Question

Bruin, Inc., has identified the following two mutually exclusive projects: Year -o Cash Flow (A) -$41,000 19,400 14,900 12,400 9,400 Cash Flow (B) -$41,000 5,600 12.100 18,600 22,600 mt a. What is the IRR for Project A? b. What is the IRR for Project B?

c. If the required return is 7 percent, what is the NPV for Project A?

  

d. If the required return is 7 percent, what is the NPV for Project B?

  

e. At what discount rate would the company be indifferent between these two projects?

Answer 1

NPV is given by:

NPV = L Rt/(1 + i) ,t varies from 1 ton where Rt = Cash flow netted (Inflow - Outflow) during the period "t" i = Discount rate t = number of periods

Now, the discount rate at which NPV = 0 is known as IRR

Answer a)

SUM X v fx =lf nm + B Discount Rate Year Project A F 0 -$41,000] 1 $19,400 $14,900 3 $12,400 $9,400 IRR FIRR( C3:07) 00

Discount Rate Year Project A 0 -$41,000 1 $19,400 2 $14,900 3 $12,400 $9,400 IRR 15.91%! 41

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Answer b)

SUM Xv fx =IRR(D3:07) В Discount Rate Year 2 Project A Project B -$41,000 -$41,000 $19,400 $5,600 $14,900 $12,100 $12,400 _ $18,600 $9,400! $22,600 15.91% =IRR( D3:07) 3 IRR

D8 Year @fx =IRR(D3:07) в с D Discount Rate Project A Project B -$41,000 -$41,000 1 $19,400 $5,600 2 $14,900 $12,100 3 $12,400 $18,600 4 $9,400 $22,600 IRR 15.91% 13.18%!

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Answer c)

SUM X v fx =NPV(C1,04:C7)+c3 M + Discount Rate 17% Year Project Project B -$41,000l -$41,000 1 $19,400 $5,600 $14,900 $12,100 3 $12,400 $18,600 $9,400 $22,600 IRR 15.91% 13.18% NPV =NPV(C1, C4:07 )+ C3 0 00

09 @ fx =N ДА B Discount Rate Year o 1 7% Project A F $41,000 $19,400 $14,900 $12,400 $9,400 15.91% $7,438.39 IRR NPV

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Answer d)

SUM fx =NPV(D1,04:07)+D3 В Discount Rate 7% Year Project Project B 0 -$41,000 -$41,000 1 $19,400 $5,600 $14,900 $12,100 $12,400 $18,600 $9,400 $22,600 IRR 15.91% 13.18% NPV $7,438.39 =NPV(D1, D4:07 )+D3

Discount Rate Year 0 1 2 7% Project A Project B -$41,000 -$41,000 $19,400 $5,600 $14,900 $12,100 $12,400 $18,600 $9,400 $22,600 15.91% 13.18% $7,438.39 $17,900.00 IRR NPV

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Answer E)

Company will be indifferent between these 2 at cross over rate

For cross over rate

Step 1: Subtract cashflow B from Cashflow A

Step 2: FInd IRR of difference

SUM ✓ fx =C3-D3 Discount Rate 7% Year Project A Project B. ol $41,000! $41,000| 1 $19,400 $5,600 $14,900 $12,100 Project A - Project B =C3 - D3 13800 2800

SUM - A E F G H Project A - Project B Ham to 0009 X v fx =IRR(F3:F7) B C D Discount Rate 7% Year Project A Project B 0 -$41,000 -$41,000 1. $19,400 $5,600 2 $14,900 $12,100 3. $12,400 $18,600 $9,400 $22,600 IRR 15.91% 13.18% $7,438.39 $17,900.00 13800 2800 -6200 -13200 |<---- Cross Over Rate =IRR(F3:F7) IC NPV

F8 @ fx =IRR(F3:F7) E G H Year Project A - Project B В C D Discount Rate 7% Project A Project B 0 -$41,000 $41,000 1. $19,400 $5,600 2 $14,900 $12,100 3 $12,400 $18,600 $9,400 $22,600 IRR 15.91% 13.18% NPV $7,438.39 $17,900.00 13800 2800 -6200 -13200 6.41% <---- Cross Over Rate 41 170

Company will be indifferent between these 2 at cross over rate = 6.41%