CHAPTER 9
B-165
B:
$40,000 = $19,000/(1+IRR) + $12,000/(1+IRR)
2
+ $18,000/(1+IRR)
3
+ $10,500/(1+IRR)
4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find
that:
IRR = 19.50%
IRR decision rule implies we accept project B because IRR for B is greater than IRR for A.
e.
The profitability index for each project is:
A:
PI = ($20,000/1.15 + $50,000/1.15
2
+ $50,000/1.15
3
+ $390,000/1.15
4
) / $300,000 = 1.037
B:
PI = ($19,000/1.15 + $12,000/1.15
2
+ $18,000/1.15
3
+ $10,500/1.15
4
) / $40,000 = 1.086
Profitability index criterion implies accept project B because its PI is greater than project A’s.
f.
In this instance, the NPV criteria implies that you should accept project A, while profitability index,
payback period, discounted payback, and IRR imply that you should accept project B. The final
decision should be based on the NPV since it does not have the ranking problem associated with the
other capital budgeting techniques. Therefore, you should accept project A.
18.
At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across
time. So, the NPV of the project at a zero percent required return is:
NPV = –$684,680 + 263,279 + 294,060 + 227,604 + 174,356 = $274,619
If the required return is infinite, future cash flows have no value. Even if the cash flow in one year is $1
trillion, at an infinite rate of interest, the value of this cash flow today is zero. So, if the future cash
flows have no value today, the NPV of the project is simply the cash flow today, so at an infinite
interest rate:
NPV = –$684,680
The interest rate that makes the NPV of a project equal to zero is the IRR. The equation for the IRR of
this project is:
0 = –$684,680 + $263,279/(1+IRR) + $294,060/(1+IRR)
2
+ $227,604/(1+IRR)
3
+ 174,356/(1+IRR)
4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 16.23%