Question

You are a financial analyst for the Brittle Company. The director of capital budgeting has asked you to analyze two proposed capital investments: Projects X and Y. Each project has a cost of $10,000, and the cost of capital for each is 12%. The projects' expected net cash flows are shown in the table below.
Expected Net Cash Flows

Year	Project X	Project Y
0	– $10,000	– $10,000
1	6,500	3,500
2	3,000	3,500
3	3,000	3,500
4	1,000	3,500

1. Use the Homework Student Workbook to calculate each project's net present value (NPV), internal rate of return (IRR), modified internal rate of return (MIRR), and profitability index (PI).
2. Which project or projects should be accepted if they are independent and Which project or projects should be accepted if they are mutually exclusive?

Assignment 5-2, Question 1                                                                  
a.  Net Present Value (NPV):                                                               
NPVx =   -$10,000   +   $    +   $    +   $    +   $    =   $          
NPVy =   -$10,000   +   $    +   $    +   $    +   $    =   $          
   Internal Rate of Return (IRR):                                                              
   To solve for each project's IRR, find the discount rates that equate each NPV to zero:                                                          
           IRRx   =   %                                              
           IRRy   =   %                                              
       Modified Internal Rate of Return (MIRR):                                                              
To obtain each project's MIRR, begin by finding each project's terminal value (TV) of cash inflows: TVx   =   $6,500 (1.12)^3       +   $       +   $       +   $1,000   =   $  
           TVy   =   $       +   $       +   $       +   $3,500   =   $  
Now, each project's MIRR is the discount rate that equates the PV of the TV to each project's cost, $10,000:                                               MIRRx   =   %                                              
   MIRRy    =   %                                              
Profitability Index (PI):                                                              
To obtain each project's PI, divide its present value of future cash flows by its initial cost. The PV of future cash flows can be found from the NPV calculated earlier:              

PVx   =   NPVx   +   Cost of X                                      
= $   +   $10,000   =   $                              
                                                                  
PVy   =   NPVy   +   Cost of Y                                      
= $   +   $   =   $                              
                                                                  
PIx   =   PVx   ÷   Cost of X                                      
= $   ÷   $   =                                  
                                                                  
PIy   =   PVy   ÷   Cost of Y                                      
= $   ÷   $   =                                  

Answer 1

Net Present Value = Total cash outflows – Present value of Cash inflows

Present Value of Cash inflows = Cash inflow/((1+d)^n)

D denotes discount rate, n is the number of periods

For Project X

Net Present Value = 10000 -

(6500/1+12%)^1 + (3000/1+12%)^2 +(3000/1+12%)^3+(1000/1+12%)^4

= 10,000 – (5803.57+2391.58+2135.34+635.52)

= 966.02

For Project Y

Net Present Value = 10000 -

(3500/1+12%)^1 + (3500/1+12%)^2 +(3500/1+12%)^3+(3500/1+12%)^4

= 10,000 – (3125.00+2790.18+2491.23+2224.31)

= 630.72

2. Internal Rate of return

Discount rate that equates the cash outflows with the present value of cash inflows using trial and error method.

The discount rate is 18% for Project X

10,000 = (6500/(1.18)^1) + (3000/(1.18)^2) +(3000/(1.18)^3)+(1000/(1.18)^4)

10000 = 10004

Project Y = 15%

10,000 = (3500/(1.15)^1) + (3500/(1.15)^2) +(3500/(1.15)^3)+(3500/(1.15)^4)

10000 = 10000

3. Modified Internal Rate of Return

For Project X

Cost = Summation of Cash inflows (1+r)^n-t/(1+MIRR)^n

10000 = (6500/(1.12)^3) + (3000/(1.12)^2) +(3000/(1.12)^1)+(1000/(1.12)^0 / (1+MIRR)^4

10000 = 17375.23/(1+MIRR)^n

(1+MIRR)^4 = 17375.23/10000 =

(1+MIRR)^4 = 1.737523

= MIRR = (1.737523^1/4 ) – 1.0

=0.1481 = 14.81%

For Project Y

Cost = Summation of Cash inflows(1+r)^n-t/(1+MIRR)^n

10000 = (3500/(1.12)^3) + (3500/(1.12)^2) +(3500/(1.12)^1)+(3500/(1.12)^0 / (1+MIRR)^4

10000 = 16727.65 /(1+MIRR)^n

(1+MIRR)^4 = 16727.65/10000 =

(1+MIRR)^4 = 1.6727.65

= MIRR = (1.672765^1/4 ) – 1.0

=0.1373 = 13.73%

4. Profitability Index

Present Value of Cash inflows/ Initial Cost or Cash outflows

Project X = 10966.02/10000 = 1.096602

Project Y =10630.72/10000 = 1.063072

CRITERION	RRank
NPV	PProject X
IRR	PProject X
MIRR	PProject X
PI	PProject X

BOTH PROJECTS SHOULD BE ACCEPTED IF THEY ARE INDEPENDENT

PROJECT X IS SELECTED IF THEY ARE MUTUALLY EXCLUSIVE