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Chapter 15: Problem 4

A bond has two years to mature. It makes a coupon payment of \(\$ 100\) after one year and both a coupon payment of \(\$ 100\) and a principal repayment of \(\$ 1000\) after two years. The bond is selling for \(\$ 966 .\) What is its effective yield?

Short Answer

Expert verified
The effective yield of the bond should be calculated using a financial calculator or spreadsheet by solving the equation: \$966 = \(\frac{\$100}{{(1+YTM)^1}}\) + \(\frac{\$1100}{{(1+YTM)^2}}\). Please note, your calculated YTM would be in decimal format; for a percentage, you need to multiply it by 100.

Step by step solution

01

Understanding the Concept of Effective Yield

The effective yield of a bond, also known as the yield to maturity (YTM), is the Internal Rate of Return (IRR) on the bond's cash flows: the initial cost (the price of the bond), the coupon payments, and the principal repayment. The equation to find it is: \(PV = \sum \frac{CF_t}{{(1+YTM)}^t}\), where PV is the present value or price of the bond (\$966), \(CF_t\) are the cash flows at period t (Coupon payments of \$100 after the first year and \$1100 after the second year), and t is the time period.
02

Setting up the Equation

By plugging in the known values into the equation we get: \$966 = \(\frac{\$100}{{(1+YTM)^1}}\) + \(\frac{\$1100}{{(1+YTM)^2}}\)
03

Solving the Equation

This problem requires the solution of a quadratic equation. While it can be solved by algebraic methods, the most efficient way to solve this equation is by using a financial calculator or computer-based tools, such as a spreadsheet.
04

Finding the Yield to Maturity (YTM)

The solution of the equation gives the YTM. The YTM is the bond's internal rate of return, given its price, coupon payments, and principal repayment.

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Most popular questions from this chapter

Suppose the interest rate is 10 percent. What is the value of a coupon bond that pays \(\$ 80\) per year for each of the next five years and then makes a principal repayment of \(\$ 1000\) in the sixth year? Repeat for an interest rate of 15 percent.

The market interest rate is 5 percent and is expected to stay at that level. Consumers can borrow and lend all they want at this rate. Explain your choice in each of the following situations: a. Would you prefer a \(\$ 500\) gift today or a \(\$ 540\) gift next year? b. Would you prefer a \(\$ 100\) gift now or a \(\$ 500\) loan without interest for four years? c. Would you prefer a \(\$ 350\) rebate on an \(\$ 8000\) car or one year of financing for the full price of the car at 0 percent interest? d. You have just won a million-dollar lottery and will receive \(\$ 50,000\) a year for the next 20 years. How much is this worth to you today? e. You win the "honest million" jackpot. You can have \$1 million today or \(\$ 60,000\) per year for eternity right that can be passed on to your heirs). Which do you prefer? f. In the past, adult children had to pay taxes on gifts of over \(\$ 10,000\) from their parents, but parents could make interest-free loans to their children. Why did some people call this policy unfair? To whom were the rules unfair?

A consumer faces the following decision: She can buy a computer for \(\$ 1000\) and \(\$ 10\) per month for Internet access for three years, or she can receive a \(\$ 400\) rebate on the computer (so that its cost is \(\$ 600\) ) but agree to pay \(\$ 25\) per month for three years for Internet access. For simplification, assume that the consumer pays the access fees yearly (i.e., \(\$ 10\) per month \(=\$ 120\) per year). a. What should the consumer do if the interest rate is 3 percent? b. What if the interest rate is 17 percent? c. At what interest rate will the consumer be indifferent between the two options?

You are offered the choice of two payment streams: (a) \(\$ 150\) paid one year from now and \(\$ 150\) paid two years from now; (b) \(\$ 130\) paid one year from now and \(\$ 160\) paid two years from now. Which payment stream would you prefer if the interest rate is 5 percent? If it is 15 percent?

Suppose the interest rate is 10 percent. If \(\$ 100\) is invested at this rate today, how much will it be worth after one year? After two years? After five years? What is the value today of \(\$ 100\) paid one year from now? Paid two years from now? Paid five years from now?
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