Question

In cell B9, enter a formula using NPV to calculate the present value of a payment plan with variable annual payments as shown in cells B11:B14. The interest rate is stored in cell B2. Use a cell range as a single Value argument.

Answer 1

In Excel, cell B9's NPV formula would be =NPV(B2, B11:B14), reflecting the interest rate in B2 and the variable payments in B11:B14. As interest rates rise, the present value of future payments falls since they are discounted more heavily, potentially lowering the value of an investment like a bond.

Step-by-step explanation:

In order to calculate the present value of a payment plan with variable annual payments in cell B9 using the NPV function in Excel, you would write the formula =NPV(B2, B11:B14). Here, B2 contains the interest rate, which is used as the discount rate for the NPV calculation, and B11:B14 contains the list of variable annual payments. This formula takes into account the interest rate being stored in cell B2 to discount the future payments to their present value.

It is important to note that when the interest rate rises, the present value of future payments will decrease. This is because future cash flows are discounted at a higher rate, reflecting the increased opportunity cost of the funds, or the increased rate at which the funds could have been invested. As such, if an investor wishes to sell an investment like a bond when interest rates have risen, they may find that the value of these future payments—and therefore the investment itself—has fallen.

Moreover, the final present value is the sum of all individual present values calculated for each payment period. The calculation is made based on the provided interest rates, and the fact that the received future dollar payments do not change.

Answer 2

To calculate the present value of variable annual payments in a spreadsheet, use the formula =NPV(interest rate, payment range). Rising interest rates lead to a lower present value of future payments.

Step-by-step explanation:

The student's question pertains to the use of the Net Present Value (NPV) formula in a spreadsheet to calculate the present value of a payment plan with variable annual payments. To calculate the present value in cell B9, the formula would be =NPV(B2, B11:B14). The NPV function uses the interest rate from cell B2 and the range of payments from cells B11 to B14. When interest rates rise, the present value of future payments decreases because the payments are discounted at a higher rate. This is important to consider when evaluating the value of investments, such as bonds, under changing interest rate conditions.

For example, if the interest rate increases from 8% to 11%, the present value of the future cash flows would decrease, reflecting a lower value for the payments when discounted at the new, higher interest rate. The formula provided helps to understand how the interest rate affects the present value of an investment.