Question

A company has a 13% 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	$135	$135	$135	$135	$135	$135	$0

a. What is each project's NPV? Round your answer to the nearest cent. Do not round your intermediate calculations.

Project A $

Project B $

b. What is each project's IRR? Round your answer to two decimal places.

Project A  %

Project B  %

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

Project A  %

Project B  %

d. Construct NPV profiles for Projects A and B. Round your answers to the nearest cent. Do not round your intermediate calculations. Negative value should be indicated by a minus sign.

Discount Rate	NPV Project A	NPV Project B
0%	$	$
5
10
12
15
18.1
24.29

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

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

Project A  %

Project B  %

Answer 1

Project A

cost of capital, WACC, (R)= 13% = 0.13

Cash flow for year 1, C1 = -$387

Cash flow for year 2, C2 = -$193

Cash flow for year 3, C3 = -$100

Cash flow for year 4, C4 = $600

Cash flow for year 5, C5 = $600

Cash flow for year 6, C6 = $650

Cash flow for year 7, C7 = $180

Initial investment , I = $300

NPV of project A = [ (C1/(1.13)¹) + (C2/(1.13)²) + (C3/(1.13)³) + (C4/(1.13)⁴) + (C5/(1.13)⁵) + (C6/(1.13)⁶) + (C7/(1.13)⁷) ] - I

= [ (-387/(1.13)¹) + (-193/(1.13)²) + (-100/(1.13)³) + (600/(1.13)⁴) + (600/(1.13)⁵) + (850/(1.13)⁶) + (-180/(1.13)⁷)] - 300

= $162.48

Project B

Cash flow for year 1, C1 = $135

Cash flow for year 2, C2 = $135

Cash flow for year 3, C3 = $135

Cash flow for year 4, C4 = $135

Cash flow for year 5, C5 = $135

Cash flow for year 6, C6 = $135

Cash flow for year 7, C7 = 0

Initial investment , I = $405

NPV of project B = [ (C1/(1.13)¹) + (C2/(1.13)²) + (C3/(1.13)³) + (C4/(1.13)⁴) + (C5/(1.13)⁵) + (C6/(1.13)⁶) + (C7/(1.13)⁷) ] - I

= [ (135/(1.13)¹) + (135/(1.13)²) + (135/(1.13)³) + (135/(1.13)⁴) + (135/(1.13)⁵) + (135/(1.13)⁶)+ 0 ] - 405

= $134.67

b)

IRR is the rate of return for which NPV = 0

NPV = Present value of cash inflows of the project - initial investment

Putting NPV = 0

Present value of cash inflows of the project = initial investment

[ (C1/(1+IRR)¹) + (C2/(1+IRR)²) + (C3/(1+IRR)³) + (C4/(1+IRR)⁴) + (C5/(1+IRR)⁵) + (C6/(1+IRR)⁶) + (C7/(1+IRR)⁷) ] = I

[ (-387/(1+IRR)¹) + (-193/(1+IRR)²) + (-100/(1+IRR)³) + (600/(1+IRR)⁴) + (600/(1+IRR)⁵) + (850/(1+IRR)⁶) + (-180/(1+IRR)⁷) ] = 300

We have to find IRR by trial and error method

by assuming any value and substituting the assumed value in the above equation

we want IRR such that

Leht Hand side of equation(LHS) = Right hand side of equation (RHS) = 300

by following this method we find that for IRR = 18.09671%

LHS = RHS

hence IRR For project A= 18.09671% or 18.10% ( rounding off to two decimal places)

For project B

Present value of cash inflows of the project B = initial investment

[ (C1/(1+IRR)¹) + (C2/(1+IRR)²) + (C3/(1+IRR)³) + (C4/(1+IRR)⁴) + (C5/(1+IRR)⁵) + (C6/(1+IRR)⁶) + (C7/(1+IRR)⁷) ] = I

[ (135/(1+IRR)¹) + (135/(1+IRR)²) + (135/(1+IRR)³) + (135/(1+IRR)⁴) + (135/(1+IRR)⁵) + (135/(1+IRR)⁶) + (0/(1+IRR)⁷) ] = 405

We have to find IRR by trial and error method

by assuming any value and substituting the assumed value in the above equation

we want IRR such that

Leht Hand side of equation(LHS) = Right hand side of equation (RHS) = 405

by following this method we find that for IRR = 24.29247%

LHS = RHS

hence IRR For project B= 24.29247% or 24.29% ( rounding off to two decimal places)

c)

future value of cash flows for project A = C4*(1+R)³ + C5*(1+R)² + C6*(1+R)¹

= 600*(1.13)³ + 600*(1.13)² + 850*(1.13)

= 2592.378

present value of costs = -300 -[387/(1.13)] - [193/(1.13)²] -[100/(1.13)³] -[180/(1.13)⁷] = -300 -342.478 - 151.147-69.305 - 76.5109 = -939.441

MIRR = (future value/cost)^{(1/period of investment)} -1

= (2592.378/939.441)^(1/7) - 1 = 0.156047 = 15.6047% OR 15.60%

PROJECT B

future value of cash flows for project A = C1*(1+R)⁶ + C2*(1+R)⁵ + C3*(1+R)⁴ + C4*(1+R)³ + C5*(1+R)² + C6*(1+R)¹ + C7

=  135*(1.13)⁶ + 135*(1.13)⁵ + 135*(1.13)⁴ + 135*(1.13)³ + 135*(1.13)² +  135*(1.13)

= 1269.629

MIRR = (future value/cost)^{(1/period of investment)} -1

= (1269.629/405)^(1/7) - 1 = 0.177304 = 17.7304% OR 17.73%

d)

1. when discount rate = 0

NPV of A = -300 -387 - 193 -100+600 + 600+ 850 -180 = 890

NPV of B = -405 +135 +135 +135 +135 + 135+ 135 +0 = 405

2.) when discount rate = 5% = 0.05

NPV for A = [ (-387/(1.05)¹) + (-193/(1.05)²) + (-100/(1.05)³) + (600/(1.05)⁴) + (600/(1.05)⁵) + (850/(1.05)⁶) + (-180/(1.05)⁷)] - 300

= $540.09

NPV for B = [ (135/(1.05)¹) + (135/(1.05)²) + (135/(1.05)³) + (135/(1.05)⁴) + (135/(1.05)⁵) + (135/(1.05)⁶) + 0] - 405

= $280.22

3) when discount rate = 10% = 0.10

NPV for A = [ (-387/(1.10)¹) + (-193/(1.10)²) + (-100/(1.10)³) + (600/(1.10)⁴) + (600/(1.10)⁵) + (850/(1.10)⁶) + (-180/(1.10)⁷)] - 300

= $283.34

NPV for B = [ (135/(1.10)¹) + (135/(1.10)²) + (135/(1.10)³) + (135/(1.10)⁴) + (135/(1.10)⁵) + (135/(1.10)⁶) + 0] - 405

= $182.96

4)

when discount rate = 12% = 0.12

NPV for A = [ (-387/(1.12)¹) + (-193/(1.12)²) + (-100/(1.12)³) + (600/(1.012)⁴) + (600/(1.12)⁵) + (850/(1.12)⁶) + (-180/(1.12)⁷)] - 300

= $200.41

NPV for B = [ (135/(1.12)¹) + (135/(1.12)²) + (135/(1.12)³) + (135/(1.12)⁴) + (135/(1.12)⁵) + (135/(1.12)⁶) + 0] - 405

= $150.04

5)

when discount rate = 15% = 0.15

NPV for A = [ (-387/(1.15)¹) + (-193/(1.15)²) + (-100/(1.15)³) + (600/(1.15)⁴) + (600/(1.15)⁵) + (850/(1.15)⁶) + (-180/(1.15)⁷)] - 300

= $92.96

NPV for B = [ (135/(1.15)¹) + (135/(1.15)²) + (135/(1.15)³) + (135/(1.15)⁴) + (135/(1.15)⁵) + (135/(1.15)⁶) + 0] - 405

= $105.91

6)

when discount rate = 18.1% = 0.181

NPV for A = [ (-387/(1.181)¹) + (-193/(1.181)²) + (-100/(1.181)³) + (600/(1.181)⁴) + (600/(1.181)⁵) + (850/(1.181)⁶) + (-180/(1.181)⁷)] - 300

= -$0.09

NPV for B = [ (135/(1.181)¹) + (135/(1.181)²) + (135/(1.181)³) + (135/(1.181)⁴) + (135/(1.181)⁵) + (135/(1.181)⁶) + 0] - 405

= $65.97

7)

when discount rate = 24.29% = 0.2429

NPV for A = [ (-387/(1.2429)¹) + (-193/(1.2429)²) + (-100/(1.2429)³) + (600/(1.2429)⁴) + (600/(1.2429)⁵) + (850/(1.2429)⁶) + (-180/(1.2429)⁷)] - 300

= -$143.39

NPV for B = [ (135/(1.2429)¹) + (135/(1.2429)²) + (135/(1.2429)³) + (135/(1.2429)⁴) + (135/(1.2429)⁵) + (135/(1.2429)⁶) + 0] - 405

= $0.02

12 13 Discount rate NPV proiect A NPV proiect B 14 15 16 17 18 19 20 0 0.05 0.1 0.12 0.15 0.181 0.2429 890.00 540.09 283.34 200.41 92.96 -0.09 -143.39 405.00 280.22 182.96 150.04 105.91 65.97 0.02