9
Problems Chapter 1-23
Input boxes in tan Output boxes in yellow Given data in blue Calculations in red Answers in green
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
B
C
D
E
Chapter 9
Question 1 Input area:
Year 0 1 2 3 4
Cash flow $(4,800) 1,200 2,500 3,400 1,700
Output area:
Payback period
2.32
Chapter 9
Question 2 Input area:
Annual cash inflow # of years Initial cost . Output area:
$840 8 $3,000
Payback period
3.57
Chapter 9
Question 3 Input area:
Year 0 1 2 3 4
Cash Flow (A) $(50,000) 30,000 18,000 10,000 5,000
Cash Flow (B) $(70,000) 9,000 25,000 35,000 425,000 3
Required payback
Output area:
Project A Payback Project A Project B Payback Project B
2.200 Accept 3.002 Reject
Chapter 9
Question 4 Input area:
Annual cash inflows: Year 1 Year 2 Year 3 Year 4 Discount rate Initial cost . Output area:
$7,000 7,500 8,000 8,500 14% $8,000
Discounted payments: Year 1 Year 2 Year 3 Year 4 Payback period
$6,140.35 $5,771.01 $5,399.77 $5,032.68 1.32
Chapter 9
Question 5 Input area:
Annual cash flow Discount rate Initial cost # of years . Output area:
$2,100 0% $10,000 6
Year 0 1 2 3 4 5 6 Payback period
Discounted Cash Flow $(10,000.00) 2,100.00 2,100.00 2,100.00 2,100.00 2,100.00 2,100.00 4.76
Chapter 9
Question 6 Input area:
Installation cost # of years Projected net income: Year 0 Year 1 Year 2 Year 3 . Output area:
$15,000,000 4 $1,416,000 $1,868,000 $1,562,000 $985,000
Average net income Average book value AAR
$1,457,750 $7,500,000 19.44%
Chapter 9
Question 7 Input area:
Required Return Annual cash flows: Year 0 Year 1 Year 2 Year 3 . Output area:
18% $(30,000) $20,000 $14,000 $11,000
IRR Accept/Reject
26.48% Accept
Chapter 9
Question 8 Input area: Required Return Required Return Annual cash flows: Year 0 Year 1 Year 2 Year 3 . Output area: NPV at Accept./Reject NPV at Accept/Reject 11% $7,423.84 Accept 30% $(1,324.53) Reject 11% 30% $(30,000) $20,000 $14,000 $11,000
Chapter 9
Question 9 Input area:
Required Return Annual cash flows Costs # of years . Output area:
8% $14,000 $70,000 9
NPV Accept/Reject IRR
$17,456.43 Accept 13.70%
Indifferent about the project when R = IRR.
Chapter 9
Question 10 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 . Output area:
$(8,000) $3,200 $4,000 $6,100
IRR
26.83%
Chapter 9
Question 11 Input area: Annual cash flows: Year 0 Year 1 Year 2 Year 3 Discount rate . Output area: NPV $5,300.00
$(8,000) $3,200 $4,000 $6,100 0%
Chapter 9
Question 12 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Year 4 Required return
A $(34,000) $16,500 $14,000 $10,000 $6,000
B $(34,000) $5,000 $10,000 $18,000 $19,000 11%
Output area:
IRR (A) 16.60% IRR (B) 15.72% The implication of ranked IRR is to accept Project A This may not be a correct decision however, because the IRR has a ranking problem for mutually exclusive projects To see if the ranked IRRs lead to the correct decision or not, we need to evaluate the project NPVs. NPV (A) NPV (B) The NPV decision rule implies you accept CF difference $$11,500 $4,000 $(8,000) $(13,000) 13.75% $3,491.88 $4,298.06 Project B
Year 0 Year 1 Year 2 Year 3 Year 4 Crossover rate
Chapter 9
Question 13 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3
X $(5,000) $2,700 $1,700 $2,300
Y $(5,000) $2,300 $1,800 $2,700
Output area:
IRR (X) IRR (Y) CF difference $$400 $(100) $(400)
16.82% 16.60%
Year 0 Year 1 Year 2 Year 3 Crossover rate Discount Rate 0% 5% 10% 15% 20% 25%
13.28% NPV (X) $1,700.00 $1,100.21 $587.53 $145.56 $(238.43) $(574.40) NPV (Y) $1,800.00 $1,155.49 $607.06 $136.35 $(270.83) $(625.60)
Chapter 9
Question 14 Input area: Annual cash flows: Year 0 Year 1 Year 2 Required return Output area: NPV IRR Accept/Reject $13,570,247.93 Accept
$(28,000,000) $53,000,000 $(8,000,000) 10%
72.75% -83.46% When there are multiple IRRs, the IRR decision rule is ambiguos; in this case, if the correct IRR = 72.75%, then we would accept the project, but if the correct IRR is -83.46%, we would reject the project.
Chapter 9
Question 15 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Discount rate
$(7,000) $3,200 $3,900 $2,600 10%
Output area:
Profitability index
1.155
Chapter 9
Question 16 Input area: Annual cash flows: Year 0 Year 1 Year 2 Year 3 Required return Output area: Profitability index (I) Profitability index (II) The profitability index implies accept NPV (I) NPV (II) NPV decision rule implies accept 1.243 1.393 Project II $7,302.78 $1,963.19 Project I I $(30,000) $15,000 $15,000 $15,000 II $(5,000) $2,800 $2,800 $2,800 10%
Using the profitability index to compare mutually exclusive projects can be ambiguous when the magnitude of the cash flows for the two projects are of different scale.
Chapter 9
Question 17 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Year 4 Required return
A $(210,000) $15,000 $30,000 $30,000 $370,000
B $(21,000) $11,000 $9,000 $11,000 $9,000 15%
Output area:
a. Payback (A) Payback (B) Payback criterion implies accept because it pays back sooner. b. Discounted cash flows Year 0 1 2 3 4
3.36 2.09 Project B
A $(210,000.00) 13,043.48 22,684.31 19,725.49 211,548.70
B $(21,000.00) 9,565.22 6,805.29 7,232.68 5,145.78 3.73 2.64 Project B
Discounted payback (A) Discounted payback (B) Discounted payback criterion, implies accept because it pays back sooner. c. NPV (A) NPV (B) NPV criterion implies accept because it has a higher NPV.
$57,001.98 $7,748.97 Project A
d. IRR (A) IRR (B) IRR decision rule implies accept because its IRR is greater. e. PI (A) PI (B) Profitability index criterion implies accept because its PI is larger.
22.97% 32.73% Project B
1.271 1.369 Project B
f. The only decision rule that can rank mutually exclusive projects is NPV: therefore you should accept Project A
Chapter 9
Question 18 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Year 4
$(568,240) $289,348 $196,374 $114,865 $93,169
Output area:
NPV @ 0% NPV @ infinity IRR
$125,516 $(568,240) 10.71%
Chapter 9
Question 19 Input area:
*The NPV index is defined as the ratio of NPV to cost.
Output area:
Since the NPV index has the cost subtracted in the numerator, NPV index = PI - 1.
Chapter 9
Question 20 Input area:
Annual cost Required return Pays # of years
I R C N
Output area:
To have a payback equal to the project's life, given C is a constant cash flow for N years, C = I/N To have a positive NPV, I < C(PVIFAR%,N). Thus, C > I / (PVIFAR%,N) Benefits = C (PVIFAR%,N) = 2 costs = 2I C = 2I / (PVIFAR%,N)
Chapter 9
Question 21 Input area:
Cost Required Return Payback . Output area:
$483,000 12% 7
Given the six year payback, the worst case is the payback occurs at the end of the sixth year. Thus, Worst-case NPV $(264,515.33) The best case has infinite cash flows beyond the payback point. Thus, the best-case NPV is infinite.
Chapter 9
Question 22 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Year 4 . Output area:
$(504) $2,862 $(6,070) $5,700 $(2,000)
From trial and error, IRRs of 25.00% 33.33% 42.86% 66.67% found. Take the project when NPV>0, for required returns between 25% and 33.33% or between 42.86% and 66.67%.
Chapter 9
Question 23 Input area:
Initial investment Net cash flow (year 1) Cash flow growth per year Required return . Output area:
$(780,000) $50,000 6% 13%
PV of cash flows NPV Accept/Reject Necessary growth rate
$714,285.71 ($65,714.29) Reject 6.59%