question

2

>

S

h

e

et

1

a b

le>

1

0

.7 A B -1

5000000 -150

00000
5000000

20

000000 10

000000 10000000 20000000 6000000 $16,108,951.52 $

18

,

3

0

0,939.

4

2 5% npv

a
$

12

,836,213.37 $15,954,169.80 10% $10,059,587.41 $13,897,838.42 15% 43.97% 82.03% irr

b
10.8 Truck Pulley -17100 -22430 0.

14 5100 7500

5100 7500
5100 7500
5100 7500
5100 7500

14.99% 19.999%

irr
$408.71 $3,318.11

npv

accept both projects 14.54% 17.19% mirr 10.10 Project S Project

L -10000 –

25

000 3000 7400

3000 7400
3000 7400
3000 7400
3000 7400

$814.33 $1,675.34

npv L L
15.24% 14.67%

irr S
13.77% 13.46%

mirr S
1.081 1.067 pi

S
10.13 Interest rate NPV

A NPVB

A B
0

$1,288.00 $

820

.00 -400 -650 10

$478.83 $372.37 -528 210 12

$366.13 $308.39 -219

210
14

$265.40 $

250

.54

-150 210
18

$94.46 $150.42 1100

210
20

$21.98 $106.96

820 210
25

($128.74) $13.84 990

210
30

($244.71) ($61.56) -325

210
a
20.7% 25.8%

b
Select

A

at 10% cost o

f

capital c. $133.76 $173.70

c.

Select B at

17%

cost of capital 14.91% 17.35% d. mirr at 10% 18.76% 21.03%

d. 17%
Crossover rate CFA-CFB 250

Below the crossover rate, select A, above the crossover rate

select B

. -738 -429 -360 890 610 780 -535 14.76% 10.18 NPV
190-3 360-6 -190000 -360000 87000 98300

87000 98300
87000 98300

98300

98300
98300

$11,981.99 $22,256.02 $5,161.02 $5,723.30

select B
The value of the firm would increase by the npv. 10.12 Initial investment –

1065000 Purchase price 900000 350000 Installation costs 165000

350000
Initial investment 350000
1065000 350000
350000
$136,578.34 19.22% 10.21

A B
a. Period Annual CF

Annual CF
0

-25000000

-25000000
1 5000000 20000000
2 10000000 10000000
3

15000000 8000000 4 20000000 6000000
Payback 2

years 0.6666666667

A a.
2.67

years
1 year 0.5 Payback

1.5 years

B
b. Discounted Payback A B
Period Annual CF Annual CF

Disc Rate Disc CF-A Disc CF-B

0 -25000000 -25000000

1 5000000 20000000

0.9090909091 4545454.54545454 18181818.1818182 2 10000000 10000000

0.826446281 8264462.80991735

8264462.80991735
3 15000000 8000000

0.7513148009 11269722.0135237 6010518.40721262 4 20000000 6000000

0.6830134554 13660269.1073014 4098080.73219042 Discounted Payback A 24079639.3688956 3years 0.0673750005 3.067375

b
Discounted Payback B 1 year

0.825 1.825

years
A B
$12,739,908.48 $11,554,880 A and B should be selected with positive npvs

c.
$18,243,813.02 $14,964,829 A should be selectedwith the higher npv.

d.
$8,207,071.16 $8,643,390.4 B should be selected.

e
f
CFA – CFB 0
-15000000

0

7000000 14000000 13.53% 21.93% 20.96% g.

2

>Sheet

1

.7

0

1 5000000
2

2

,836,213.37

1

>0

Time CF
0

00000

1 20000000

2 10000000

3

,300,939.42

Accept NPV>0

Accept

B

>5% >10% >15% Accept

NPV

NPV

Accept

PV of cash flows

Accept

IRR

14.00%

MIRR

Accept

MIRR

Future value of annuity

MIRR

>14% Accept

pv of cash flows

npv Accept

IRR

Project S

Accept

Project L

MIRR Project S
Future value of annuity

MIRR

Accept

MIRR Project L
Future value of annuity

)

MIRR

Project S

Accept

Project L 1.07

Annuity

PV of cash flows

npv

%

accept

r

10

12

18

22

A

$478.83

-150
b.

A

B

B

MIRR

MIRR A
0 -400

-528

-219 210

-150 210

1100 210

820 210

990 210

-325 210

Crossover rate

NPV

million

Equivalent Annual Annuity

NPV

EAA

millions

A B
0

1 5000000
2 10000000

3

4 20000000

A

Year Annual CF 1.5 years

B

0 -25000000
1 20000000
2 10000000

3

4 6000000

B

Annual CF

0 -25000000 0 0
1 20000000

2 10000000

3 8000000

4 6000000

Discounted Payback Payback

years

A
Period Annual CF Discount Rate Discount CF
0 -25000000 0 0

1 5000000 0.9090909091

2 10000000 0.826446281 8264462.80991735

3 15000000 0.7513148009

4 20000000 0.6830134554

years

																																																						1											0	Chapte	r	10
					A	Uneven Cash Flow Stream
	Time		CF
-1			5000000
					10000000
					3						20000000
$16,108,95	1.5	$	12	$10,059,587.				4
											Accept						NPV
						B
		-150
		6000000
$	18	$15,954,169.80	$13,897,838.42
	b.		IRR
A	43.97%		>5%		>10%		>15%
82.03%
10.8
	Annuity
		PV of cash flows	$17,508.71	$408.71
$25,748.11	$3,318.11
	14.00%
Truck
									MIRR
			Future value of annuity	($33,711.53)
14.54%		>14%
Pulley
$49,575.78
17.19%
10.10′
			Project S
	pv of cash flows	$10,814.33	$814.33			npv
			Project L
$26,675.34	$1,675.34
15.24%
14.67%
($19,058.54)
13.77%
($47,01	1.07
13.46%
Profitability Index
PI	PV of cash flows/Initial investment
1.08
Project L to be selected on the basis of NPV
10.12
a.
Purchase price	900000
Installation cost	165000
1065000
$1,201,578.34
Less: Initial	$136,578.34		accept
Irr	19.	22	irr	irr>cost of capital
Reduce the cash flows by the amount of environmental costs	c.
NPVA	NPVB
	$478.83	$372.37
$366.13	$308.39
$94.46	$150.42
($43.14)	$67.26
	-400
	-528
	-219
	1100
	820
	990
	-325
20.65%
25.84%
d. MIRR
Future value of an annuity	$1,992.31
17.35%
14.91%
Select B at a cost of capital of 10%
e.	Crossover rate
	Year	A CF	B CF	Difference
-650	250
						210	-738
-429
-360
890
610
780
-535
14.76%	below the crossover rate, choose A
above the crossover rate, choose Bz
10.16.
	Equivalent Annual Annuity	Plane A
Present Value of Cash Flows	$108.14		million	shorter life	$8.14
	EAA	$2.26
Plane B
$9.26		millions	longer life
$1.64
Select A
10.21
Year				Annual CF
			-25000000
	15000000
	Payback	2.6666666667				years
Payback B
	8000000
	Discounted Payback
	Period		Discount Rate		Discount CF
	0.9090909091	18181818.1818182
	0.826446281		8264462.80991735
	0.7513148009	6010518.40721262
	0.6830134554	4098080.73219042
1.825	26446280.9917355	6818181.81818182
4545454.54545454
11269722.0135237
13660269.1073014
24079639.3688956
920360.631104436
Disc Payback	3.067375