Question

1. A one-year discount bond promises to pay 132,000 dollars next year. Brad requires a 20% rate of return from this bond. In other words, if he thinks that the rate of return from this bond is less than 20%, he will not buy it. Another way of saying the same thing is that, Brad is not willing to pay a penny more than ______ dollars for this bond.

2. Suppose that a special bank account is paying an annual interest of R = 10 percent on deposits. You open an account in this bank on January 1, 2019 and deposit $1,000 in it. You leave the money in the account for two years until January 1, 2021. After one year, on January 1, 2020, you deposit another $1000 in the same account and leave it there for one year until January 1, 2021. On January 1, 2021 you will have a total of ____ dollars on your account at this bank.

3. Suppose that a one-year Treasury bond has a face value of $110,000.00 and is currently selling in the bond market for $100,000.00. This bond is safe, because the U.S. Treasury never defaults on its promises. For the sake of this question (and to make life easier for all of us), assume that the face value and the price of this bond will remain the same throughout the story.The Treasury issues another one-year bond with a face value of $58,300.00 and a starting price of $55,000. However, nobody buys this bond. People think it is too expensive. Consequently, the price of this bond in the bond market drops to ____ dollars.

4. A one-year U.S. Treasury bond has a face value of $52,500.00 and is selling for $50,000.00 today. A corporation bond has a face value of $45,000.00. The corporation bond is quite risky and carries a risk premium of 20% over the Treasury bond. So, the price of the corporation bond in the market should be ___ dollars.

Answer 1

Question 1

Amount that bond will pay in one year = $132,000

Rate of return required = 20%

Time period = 1 year

Calculate the Present Value of bond -

PV = 132,000/(1+0.20)¹

PV = 132,000/(1.20)

PV = 110,000

The present worth of bond at 20% rate of return is $110,000.

This means if bond is priced $110,000 today than it can provide 20% return if it pays $132,000 in one year.

So,

Brad is not willing to pay a penny more than 110,000 dollars for this bond.

Question 2

Deposit made on Jan 1, 2019 = $1,000

Deposit made on Jan 1, 2020 = $1,000

Interest rate = 10% or 0.10

Calculate the amount in bank on Jan 1, 2021 -

Amount in bank = [$1,000/(1+0.10)²] + [$1,000/(1+0.10)¹]

Amount in bank = [$1,000 * 1.21] + [$1,000 * 1.10]

Amount in bank = $2,310

Thus,

On Jan 1, 2021, the person will have a total of 2,310 dollars in his account at the bank.