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# Price of bond and Annual Lease Payment

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Hi I've actually already submitted these two problems before, however, I need a clearer explanation of the problems. My concern is that the previous explanations I was given were more advanced than what I should have learned from reading my text. When I went back in and tried to solve the problems myself, I couldn't find how the explanations related to my text. Can someone please give me a clearer explanation of these problems and how they relate to my text? I want to learn how to do the problems, and I don't want my instructor to think I've cheated.

I've attached a Word document with the two problems. I've also attached two pdf files with the sections of my text that relate to the two problems. Please note that there is a readily available solution on the Internet for the last problem. However, I feel that it incorporates too many things, and does not address the hints that the instructor has given. I'd like specific information on how to solve steps A through C.

I really appreciate the help. These two problems are driving me CRAZY!!! I envy those of you who can solve problems like this quickly!

Questions (also attached)

1. Ross, Chapter 20, page 584, Problem 20.6
KIC, Inc. plans to issue \$5 million of perpetual bonds. The face value of each bond is \$1,000. The annual coupon on the bonds is 12%. Market interest rates on one-year bonds are 11%. With equal probability, the long-term market interest rate will be either 14% or 7% next year. Assume investors are risk-neutral.
a. If KIC bonds are noncallable, what is the price of the bonds? *Need the formula and solution for figuring noncallable bonds. Only formula that I can find in this chapter is: first-year coupon + expected price at end of year/1 + r (this is on page 569 of chapter 20)
b. If the bonds are callable one year from today at \$1,450, will their price be greater than or less than the price you computed in part (a)? Why? *Same thing here. I need the formula and solution for figuring callable bonds as it relates to chapter 20.

2. Present Value Lease Problem-Calculating Annual Payments
Leases R Us, Inc. (LRU) has been contracted by Robotics of Beverly Hills (RBH) to provide lease financing for a machine that would assist in automating a large part of their current assembly line. Annual lease payments will start at the beginning of each year. The purchase price of this machine is \$200,000, and it will be leased by RBH for a period of 5 years. LRU will utilize straight-line depreciation of \$40,000 per year with a zero book salvage value. However, salvage value is estimated to actually be \$35,000 at the end of 5 years. LRU is required to earn a 14%, after-tax rate of return on the lease. LRU uses a marginal tax rate of 40%. Calculate the annual lease payments. (Remember, these payments are to be considered at the beginning of each year-annuity due.)

? There's an explanation with a spreadsheet on the web with the answers to this problem (http://answers.google.com/answers/threadview?id=507739) However, it doesn't really give a clear explanation, and I think it may be more advanced than what we've learned in class. I don't want to copy this example, because I'm sure other's have seen it and turned it in. Chapter 21 is inclusive of what we have learned about lease payments. So, I need the formula for how to calculate the annual lease payment.
? Please explain & solve for Step A: You need to calculate the amount to be amortized. This would be the cost of the machine less the PV of the after tax salvage value of the machine and less the PV of the depreciation tax shield
? Please explain & solve for Step B: You need to calculate the annual after-tax required lease income. (Remember, in this step, you need to calculate it as an annuity due-a beginning of the year payment.) Take your answer from Step A as a present value, and using the number of years and the required rate of return, calculate the payment.
? Please explain & solve for Step C: Calculate the lease payment. You need to adjust for the appropriate tax rate. Therefore, take your answer in Step B and divide it by (1 - the tax rate). This will give you the required lease payment.

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#### Solution Preview

In the attached file, I have tried to explain to you step by step how you can go about solving the problem.

KIC, Inc. plans to issue \$5 million of perpetual bonds. The face value of each bond is \$1,000. The annual coupon on the bonds is 12%. Market interest rates on one-year bonds are 11%. With equal probability, the long-term market interest rate will be either 14% or 7% next year. Assume investors are risk-neutral.
a. If KIC bonds are noncallable, what is the price of the bonds? *Need the formula and solution for figuring noncallable bonds. Only formula that I can find in this chapter is: first-year coupon + expected price at end of year/1 + r (this is on page 569 of chapter 20)
b. If the bonds are callable one year from today at \$1,450, will their price be greater than or less than the price you computed in part (a)? Why? *Same thing here. I need the formula and solution for figuring callable bonds as it relates to chapter 20.
For this question you need to know the following -
1. The present value of a perpetuity is given by Cash Flows/Discounting rate (CF/r)
2. The expected value is the sum of probability multiplied by the value.
3. Cash flows are discounted by dividing by (1+r) raised to the power of the year

Let us take a.
The face value of the bond is \$1000. At 12% coupon rate you would get \$ 120 as interest. A perpetual bond is a perpetuity. You will get \$120 every year but never the principal back. As given in point 1 above the present value ( which is the same as the price of the bond today) is given by dividing the period cash flows by the discounting rate. The period here is 1 year and the cash flow is 120. The discounting rate is the return required by the investor and can be different from the coupon rate. It is given that market interest rate is 11%, therefore this is the required ...

#### Solution Summary

The solution has two problems - the first one dealing with the price of a callable bond and the second one with the calculation of annual lease payments

\$2.19