Question

Here are the cash flows for two mutually exclusive projects: Ce - 34,400 -34,400 C2 +513,700 Cs +5 13,700 4,200 Project A +513,700 a. Given the following interest rates (0 % , 2 % , 4 % , 6 % , 8 % , 10 % 12 % 14 % , 16 % , 18% , 20 % ), above what interest rates would you prefer project A to B? Interest rates abave b. What is the IRR of each project? (Round your answers to 2 decimal pleces.) Project B Project A IRR

Answer 1

Part a.

To find the answer to this, we create NPV profiles for the two projects i.e. we find the NPVs of the two projects using the given interest rates as the discounting factor for cost of capital. The NPVs from 0% to 10% come out to be as given below (calculated using Excel's NPV function as shown in formula view):

6% Rate NPVA NPVB 0% 2% 4% $ 6,700.00 $ 5,109.20 $ 3,618.75 $ 8,800.00 $ 6,308.32 $ 4,004.64 $ 2,220.26 $ 1,871.55 $ $ 8% 906.23 $ -106.45 $ 10% -330.13 -1,943.20

Now, as we can see, the NPV of project B remains greater than NPV of A till the interest rate of 4% beyond which NPV of A becomes higher than B. So from among the given interest rates, we can say that above the rate of 4% we would prefer project A to B.

Part b.

The IRRs of the 2 projects can easily be found using the IRR function of Excel or any financial calculator. Below we have found the IRRs using Excel's IRR function as:

IRRA IRR B 9.45% 7.89%

Formula view showing Excel formulas used:

project C1 C2 13700 13700 -34400 -34400 C3 13700 43200 0.1 6 Rate 7 NPVA 8 NPVB 0.02 0.04 0.06 0.08 =NPV(B6,$D$3:$F$3)+$C$ =NPV(C6, $D$3:$F$3)+$C$ =NPV(D6, $D$3:$F$3)+$C$ =NPV(E6, $D$3:$F$3)+$C$ =NPV(F6, $D$3:$F$3)+$C$: ENPV(G6,$D$3:$F$3)+$C$3 =NPV(B6,$D$4:$F$4)+$C$ =NPV(C6,$D$4:$F$4)+$C$ =NPV(D6,$D$4:$F$4)+$C$ =NPV(E6,$D$4:$F$4)+$C$ =NPV(F6,$D$4:$F$4)+$C$ =NPV(G6,$D$4:$F$4)+$C$4 11 12 IRRA IRR B =IRR(C3:F3) =IRR(C4:F4,15%)