Suppose the term structure of interest rates is shown below: The net present value (NPV)of an investment that costs $4320 and pays $1600 certain at the end of one, three, and five years is closest to ________.
A)$91.37
B)$137.05
C)$114.21
D)-$114.21

Question

Suppose the term structure of interest rates is shown below:  The net present value (NPV)of an investment that costs $4320 and pays $1600 certain at the end of one, three, and five years is closest to ________.
A)$91.37 
B)$137.05 
C)$114.21 
D)-$114.21

Quizplus · Accepted Answer

To calculate the NPV of the investment, we need to discount the cash flows at the appropriate spot rates from the term structure. Using the given spot rates, we can calculate the discount factors as follows:

Year 1: 1/(1+0.03) = 0.9709
Year 3: 1/(1+0.035)³ = 0.8885
Year 5: 1/(1+0.042)⁵ = 0.7730

Next, we can calculate the present value of each cash flow by multiplying the cash flow by the corresponding discount factor:

PV of $1600 received in year 1 = 1600 x 0.9709 = $1558.24
PV of $1600 received in year 3 = 1600 x 0.8885 = $1421.60
PV of $1600 received in year 5 = 1600 x 0.7730 = $1236.80

Finally, we can calculate the NPV of the investment by subtracting the initial cost of $4320 from the sum of the present values:

NPV = -4320 + 1558.24 + 1421.60 + 1236.80
NPV = -$114.21

Therefore, the closest answer is (D) -$114.21.

Suppose the Term Structure of Interest Rates Is Shown Below