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
    a. -$10.22  
   b. -$10.85  
   c. -$9.04  
   d. -$10.13  
   e. -$11.12  
   

Answer 1

At 10%:

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=410[1-(1.1)^-3]/0.1

=410*2.486851991

=$1019.61

NPV=Present value of inflows-Present value of outflows

=$1019.61-$1000

=$19.61(Approx).

At 9.5%:

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=410[1-(1.095)^-3]/0.095

=410*2.508906828

=$1028.65

NPV=Present value of inflows-Present value of outflows

=$1028.65-$1000

=$28.65(Approx).

Hence change in NPV=(28.65-19.61)

=$9.04(Approx).