Question

An investor is buying a bond that pays semi-annual interest. The par value is $900 and the coupon rate is 6%. The investor plans to hold the bond to its maturity, which is 5 years from now. If her typical required rate of return is 7%, what is the most the investor should pay for the bond

Answer 1

To calculate the most the investor should pay for the bond, consider the present value of the bond's future cash flows, and calculate the present value of the ten semi-annual payments using the investor's required rate of return.

Step-by-step explanation:

When buying a bond, the investor should consider the present value of the bond's future cash flows. In this case, the bond pays semi-annual interest, so the investor will receive $30 ($900 x 6% / 2) every six months for a total of ten payments over the five-year period.

Next, the investor needs to calculate the present value of these cash flows at their required rate of return. Using a financial calculator or spreadsheet, the present value of the ten semi-annual payments is $242.58, which is the most the investor should pay for the bond.

Answer 2

The investor should pay a maximum of approximately $897.77 for the bond to achieve her required rate of return of 7%.

Step-by-step explanation:

To determine the maximum amount the investor should pay for the bond, we can use the present value formula. Here are the steps:

1. Calculate the number of semi-annual periods until maturity: Since the bond pays semi-annual interest and has a maturity of 5 years, there will be 2 x 5 = 10 semi-annual periods.

2. Determine the coupon payment: The coupon rate is 6% and the par value is $900. Since the bond pays semi-annual interest, the coupon payment will be 6% x $900 / 2 = $27 per semi-annual period.

3. Determine the required rate of return: The investor's required rate of return is 7%.

4. Use the present value formula: The formula to calculate the present value of a bond is
`PV = C x [1 - (1 + r)^(^-^n^)] / r + M / (1 + r)^n`, where PV is the present value, C is the coupon payment, r is the required rate of return per period, n is the number of periods, and M is the par value.

Plugging in the values:

`PV = $27 x [1 - (1 + 0.07)^(^-^1^0^)] / 0.07 + $900 / (1 + 0.07)^1^0`

By calculating this equation, the maximum amount the investor should pay for the bond is approximately $897.77.

Therefore, the investor should pay a maximum of approximately $897.77 for the bond to achieve her required rate of return of 7%.