Fundamentals of Corporate Finance - Ross - 9th Edition - FCF - Case Solutions
FCF 9th Edition Chapter 09
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Transcript of FCF 9th Edition Chapter 09
Chapter 9Problems 1-28Input boxes in tan Output boxes in yellow Given data in blue Calculations in red Answers in green NOTE: Some functions used in these spreadsheets may require that the "Analysis ToolPak" or "Solver Add-In" be installed in Excel. To install these, click on the Office button then "Excel Options," "Add-Ins" and select "Go." Check "Analyis ToolPak" and "Solver Add-In," then click "OK."
require that
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 9Question 1 Input area:
Year 0 1 2 3 4
$
Cash flow (6,400) 1,600 1,900 2,300 1,400
Output area:
Payback period
3.43
Chapter 9Question 2 Input area:
Annual cash inflow $ # of years Initial cost $
765 8 2,400
Output area:
Payback period
3.14
Chapter 9Question 3 Input area:
Year 0 1 2 3 4
Cash Flow (A) Cash Flow (B) $ (40,000) $ (60,000) 19,000 14,000 25,000 17,000 18,000 24,000 6,000 270,000 3
Required payback
Output area:
Project A Payback Project A Project B Payback Project B
1.840 Accept 3.019 Reject
Chapter 9Question 4 Input area:
Annual cash inflows: Year 1 $ Year 2 Year 3 Year 4 Discount rate Initial cost $
4,200 5,300 6,100 7,400 14% 13,000
Output area:
Discounted payments: Year 1 $ Year 2 $ Year 3 $ Year 4 $ Payback period
3,684.21 4,078.18 4,117.33 4,381.39 3.26
Chapter 9Question 5 Input area:
Initial cost Annual cash flow # of years Discount rate . Output area:
$ $
15,000 4,300 6 0%
Discounted Year Cash Flow 0 $ (15,000.00) 1 4,300.00 2 4,300.00 3 4,300.00 4 4,300.00 5 4,300.00 6 4,300.00 Payback period 3.49
Chapter 9Question 6 Input area:
Installation cost # of years Projected net income: Year 0 Year 1 Year 2 Year 3 . Output area:
$ 15,000,000 4 $ $ $ $ 1,938,200 2,201,600 1,876,000 1,329,500
Average net income Average book value AAR
$1,836,325 $7,500,000 24.48%
Chapter 9Question 7 Input area:
Required Return Annual cash flows: Year 0 Year 1 Year 2 Year 3 . Output area:
16% $ $ $ $ (34,000) 16,000 18,000 15,000
IRR Accept/Reject
20.97% Accept
Chapter 9Question 8 Input area:
Required Return Required Return Annual cash flows: Year 0 Year 1 Year 2 Year 3 . Output area:
11% 30% $ $ $ $ (34,000) 16,000 18,000 15,000
NPV at $ Accept./Reject NPV at $ Accept/Reject
11% 5,991.49 Accept 30% (4,213.93) Reject
Chapter 9Question 9 Input area:
Annual cash flows # of years Costs Required Return . Output area:
$ $
28,500 9 138,000 20%
NPV Accept/Reject IRR
($23,117.45) Reject 14.59%
Indifferent about the project when R = IRR.
Chapter 9Question 10 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 . Output area:
$ $ $ $
(19,500) 9,800 10,300 8,600
IRR
22.64%
Chapter 9Question 11 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Discount rate . Output area:
$ $ $ $
(19,500) 9,800 10,300 8,600 0%
NPV
$
9,200.00
Chapter 9Question 12 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Year 4 Required return
$ $ $ $ $
A (43,000) 23,000 17,900 12,400 9,400
$ $ $ $ $
B (43,000) 7,000 13,800 24,000 26,000 11%
Output area:
IRR (A) 20.44% IRR (B) 18.84% 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 $ $ 16,000 $ 4,100 $ (11,600) $ (16,600) 15.30% $ $ 7,507.61 9,182.29 Project B
Year 0 Year 1 Year 2 Year 3 Year 4 Crossover rate
Chapter 9Question 13 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3
$ $ $ $
X (15,000) 8,150 5,050 6,800
$ $ $ $
Y (15,000) 7,700 5,150 7,250
Output area:
IRR (X) IRR (Y) CF difference $ $ 450 $ (100) $ (450)
16.57% 16.45%
Year 0 Year 1 Year 2 Year 3 Crossover rate Discount Rate 0% 5% 10% 15% 20% 25%
11.73% NPV (X) 5,000.00 3,216.50 1,691.59 376.59 (766.20) (1,766.40) NPV (Y) 5,100.00 3,267.36 1,703.23 356.78 (811.34) (1,832.00)
$ $ $ $ $ $
$ $ $ $ $ $
Chapter 9Question 14 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Required return
$ $ $
(45,000,000) 78,000,000 (14,000,000) 12%
Output area:
NPV Accept/Reject IRR
$13,482,142.86 Accept
53.00% -79.67% When there are multiple IRRs, the IRR decision rule is ambiguous; in this case, if the correct IRR = 53.00%, then we would accept the project, but if the correct IRR is -79.67%, we would reject the project.
Chapter 9Question 15 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Discount rate
$ $ $ $
(14,000) 7,300 6,900 5,700 22%
Output area:
Profitability index
0.983
Chapter 9Question 16 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Required return
$ $ $ $
I (53,000) 27,000 27,000 27,000
$ $ $ $
II (16,000) 9,100 9,100 9,100 10%
Output area:
Profitability index (I) Profitability index (II) The profitability index implies accept
1.267 1.414 Project II
NPV (I) NPV (II) NPV decision rule implies accept
$ 14,145.00 $ 6,630.35 Project I
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 9Question 17 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Year 4 Required return
$ $ $ $ $
A (300,000) 20,000 50,000 50,000 390,000
$ $ $ $ $
B (40,000) 19,000 12,000 18,000 10,500 15%
Output area:
a. Payback (A) Payback (B) Payback criterion implies accept because it pays back sooner. b. Discounted cash flows Year A 0 $ (300,000.00) 1 17,391.30 2 37,807.18 3 32,875.81 4 222,983.77 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.
3.46 2.50 Project B
B $ (40,000.00) 16,521.74 9,073.72 11,835.29 6,003.41 3.95 3.43 Project B
$ 11,058.07 $ 3,434.16 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.
16.20% 19.50% Project B
1.037 1.086 Project B
f. The only decision rule that can rank mutually exclusive projects is NPV: therefore you should accept Project A
Chapter 9Question 18 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Year 4
$ $ $ $ $
(684,680) 263,279 294,060 227,604 174,356
Output area:
NPV @ 0% NPV @ infinity IRR
$ $
274,619 (684,680) 16.23%
Chapter 9Question 19 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Interest rate
$ $ $ $ $ $
(16,000) 6,100 7,800 8,400 6,500 (5,100) 10%
Output area:
Discounting approach: Year 0 1 2 3 4 5 MIRR Reinvestment approach: Year 0 1 2 3 4 5 MIRR
$ $ $ $ $ $
CF (19,166.70) 6,100.00 7,800.00 8,400.00 6,500.00 18.18%
$ $ $ $ $ $
CF (16,000.00) 31,526.81 14.53%
Combination approach: Year 0 1 2 3 4 5 MIRR
CF $ (19,166.70) $ $ $ $ $ 36,626.81 13.83%
Chapter 9Question 20 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Discount rate Reinvestment rate
$ $ $ $ $ $
(16,000) 6,100 7,800 8,400 6,500 (5,100) 11% 8%
Output area:
Discounting approach: Year 0 1 2 3 4 5 MIRR Reinvestment approach: Year 0 1 2 3 4 5 MIRR
$ $ $ $ $ $
CF (19,026.60) 6,100.00 7,800.00 8,400.00 6,500.00 18.55%
$ $ $ $ $ $
CF (16,000.00) 29,842.50 13.28%
Combination approach: Year 0 1 2 3 4 5 MIRR
$ $ $ $ $ $
CF (19,026.60) 34,942.50 12.93%
Chapter 9Question 21 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 9Question 22 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 9Question 23 Input area:
Cost Required Return Payback . Output area:
$
724,000 12% 7
Given the six year payback, the worst case is the payback occurs at the end of the seventh year. Thus, Worst-case NPV $ (396,499.17) The best case has infinite cash flows beyond the payback point. Thus, the best-case NPV is infinite.
Chapter 9Question 24 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Year 4 . Output area:
$ $ $ $ $
(1,512) 8,586 (18,210) 17,100 (6,000)
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 9Question 25 Input area:
Net cash flow (year 1) $ Cash flow growth per year Initial investment $ Required return . Output area:
85,000 6% (1,400,000) 13%
PV of cash flows NPV Accept/Reject Necessary growth rate
$1,214,285.71 ($185,714.29) Reject 6.93%
Chapter 9Question 26 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Required return
$ $ $
58,000 (34,000) (45,000) 24%
Output area:
IRR NPV $
22.14% 1,314.26
The cash flows for the project are unconventional. Since the initial cash flow is positive and t remaining cash flows are negative, the decision rule for IRR in invalid in this case. The NPV is upward sloping, indicating that the project is more valuable when the interest rate increase
ial cash flow is positive and the nvalid in this case. The NPV profile hen the interest rate increases.
Chapter 9Question 27 Input area:
Annual cash flows: Year 0 Year 1 Year 2
$ $ $
20,000 (26,000) 13,000
Output area:
IRR
#NUM!
It is possible that the cash flows do not have an IRR. That is the case here. There is no real root to the IRR equation.
Chapter 9Question 28 Input area:
Annual cash flows: Year 0 Year 1 Year 2 Year 3 Year 4 Reinvestment rate Required return
$ $ $ $ $
(750,000) 205,000 265,000 346,000 220,000 4% 11%
Output area:
Year 0 1 2 3 4 5 NPV IRR
$ $ $ $ $ $ $
CF (750,000.00) 213,200.00 275,600.00 359,840.00 228,800.00 (2,626.33) 10.89%