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Unformatted text preview: Solutions to Lab Problems for Chapter 14 21. Section: 14.2 Estimating and Discounting Cash Flows
Learning Objective: 14.2
Level of difficulty: Difficult
Solution:
Step 1: initial cash flow=CF0=$4,000.
Step 2: PV of aftertax operating cash flow
Discount rate=0.10, payment=$2,000*(1tax rate)=$2,000*(10.4),
N=3, and PV=2,984.22.
Step 3: PV of CCA tax shield.
There is no capital gain, capital recapture, or terminal loss.
Using formula [147], C0dT/(d+k)=1,200.00, (1+0.5k)/(1+k)=0.954545,
SVdT/(d+k)=0, 1/(1+k)n=0.751315, and PV of CCA tax shield=1,145.45
Step 4: PV of ECF
Discount rate=0.10, future value=salvage value=0
N=3, and PV=0
Step 5: PV of capital gains taxes paid=0
Step 6: Using formula [1410], NPV=129.67
This project has a positive NPV. The company should take it.
33. Section: 14.3 Sensitivity to Inputs
Learning Objective: 14.3
Level of difficulty: Difficult
Solution:
a.
Year
0
1
2
3
4 Cash flow UCC
(open) $2,500.00
$700.00
1,250
$735.00
2,375
$771.75 2,137.50
$810.34 1,923.75 CCA UCC Aftertax cash
(close)
flow $2,500.00
$125.00 2,375
$556.25
$237.50 2,137.50
$610.63
$213.75 1,923.75
$632.25
$192.38 1,731.37
$655.85 Present value of aftertax cash flows: PV of aftertax cash
flow
$2,500.00
$519.86
$533.34
$516.10
$500.34
$430.35 The asset will be scrapped (salvage = $0) zero capital gains. As the asset class is large
and will continue we do not have to deal with CCA recapture and terminal loss in year 4.
b. Worst case
Year Base case AfterPV of
Cash flow tax cash aftertax
flow cash flow Cash
flow Best case AfterPV of
tax cash aftertax
flow cash flow PV of
Afteraftertax
tax cash
cash
flow
flow Cash
flow Growth
rate 2.00% 5.00% 8.00% Year 1
cash flow $300 $700 $ 900 0
1
2
3
4
NPV 2,500
300.00
306.00
312.12
318.36 2,500
256.25
288.88
287.53
286.87 2,500
239.49
252.32
234.71
218.85
$1,554.63 2,500
700.00
735.00
771.75
810.34 2,500
556.25
610.63
632.25
655.85 2,500
2,500
519.86 900.00
533.35 972.00
516.10 1,049.76
500.34 1,133.74
$430.35 2,500
706.25
788.38
840.76
898.40 2,500
660.05
688.60
686.31
685.39
$220.35 The expected value of the project is: .3*(–1,554.63) + .55*(430.35) + .15*(220.35) = –
$670.03
c.
Year PV of cash flows Growth rate 0.03 0.05 0.07 0.03 0.05 0.07 0.03 0.05 0.07 Year 1 cash
400
400
400
700
700
700
1,000 1,000 1,000
flow
NPV
1,278.46 1,248.18 1,217.13 483.34 430.35 376.01 311.78 387.48 465.12
Given that this project is only 4 years long, the impact of any errors on the initial cash
flow estimate will be more important than growth rate errors. With only 4 years to grow,
a small error in the growth rate does not have time to compound into a huge error.
d. Using the solver function in Excel, we find that the initial cash flow that results in a
breakeven or zero NPV is $857.86
B
47 Year Growth
48 rate
Year 1
49 cash flow C
CCA D
Cash flow
0.05
857.862619935937 E
Aftertax cash flow F
PV of aftertax cash
flows 0
1
2
3
4 50
51
52
53
54
55 125
237.5
213.75
192.375
NPV 2500
=D50
=+D52*(1+G$17)
=+D53*(1+G$17)
=+D54*(1+G$17) 2500
=D52*0.75+$C52*0.25
=D53*0.75+$C53*0.25
=D54*0.75+$C54*0.25
=D55*0.75+$C55*0.25 =E51/(1.07)^$B51
=E52/(1.07)^$B52
=E53/(1.07)^$B53
=E54/(1.07)^$B54
=E55/(1.07)^$B55
=SUM(F51:F55) 45. Section: 14.4 Replacement Decisions
Learning Objective: 14.4
Level of difficulty: Challenging
Solution: Because we are dealing with a replacement problem, we have to examine the
incremental cash flows. As the old machine was fully depreciated 8 years ago and will be
scrapped if we replace it, we will assume that the UCC for this asset class at year zero is
close to zero (i.e., we will not have to deal with any CCA recapture/loss or capital gains
at time zero if we replace the old machine).
New machine
CCA schedule
UCC
Year
CCA
begin
0
1
2
3
4
5 Old machine New machine UCC
Rev. Maint. Invest. Maint. New  Old
end
25000 12500
22500
18000
14400
11520 2500
4500
3600
2880
2304 Incremental after tax CF 22500
18000
14400
11520
9216 1500
1500
1500
1500
1500 5000
6000
7000
8000
9000 500
500
500
500
500 25000
1980
2640
3300
3960
4620 CCA
Tax
shield
850
1530
1224
979.2
783.36 Total
25000
2830
4170
4524
4939.2
5403.36 The cash flows are given as nominal values so we need to use the appropriate nominal
discount rate: the approximation is 7% +3%= 10%. The more exact value for the nominal
rate would be 1.07*1.03 1 = 10.21%
NPV of incremental cash flows:
+ PV of salvage value of new machine
 PV of CCA terminal loss
NPV of replacing old machine: $8,853.44
3104.60662
890.053461
$4,858.78 Based on the analysis above, the old machine should not be replaced. ...
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This note was uploaded on 01/10/2012 for the course TEFLER 2350 taught by Professor Rentz during the Winter '11 term at University of Ottawa.
 Winter '11
 Rentz

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