Question

A company has a 12% WACC and is considering two mutually exclusive investments (that cannot be repeated) with the following cash flows:

0

1

2

3

4

5

6

7

Project A	-$300	-$387	-$193	-$100	$600	$600	$850	-$180
Project B	-$405	$132	$132	$132	$132	$132	$132	$0

1. What is each project's NPV? Negative values, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to the nearest cent.

   Project A: $  

   Project B: $  

2. What is each project's IRR? Do not round intermediate calculations. Round your answers to two decimal places.

   Project A:   %

   Project B:   %

3. What is each project's MIRR? (Hint: Consider Period 7 as the end of Project B's life.) Do not round intermediate calculations. Round your answers to two decimal places.

   Project A:   %

   Project B:   %

4. From your answers to parts a-c, which project would be selected?

   -Select-Project AProject BItem 7

   If the WACC was 18%, which project would be selected?

   -Select-Project AProject BItem 8

5. Construct NPV profiles for Projects A and B. If an amount is zero, enter 0. Negative values, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to the nearest cent.

   Discount Rate	NPV Project A	NPV Project B
   0%	$	$
   5
   10
   12
   15
   18.1
   23.33

6. Calculate the crossover rate where the two projects' NPVs are equal. Do not round intermediate calculations. Round your answer to two decimal places.

     %

7. What is each project's MIRR at a WACC of 18%? Do not round intermediate calculations. Round your answers to two decimal places.

   Project A:   %

   Project B:   %

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Answer 1

Part a:

NPV of the two projects is calculated below:

Project A:

Year	CF	Discount Factor		Discounted CF
0	$ -300.00	1/(1+0.12)^0=	1	1*-300=	$ -300.00
1	$ -387.00	1/(1+0.12)^1=	0.892857143	0.892857142857143*-387=	$ -345.54
2	$ -193.00	1/(1+0.12)^2=	0.797193878	0.79719387755102*-193=	$ -153.86
3	$ -100.00	1/(1+0.12)^3=	0.711780248	0.711780247813411*-100=	$    -71.18
4	$    600.00	1/(1+0.12)^4=	0.635518078	0.635518078404831*600=	$    381.31
5	$    600.00	1/(1+0.12)^5=	0.567426856	0.567426855718599*600=	$    340.46
6	$    850.00	1/(1+0.12)^6=	0.506631121	0.506631121177321*850=	$    430.64
7	$ -180.00	1/(1+0.12)^7=	0.452349215	0.452349215336893*-180=	$    -81.42
				NPV = Sum of all Discounted CF	$    200.41

Project B:

Year	CF	Discount Factor		Discounted CF
0	$ -405.00	1/(1+0.12)^0=	1	1*-405=	$ -405.00
1	$    132.00	1/(1+0.12)^1=	0.892857143	0.892857142857143*132=	$    117.86
2	$    132.00	1/(1+0.12)^2=	0.797193878	0.79719387755102*132=	$    105.23
3	$    132.00	1/(1+0.12)^3=	0.711780248	0.711780247813411*132=	$      93.95
4	$    132.00	1/(1+0.12)^4=	0.635518078	0.635518078404831*132=	$      83.89
5	$    132.00	1/(1+0.12)^5=	0.567426856	0.567426855718599*132=	$      74.90
6	$    132.00	1/(1+0.12)^6=	0.506631121	0.506631121177321*132=	$      66.88
				NPV = Sum of all Discounted CF	$    137.71

Part b: IRR is calculated either by hit and trial or by use of a financial calcualtor or Excel's goal seek function:

Project A: IRR = 18.10% rounded to 2 decimal places

Year CF Discount Factor 0 $ -300.00 1/(1+0.18096706596689)^0= 1 $ -387.00 1/(1+0.18096706596689)^1= 2 $ - 193.00 1/(1+0.18096706596689)^2= 3 $ -100.00 1/(1+0.18096706596689)^3= 4 $ 600.00 1/(1+0.18096706596689)^4= 5 $ 600.00 1/(1+0.18096706596689)^5= 6 $ 850.00 1/(1+0.18096706596689)^6= 7 $ -180.00 1/(1+0.18096706596689)^7= Discounted CF 1 1*-300= $-300.00 0.846763664 0.846763664134251*-387= $-327.70 0.7170087030.717008702898063*-193= $ -138.38 0.607136916 0.60713691648211*-100= $ -60.71 0.51410148 0.514101480031562*600= $ 308.46 0.435322453 0.435322452968367*600= $ 261.19 0.368615235 0.368615235355405*850= $ 313.32 0.312129987|0.312129987345252*-180= $ -56.18 NPV = Sum of all Discounted CF $ 0.00

Project B: IRR comes to 23.33% rounded to 2 decimal places

Year CF Discount Factor 0 $ -405.00 1/(1+0.233310109087244)^0= 1 $ 132.00 1/(1+0.233310109087244)^1= 2 $ 132.00 1/(1+0.233310109087244)^2= 3 $ 132.00 1/(1+0.233310109087244)^3= 4 $132.00 1/(1+0.233310109087244)^4= 5 $ 132.00 1/(1+0.233310109087244)^5= 6 $ 132.00 1/(1+0.233310109087244)^6= Discounted CF 11*-405= $-405.00 0.810826079 0.810826079046807*132= $ 107.03 0.65743893 0.657438930462419*132= $ 86.78 0.53306863 0.53306863019957*132= $ 70.37 0.432225947 0.432225947287569*132= $ 57.05 0.3504600710.350460070101472*132= $ 46.26 0.284162165 0.284162164502846*132= $ 37.51 NPV = Sum of all Discounted CF $ 0.00

Part c:

FVpositive CF -1 MIRR = 1 PVnegative CF

3679.27 MIRRA = V 952

MIRRA = 21.30%

MIRRB = 1199.75

MIRRR = 16.78%

Part D

NPV method reigns supreme above all so the project with highest NPV should be selected, which is project A. Even though the IRR of project B is higher.

NPV of the two projects if the WACC = 18% is given below:

Project A:

Year CF Discount Factor 0 $-300.00 1/(1+0.18)^0= 1 $ -387.00 1/(1+0.18)^1= 2 $ -193.00 1/(1+0.18)^2= 3 $ -100.00 1/(1+0.18)^3= 4 $ 600.00 1/(1+0.18)^4= 5 $ 600.00 1/(1+0.18)^5= 6 $ 850.00 1/(1+0.18)^6= 7 $ -180.00 1/(1+0.18)^7= Discounted CF 11*-300= 0.847457627 0.847457627118644*-387= 0.718184430.718184429761563*-193= 0.608630873 0.608630872679291*-100= 0.515788875 0.515788875151941*600= 0.437109216 0.437109216230459*600= 0.370431539 0.370431539178355*850= 0.313925033 0.313925033201996*-180= NPV = Sum of all Discounted CF $ -300.00 -327.97 -138.61 -60.86 309.47 262.27 314.87 -56.51 886.61

Project B

Year CF Discount Factor 0 $ -405.00 1/(1+0.18)^0= 1 $ 132.00 1/(1+0.18)^1= 2 $ 132.00 1/(1+0.18)^2= 3 $ 132.00 1/(1+0.18)^3= 4 $ 132.00 1/(1+0.18)^4= 5 $ 132.00 1/(1+0.18)^5= 6 $ 132.00 1/(1+0.18)^6= Discounted CF 11*-405= 0.847457627 0.847457627118644*132= 0.718184430.718184429761563*132= 0.608630873 0.608630872679291*132= 0.515788875 0.515788875151941*132= 0.437109216 0.437109216230459*132= 0.370431539 0.370431539178355*132= 1 NPV = Sum of all Discounted CF $ -405.00 111.86 94.80 80.34 68.08 57.70 48.90 461.68

Even so Project A has a higher NPV and should be selected

NPV profile :

Rate	A	B
0%	2050	792
5%	1598.02	669.99
10%	1262.16	574.89
12%	1152.4	542.71
15%	1008.84	499.55
18%	882.85	460.5
23%	711.18	405.01
57.67%	213.99	213.99
80%	113.9	160.15
100%	69.53	129.94

2500 2000 1500 1000 500 213.99 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100%105% AB

Part f) Crossover rate is 57.67%

Part g) MIRR when WACC is 18% is calculated below:

FVpositive CF -1 MIRR = 1 PVnegative CF

4830.54 MIRRA = V 883.95

MIRRA = 27.458%

MIRRR = 1470.68

MIRRR = 20.23%

So MIRR of both the projects increased