Question

A bond is maturing in exactly 1 year. With a discount rate of 10%, which of the following purchase prices will result in an NPV of zero?

A)$890.00
B)$910.00
C)$900.00
D)$909.09

Answer 1

No option provided will give an exact NPV of zero for a bond paying $1,080 in one year with a 10% discount rate. The closest but incorrect option is D) $909.09. A purchase price of $981.82 would result in an NPV of zero, which suggests there could be an error in the question or options.

Step-by-step explanation:

The student is asking for the purchase price of a bond that will result in a net present value (NPV) of zero given a discount rate of 10%. To calculate this, we use the formula for present value (PV), which is PV = FV / (1 + r)^n, where FV is the future value of the bond, r is the discount rate, and n is the number of years until maturity. In this case, the bond will pay $1,080 one year from now, so FV is $1,080, r is 0.10 (10%), and n is 1.Using the formula, we calculate PV = $1,080 / (1 + 0.10)^1 which equals $1,080 / 1.10, resulting in a PV of $981.82. Therefore, for the NPV to be zero, the purchase price must equal the present value. The only option close to $981.82 is option D) $909.09, but none of the given options will result in an exact NPV of zero at a discount rate of 10%.

There might be a mistake in the question or options provided. To calculate the bond's price, we need to find the purchase price that will result in a Net Present Value (NPV) of zero. NPV is calculated by discounting the expected future cash flows using the discount rate. The purchase price that will result in an NPV of zero is the present value of the expected future cash flows. In this case, the expected future cash flow is $1,080, which will be received in 1 year. The discount rate is 10%. To find the present value, we can use the formula: PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of periods. Plugging in the values, we get: PV = 1080 / (1 + 0.10)^1 = 981.82. Therefore, the purchase price that will result in an NPV of zero is $981.82.

Answer 2

Using the present value calculation with a discount rate of 10%, the present value of a $1,080 payment in one year is approximately $981.82, which is the bond purchase price for an NPV of zero.

Step-by-step explanation:

The question pertains to the calculation of the purchase price of a bond that will result in a net present value (NPV) of zero when the discount rate is 10%. We are looking for the present value of the bond's payment a year from now, which is $1,080 (the sum of the final interest payment and the principal repayment of $1,000). To calculate the present value, we use the formula: Present Value = Future Payment / (1 + r), where 'r' is the discount rate. Plugging in the values, we get Present Value = $1,080 / (1 + 0.10), which simplifies to Present Value = $1,080 / 1.10, and further to approximately $981.82. The closest purchase price that will result in an NPV of zero is $981.82, which is not one of the provided options.