Question

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Problem 1 You have the following projects available: Time Period Project A -$40,000.00 $35,000.00 $15,000.00 $9,000.00 $2,000.00 $3,000.00 Project Cash Flows Project B Project C -$40,000.00 -$25,000.00 $1,000.00 $78,000.00 $4,000.00 -$55,000.00 $16,000.00 $29,000.00 $32,000.00 Project D $9,000.00 $6,000.00 $1,000.00 Discount Rate 10% 10% 15% 6% Project A Project B Project C Project D Payback Period PI NPV IRRI IRR2 (if it exists) $15,912.79 Note: For simplicity, we measure payback period in full years (unlike the textbook). Calculate the numbers for the empty cells for Projects A to D. Hint: For some projects, a second (positive) IRR may exist. For Project D, the payback period may be easier to express in words.

Problem 1) Take the difference between the payback period of Projects A and B, i.e., calculate: X = Payback Period of Project A - Payback Period of Project B.

Select one:

a)-3

b)-2

c)-1

d)0

e)1

f)2

g)3

h)Insufficient information

Problem 1) What is (are) the posiive IRR(s) of Project C?

Select one:

a)0%

b)100%

c)104.3% is one of the IRRs and another IRR exists

d)0% is one of the IRRs and another IRR exists

e)7.7% only

f)56.3% is one of the IRRs and another IRR exists

Project C has three IRR

No positive IRR exists for Project C

Problem 1) What is the IRR of Project B?

Select one:

a)10.00%

b)6.70%

c)20.00%

d)100.00%

e)19.78%

f)Project B has multiple IRRs

g)IRR doesn't exist

h)IRR is negative

Problem 1) What is the NPV of Project C?

Select one:

a)$0

b)$1,238

c)$1,078

d)$455

e)-$365

f)-$25,000

g)$55,000

The NPV cannot be calculated because the last cash flow is negative

Problem 1) What is the payback period of Project D?

Select one:

A)1

B)2

C)3

D)4

E)5

F)6

G)7

Project D never pays back the initial investment

Problem 1) What is the profitability index (PI) of Project A?

Select one:

a)1.36

b)1.60

c)2.36

d)10%

e)$1,000

f)-$40,000

g)$14,206

h)PI is negative

Answer 1

To complete the table we make the following calculations:

Project A

Year	CF	Discount Factor		Discounted CF
0	$ -40,000.00	1/(1+0.1)^0=	1	1*-40000=	-40,000.00
1	$   35,000.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*35000=	31,818.18
2	$   15,000.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*15000=	12,396.69
3	$     9,000.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*9000=	6,761.83
4	$     2,000.00	1/(1+0.1)^4=	0.683013455	0.683013455365071*2000=	1,366.03
5	$     3,000.00	1/(1+0.1)^5=	0.620921323	0.620921323059155*3000=	1,862.76
				NPV = Sum of all Discounted CF	14,205.50
				PI = 1+NPV/initial investment	1+14205.50/40000 = 1.36

IRR is the rate at which NPV = 0
IRR can be calculated using either a financial calculator or excel or through hit and trial:
Using Excel we get the IRR = 32.95% rounded to two decimal places

Year	CF	Discount Factor		Discounted CF
0	$ -40,000.00	1/(1+0.329589502635871)^0=	1	1*-40000=	-40,000.00
1	$   35,000.00	1/(1+0.329589502635871)^1=	0.752111835	0.75211183453053*35000=	26,323.91
2	$   15,000.00	1/(1+0.329589502635871)^2=	0.565672212	0.56567221164088*15000=	8,485.08
3	$     9,000.00	1/(1+0.329589502635871)^3=	0.425448765	0.425448764840164*9000=	3,829.04
4	$     2,000.00	1/(1+0.329589502635871)^4=	0.319985051	0.319985051022684*2000=	639.97
5	$     3,000.00	1/(1+0.329589502635871)^5=	0.240664544	0.240664543747016*3000=	721.99
				NPV = Sum of all Discounted CF	0.00

Payback period calculation:

Year	Opening Balance	CF	Closing Balance
0			$         40,000.00
1	$            40,000.00	$ 35,000.00	$            5,000.00
2	$              5,000.00	$ 15,000.00	$        -10,000.00

As we have to measure the payback period in full years, it will be 2 years because that is when the full initial investment of 40000

Project B:

Year	CF	Discount Factor		Discounted CF
0	$ -40,000.00	1/(1+0.1)^0=	1	1*-40000=	-40,000.00
1	$     1,000.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*1000=	909.09
2	$     4,000.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*4000=	3,305.79
3	$   16,000.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*16000=	12,021.04
4	$   29,000.00	1/(1+0.1)^4=	0.683013455	0.683013455365071*29000=	19,807.39
5	$   32,000.00	1/(1+0.1)^5=	0.620921323	0.620921323059155*32000=	19,869.48
				NPV = Sum of all Discounted CF	15,912.79
				PI	1+15912.79/40000 =1.40

Payback period:

Year	Opening Balance	Investment	CF	Closing Balance
0		$ 40,000.00		$         40,000.00
1	$            40,000.00		$   1,000.00	$         39,000.00
2	$            39,000.00		$   4,000.00	$         35,000.00
3	$            35,000.00		$ 16,000.00	$         19,000.00
4	$            19,000.00		$ 29,000.00	$        -10,000.00

IRR = 19.78% rounded to 2 decimal places

Year	CF	Discount Factor		Discounted CF
0	$ -40,000.00	1/(1+0.197801657787439)^0=	1	1*-40000=	-40,000.00
1	$     1,000.00	1/(1+0.197801657787439)^1=	0.834862762	0.834862761708967*1000=	834.86
2	$     4,000.00	1/(1+0.197801657787439)^2=	0.696995831	0.696995830888323*4000=	2,787.98
3	$   16,000.00	1/(1+0.197801657787439)^3=	0.581895864	0.581895864275061*16000=	9,310.33
4	$   29,000.00	1/(1+0.197801657787439)^4=	0.485803188	0.485803188275704*29000=	14,088.29
5	$   32,000.00	1/(1+0.197801657787439)^5=	0.405578991	0.405578991410875*32000=	12,978.53
				NPV = Sum of all Discounted CF	0.00

Project C:

Year	CF	Discount Factor		Discounted CF
0	$ -25,000.00	1/(1+0.15)^0=	1	1*-25000=	-25,000.00
1	$   78,000.00	1/(1+0.15)^1=	0.869565217	0.869565217391304*78000=	67,826.09
2	$ -55,000.00	1/(1+0.15)^2=	0.756143667	0.756143667296787*-55000=	-41,587.90
				NPV = Sum of all Discounted CF	1,238.19
				PI	$          1.05

As CFs have multiple sign changes, there will be multiple IRRs

IRR 1 = 7.67%

Year	CF	Discount Factor		Discounted CF
0	$ -25,000.00	1/(1+0.0766781545586726)^0=	1	1*-25000=	-25,000.00
1	$   78,000.00	1/(1+0.0766781545586726)^1=	0.92878266	0.92878265967038*78000=	72,445.05
2	$ -55,000.00	1/(1+0.0766781545586726)^2=	0.862637229	0.862637228904384*-55000=	-47,445.05
				NPV = Sum of all Discounted CF	-0.00

IRR 2 = 104.34%

Year	CF	Discount Factor		Discounted CF
0	$ -25,000.00	1/(1+1.0434)^0=	1	1*-25000=	-25,000.00
1	$   78,000.00	1/(1+1.0434)^1=	0.489380444	0.489380444357443*78000=	38,171.67
2	$ -55,000.00	1/(1+1.0434)^2=	0.239493219	0.239493219319489*-55000=	-13,172.13
				NPV = Sum of all Discounted CF	-

Payback period:

Year	Opening Balance	CF	Closing Balance
0			$         25,000.00
1	$            25,000.00	$   78,000.00	$        -53,000.00

Project D

Year	CF	Discount Factor		Discounted CF
0	$   -9,000.00	1/(1+0.06)^0=	1	1*-9000=	-9,000.00
1	$     6,000.00	1/(1+0.06)^1=	0.943396226	0.943396226415094*6000=	5,660.38
2	$     1,000.00	1/(1+0.06)^2=	0.88999644	0.88999644001424*1000=	890.00
				NPV = Sum of all Discounted CF	-2,449.63
				PI	0.73

As the sum of undiscounted CFs is less than initial investment, this project will not have a positive IRR

Measure	A	B	C	D
NPV	14,205.50	15,912.79	1238.19	-2449.63
PI	1.36	1.40	1.05	0.73
IRR	32.95%	19.78%	7.67%	NA
IRR2	NA	NA	104.34%	NA
Payback period	2 years	4 years	1 year	Investment is not recovered

Problem 1) X = 2-4 = -2 so correct option is b)

Problem 2) c)104.3% is one of the IRRs and another IRR exists

Problem 3) IRR of Project B is e)19.78%

Problem 4) NPV of Project C is b)$1,238

Problem 5) Project D never pays back the initial investment

Problem 6) Profitability index (PI) of Project A is a)1.36