explanation a.

30 years to maturity Present value of interest payments PVA = A × PVIFA (N = 30, %I/Y = 10) (Appendix D) PVA = $130 × 9.427 = $1,225.51 Present value of principal payment at maturity PV = FV × PVIF (N = 30, %I/Y = 10%) (Appendix B) PV = $1,000 × 0.057 = $57.00 Total present value:

Present value of interest payments Present value of principal payment

$1,225.51 57.00

Total present value or price of the bond$1,282.51

b.

20 years to maturity Present value of interest payments

PVA = A × PVIFA (N = 20, %I/Y = 10%) (Appendix D) PVA = $130 × 8.514 = $1,106.82 Present value of principal payment at maturity PV = FV × PVIF (N = 20, %I/Y = 10%) (Appendix B) PV = $1,000 × 0.149 = $149.00 Total present value:

Present value of interest payments Present value of principal payment

$1,106.82 149.00

Total present value or price of the bond$1,255.82

c.

2 years to maturity Present value of interest payments PVA = A × PVIFA (N = 2, %I/Y = 10%) (Appendix D) PV = $130 × 1.736 = $225.68 Present value of principal payment at maturity PV = FV × PVIF (N = 2, %I/Y = 10%) (Appendix B) PV = $1,000 × 0.826 = $826.00 Total present value:

Present value of interest payments Present value of principal payment

$225.68 826.00

Total present value or price of the bond$1,051.68

Midland Oil has $1,000 par value (maturity value) bonds outstanding at 12 percent interest. The bonds will mature in 10 years with annual payments. Use Appendix B and Appendix D. Compute the current price of the bonds if the present yield to maturity is: (Round "PV Factor" to 3 decimal places. Do not round intermediate calculations. Round the final answers to 2 decimal places.) Price of the bond a. 11 percent $ 1,058.68 b. 14 percent c. 17 percent

$ 895.92 $ 767.08

Explanation a. 11 percent yield to maturity Present value of interest payments PVA = A × PVIFA (n = 10, %I/Y = 11) (Appendix D) PVA = $120 × 5.889 = $706.68 Present value of principal payments at maturity PV = FV × PVIF (n = 10, %I/Y = 11) PV = $1,000 × 0.352 = $352.00

(Appendix B)

Total present value:

Present value of interest payments Present value of principal payments

$706.68 352.00

Total present value or price of the bond $1,058.68

b. 14 percent yield to maturity Present value of interest payments PVA = A × PVIFA (n = 10, %I/Y = 14) (Appendix D) PVA = $120 × 5.216 = $625.92 Present value of principal payments at maturity PV = FV × PVIF (n = 10, %I/Y = 14) PV = $1,000 × 0.270 = $270.00

(Appendix B)

Total present value:

Present value of interest payments Present value of principal payments

$625.92 270.00

Total present value or price of the bond $895.92

Bonds issued by the Coleman Manufacturing Company have a par value of $1,000, which is also the amount of principal to be paid at maturity. The bonds are currently selling for $860. They have 10 years to maturity. Annual interest is 10 percent ($100), paid semiannually. Compute the yield to maturity. (Round the final answer to 2 decimal places.) Yield to maturity

12.45 %

Explanation Approximate yield to maturity is represented by Y'.

Annual interest payment +

Principal payment − Price of the bond Number of years to maturity

Y' = 0.6 (Price of the bond) + 0.4 (Principal payment)

$1,000 – $860 $100 + 10 =

$100 + $14 =

0.6 ($860) + 0.4 ($1,000)

= 0.1245 = 12.45% $516 + $400

Bonds issued by the Tyler Food chain have a par value of $1,000, are selling for $1,430, and have 20 years remaining to maturity. Annual interest payment is 19.5 percent ($195), paid semiannually. Compute the approximate yield to maturity. (Round the final answer to 2 decimal places.) Approximate yield to maturity

13.79 13.79 Correct %

Explanation Approximate yield to maturity is represented by Y'.

Annual interest payment +

Principal payment − Price of the bond Number of years to maturity

Y' = 0.6 (Price of the bond) + 0.4 (Principal payment)

$1,000 – $1,430 $195 + 20 =

$195 – $21.5 =

0.6 ($1,430) + 0.4 ($1,000)

= 0.1379 = 13.79% $858 + $400

The Vinny Cartier Company issued bonds at $1,000 per bond. The bonds had a 20-year life when issued, with semiannual payments at the then annual rate of 12 percent. This return was in line with required returns by bondholders at that point, as described below: Real rate of return Inflation premium Risk premium Total return

3% 5 4 12%

Assume that ten years later the inflation premium is 2 percent, the risk premium has declined to 3 percent and both are appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 10 years remaining until maturity. Compute the new price of the bond. Use Appendix B and Appendix D. (Round "PV Factor" to 3 decimal places. Do not round intermediate calculation. Round the final answer to 2 decimal places.) New price of the bond

$ 1,271.40

Explanation First compute the new required rate of return (yield to maturity).

Real rate of return Inflation premium Risk premium

3% 2 3

Total return

8%

Then use this value to find the price of the bond: Present value of interest payments PVA = A × PVIFA (N = 10 × 2 = 20, %I/Y = 8%/2 = 4.00) PVA = $60 × 13.590 = $815.40 Present value of principal payment at maturity PV = FV × PVIF (N = 20, %I/Y = 4.00) PV = $1,000 × 0.456 = $456.00

(Appendix D)

(Appendix B)

Total present value

Present value of interest payments Present value of principal payment

$815.40 456.00

Total present value or price of the bond$1,271.40...