Question

Ms. Jones wants to make 14​% nominal interest compounded quarterly on a bond investment. She has an opportunity to purchase a 12​%, ​$10 comma 000 bond that will mature in 12 years and pays quarterly interest. This means that she will receive quarterly interest payments on the face value of the bond ​($10 comma 000​) at 12​% nominal interest. After 12 years she will receive the face value of the bond. How much should she be willing to pay for the bond​ today?

Answer 1

To determine Ms. Jones' willingness to pay for the bond today, we need to calculate the present value of its future cash flows. The bond pays quarterly interest at a nominal rate of 12% on a face value of $10,000, and after 12 years she receives the face value. By using the present value formula, we can calculate the present value of both the interest payments and the face value payment to find the total present value of the bond.

Step-by-step explanation:

In order to determine how much Ms. Jones should be willing to pay for the bond today, we need to calculate the present value of the bond's future cash flows.

The bond pays quarterly interest at a nominal rate of 12% on a face value of $10,000, and after 12 years she will receive the face value of the bond.

We can use the formula for present value of an ordinary annuity to calculate the present value of the interest payments, and then add the present value of the face value payment to get the total present value of the bond.

Using a nominal interest rate of 14% compounded quarterly, the present value of the interest payments can be calculated as follows:

1. Calculate the periodic interest rate: 14% / 4 = 3.5%
2. Calculate the number of periods: 12 years * 4 quarters per year = 48 quarters
3. Calculate the present value factor using the formula: (1 - (1 + periodic interest rate)^(-number of periods)) / periodic interest rate
4. Multiply the present value factor by the periodic interest payment: $10,000 * 3.5% = $350

The present value of the interest payments is $350 multiplied by the present value factor.

The present value of the face value payment can be calculated using the same formula, but with only one payment at the end of the 12-year period.

Once we have the present value of both the interest payments and the face value payment, we can sum them to find the total present value of the bond.

Answer 2

IF mrs Jones wants to make 14% on the bond this is her required return and what the ytm of the bond should be to make her want to buy the bond. Because the bond pays a coupon of 12% she will want to pay less than the face value of the bond, so that the overall return can be 14%. Whenever the coupon rate of the bond is less than the required return or ytm, the bond is sold at a discount. In order to find at what price should she buy the bond we will need a financial calculator and input the following

FV= 10,000

YTM= 3.5 ( We divide 14 by 4 to find the ytm because the bond has quarterly compounded payments)

PMT= 300 ( We find out the 12% of 10,000 and divide it by 4 because the bond has quarterly payments)

N= 48 (12 years into 4 because there will be a total of 48 quarters and 48 payments)

Put these values in a financial calculator and compute the PV

PV= 8,845

The present value of the bond is 8,845 if the required return is 14% which means she should be willing to pay $8,845 for the bond today.

Step-by-step explanation: