1. Tom Cruise Lines Inc. issued bonds five years ago at $1,000 per bond. These b
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Question
1.
Tom Cruise Lines Inc. issued bonds five years ago at $1,000 per bond. These bonds had a 30-year life when issued and the annual interest payment was then 14 percent. This return was in line with the required returns by bondholders at that point as described below:
Assume that five years later the inflation premium is only 3 percent and is appropriately reflected in the required return (or yield to maturity) of the bonds. The bonds have 25 years remaining until maturity.
Compute the new price of the bond. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.)
New Price of the Bond =
2.
Katie Pairy Fruits Inc. has a $2,700, 19-year bond outstanding with a nominal yield of 16 percent (coupon equals 16% × $2,700 = $432 per year). Assume that the current market required interest rate on similar bonds is now only 12 percent. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.
a. Compute the current price of the bond. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.)
Current Price of Bond =
b. Find the present value of 4 percent × $2,700 (or $108) for 19 years at 12 percent. The $108 is assumed to be an annual payment. Add this value to $2,700. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.)
Present Value =
3.
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 pays 6 percent annual interest and has 15 years remaining to maturity. The current yield to maturity on similar bonds is 10 percent.
a. What is the current price of the bonds? Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.)
Current Price of Bond =
b. By what percent will the price of the bonds increase between now and maturity? (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
Price increased by =
4.
You are called in as a financial analyst to appraise the bonds of Olsen’s Clothing Stores. The $1,000 par value bonds have a quoted annual interest rate of 11 percent, which is paid semiannually. The yield to maturity on the bonds is 12 percent annual interest. There are 10 years to maturity. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.
a. Compute the price of the bonds based on semiannual analysis. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
Bond Price =
b. With 5 years to maturity, if yield to maturity goes down substantially to 10 percent, what will be the new price of the bonds? (Do not round intermediate calculations. Round your final answer to 2 decimal places.)
New Bond Price =
Real rate of return 3 % Inflation premium 6 Risk premium 5 Total return 14 % Appendix B Present value of $1,PVF PV=FV Percent Period 4 Appendlx B (concluded) Percent Period 50% 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 0.640 0.592 0.549 0.510 0.444 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 0512 0.455 0.406 0.364 0.296 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 0.262 0.207 0.165 0.133 0.088 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 0.210 0.159 0.122 0.095 0.059 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 0.086 0.056 0.037 0.025 0.012 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 0.035 0.020 0.011 0.006 0.002 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045 0.023 0.012 0.006 0.003 0.001 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031 0.014 0.007 0.003 0.002 0 0.087 0.073 0.061 0.051 0.043 0.037 0.031 0.026 0.012 0.005 0.002 0.001 0 0.047 0.038 0.030 0.024 0.020 0.016 0.013 0.010 0.004 0.001 0.001 0 0.026 0.020 0.015 0.012 0.009 0.007 0.005 0.004 0.001 0Explanation / Answer
1.Calculating the new yield to maturity (required rate of return)
YTM = Real rate of return + Inflation rate + Risk premium
= 3% + 3% + 5%
= 11%
Now, price of the bond is the present value of the coupons and the present value of par value of the bond.
Time remaining for maturity = 25 years
YTM or required rate of return = 11%
Coupon = 14%*1000
= $140
Price = C * ({1 [1 / (1 + i )^n ]} / i ) + [FV / (1 + i )^n]
= 140*({1-[1/(1+0.11)^25]}/0.11 + [1000/(1+0.11)^25]
= $1179.04+ 73.60
= $1252.65
Using Appendix D
Present value annuity of Coupon
PVA = C*PVIFA(11%,25)
= 140* 8.422
= $1179.08
Using Appendix B
Present value of $1000 at maturity
PV = FV* PVIF(11%,25)
= 1000* (0.074)
= 74
Therefore bond price = PV of coupons and PV of principal amount
= $1179.08+74
= $1253.08
2a) Present value of coupons + present value of principal amount
Price = C * ({1 [1 / (1 + i )^n ]} / i ) + [FV / (1 + i )^n]
where C = coupon payment = 16%*2700 = $432
i= interest rate = 12%
n = 19 years
Price = 432* ({1- [1/(1+ 0.12)^19]}/0.12) + [ 25/(1+0.12)^19]
= 432* ({1- 0.1161}/0.12} + [2700/8.613]
= 432*7.366 + 313.488
= $3495.50
Using Appendix
Price = PVIFA( 12%,19) + PVIF (12%,19)
= 432*7.366 + 2700*0.116
= $34950
b) Present value of annual payment is the present value annuity
PVA = C*([1- {1/(1+i)^n}]/i)
where C = 4%*2700 = $108
i = 12%
n = 19
= 108* [1-{1/(1+0.12)^19}/0.12]
= 108*7.366
= $795.528
Present value of interest payment is $795.53
Appendix D
PVA = 108*PVIFA(12%,19)
= 108* 7.366
= $795.53
Adding to $2700
Bond Price = 2700+795.53
= $3495.53
3a)Calculating current Price of $1000 par value bond
Given Par value = $1000
Interest rate = 6%
Coupon = 6%*1000 = 60
Time to maturity n = 15
YTM = 10%
Price = Present value of all interest payments + Present value of the par value
= C*([1- {1/(1+i)^n}]/i) + [FV/(1+r)^n]
= 60* [1- {1/(1+0.10)^15}/0.10] + [1000/(1+0.10)^15]
=60* [1-{1/1.10^15}/0.10] + [1000/1.10^15]
= 456.34 + 239.39
= $695.76
Using Appendix D and Appendix B
PVIFA = C*(10%,15)
PVIF = FV(10%,15)
Price = 60*7.606 + 1000*0.239
= 456.36 + 239
= $695.39
b) Percentage increase in price = (Price at maturity- Price Now)/Price now
= (1000 – 695.76)/695.76
= 43.72%
4a) Present value of coupons paid semi-annually
Given Coupon = 11%*1000 = 110
Semi-annual = 110/2 = 55
Interest rate or YTM = 12%, 12/2 = 6% semiannual
Time = 10 years
n = 10*2= 20
PV = Present value of coupon + Present value of principal
Price = C*([1- {1/(1+i)^n}]/i) + [FV/(1+r)^n]
= 55* ([ 1- {1/1+0.06)^20}]/0.06 ) + [1000/(1.06)^20]
55*11.470 + 311.80
= 630.85 + 311.80
= $942.65
Using Appendix D and B
Price = C*PVIFA(6%,20) + FV*PVIF(6%,20)
= 55*11.470 + 1000*0.312
=$942.85
b) Now n= 5*2 = 10
YTM = 10%, 5% semiannually
Par value = 1000
Coupon = $55
Price = C*([1- {1/(1+i)^n}]/i) + [FV/(1+r)^n]
= 55* ([ 1- {1/1+0.05)^10}]/0.05 ) + [1000/(1.05)^10]
= $424.70+ 613.91
= $1038.61
Using Apppendix D and B
Price = C* PVIFA(5%,10) + FV*(5%,10)
= 55*7.722 + 1000*0.614
= $1038.71
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