Mathematics

Question

Last month, Lloyd's Systems analyzed the project whose cash flows are shown below. However, before the decision to accept or reject the project, the Federal Reserve took actions that changed interest rates and therefore the firm's WACC. The Fed's action did not affect the forecasted cash flows. By how much did the change in the WACC affect the project's forecasted NPV? Note that a project's projected NPV can be negative, in which case it should be rejected.

Old WACC: 10.00% New WACC: 9.50%
Year 0 1 2 3
Cash flows -$1,000 $410 $410 $410

Answers: A.
$10.85
B.
$10.13
C.
$9.04
D.
$11.12
E.
$10.22

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  • Answer:

      C.  $9.04

    Step-by-step explanation:

    The net present value of a cash flow C in year n at some interest rate r is given by ...

      NPV = C·(1 +r)^(-n)

    Adding the values of the different cash flows at the different interest rates, we get the results shown in the attached table. The NPV goes up by $9.04 when the cost of capital goes down.

    _____

    Additional comment

    Neither WACC will cause this project to be rejected. If the WACC were to increase to 11.11%, then the project would have a zero return.