Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 13: Problem 9

Suppose a risk-free bond has a face value of \(\$ 250,000\) with a maturity date four years from now. The bond also gives coupon payments of \(\$ 8,000\) at the end of each of the next four years. a. What will this bond sell for if the risk-free lending rate in the economy is 4 percent? b. What will this bond sell for if the risk-free lending rate is 5 percent? c. What is the relationship between the bond's price and the level of interest rates in the economy in this exercise?

Short Answer

Expert verified
a. The bond will sell for the present value of its future cash flows at 4 percent interest rate: \(P = \frac{8000*(1-(1+0.04)^{-4})}{0.04} + \frac{250000}{(1+0.04)^4}\) b. The bond will sell for the present value of its future cash flows at 5 percent interest rate: \(P = \frac{8000*(1-(1+0.05)^{-4})}{0.05} + \frac{250000}{(1+0.05)^4}\) c. The bond's price decreases as the level of interest rates in the economy increases.

Step by step solution

01

Understand the bond attributes

This bond has a face value of \(250,000\), it matures in 4 years, and it gives out coupon payments of \(8,000\) at the end of each year.
02

Bond Pricing for 4 percent interest rate

The price of the bond can be calculated using the bond pricing formula which is the present value of the bond's future cash flows. The formula is \[ P = \frac{C*(1-(1+r)^{-n})}{r} + \frac{FV}{(1+r)^n} \] where: \(P\) is the price of the bond, \(C\) is the annual coupon payment, \(r\) is the interest rate, \(n\) is the number of years until maturity, \(FV\) is the face value of the bond. So in this case, \(P = \frac{8000*(1-(1+0.04)^{-4})}{0.04} + \frac{250000}{(1+0.04)^4} \]
03

Bond Pricing for 5 percent interest rate

Applying the same bond pricing formula with the new interest rate of 5 percent gives: \(P = \frac{8000*(1-(1+0.05)^{-4})}{0.05} + \frac{250000}{(1+0.05)^4}\)
04

Relationship between the bond's price and the level of interest rates

As can be seen from the above calculations, as the interest rate increases, the price of the bond decreases. This is because as the interest rate increases, the present value of the bond's future cash flows reduces, thereby reducing the price of the bond. This is the relationship between the bond's price and the level of interest rates in the economy in this exercise.
05

Conclusion

Bonds are priced based on their future cash flows which include coupon payments and face value at maturity. The interest rate in the economy plays a key part in pricing these cash flows. As interest rates increase, the price that individuals are willing to pay for these future cash flows decreases, therefore decreasing the price of the bond. Conversely, when interest rates decrease, the price of bonds will increase.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You are considering buying a new laser printer to use in your part-time desktop publishing business. The printer will cost \(\$ 380,\) and you are certain it will generate additional net revenue of \(\$ 100\) per year for each of the next five years. At the end of the fifth year, it will be worthless. Answer the following questions: a. What is the value of the printer if you could lend funds safely at an annual interest rate of 10 percent? Is the purchase of the printer justified? b. Would your answer to part (a) change if the interest rate were 8 percent? Is the purchase justified in that case? Explain. c. Would your answer to part (a) change if the printer cost \(\$ 350\) ? Is the purchase justified in that case? d. Would your answer to part (a) change if the printer could be sold for \(\$ 500\) at the end of the fifth year? Is the purchase justified in that case? Explain.

In the market for Amazon.com stock, explain how each of the following events, ceteris paribus, would affect the demand curve for the stock and the stock's price. a. The interest rate on U.S. government bonds rises. b. People expect the interest rate on U.S. government bonds to rise, but it hasn't yet risen. c. Google announces that it will soon start competing with Amazon in the market for books, DVDs, and everything else that Amazon sells.

Your inventory manager has asked you to approve the purchase of a new inventory control software package. The software will cost \(\$ 200,000\) and will last for four years, after which it will become obsolete. If you do not approve this purchase, your company will have to hire two new inventory clerks, paying each \(\$ 30,000\) per year. Answer the following questions: a. Should you approve the purchase of the inventory control software if the relevant annual interest rate is 7 percent? b. Would your answer to part (a) change if the annual interest rate is 9 percent? Explain. c. Would your answer to part (a) change if the software cost \(\$ 220,000 ?\) Explain. d. Would your answer to part (a) change if the software would not become obsolete until the last day of its sixth year?

Suppose a risk-free bond has a face value of \(\$ 100,000\) with a maturity date three years from now. The bond also gives coupon payments of \(\$ 5,000\) at the end of each of the next three years. What will this bond sell for if the annual interest rate for risk-free lending in the economy is a. 5 percent? b. 10 percent?

Suppose that people are sure that a firm will earn annual profit of \(\$ 10\) per share forever. If the interest rate is 10 percent, how much will people pay for a share of this firm's stock? Suppose that people become uncertain about future profit. What would happen to the price they would be willing to pay? (Your answer will be descriptive only.)
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free