# Professor Ted Azarmi's Forum

### Author Topic: Homework 3  (Read 27121 times)

#### Ted Azarmi

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• Posts: 624
##### Homework 3
« on: November 14, 2009, 08:00:00 pm »
The Homework is attached.

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« Last Edit: December 27, 2009, 09:50:49 am by Ted Azarmi »

• Silver Member
• Posts: 5
##### Re: Homework 3
« Reply #1 on: December 03, 2009, 12:16:46 pm »
For IRR - I use Excel to solve.

1. Assume a project has normal cash flows (that is, the initial cash flow is negative, and all other cash flows are positive).  Which of the following statements is most correct?
answer: B All else equal, a project’s NPV increases as the cost of capital declines.
A project’s NPV is positive and increases as a result of decrease in cost of capital

4. As the director of capital budgeting for Denver Corporation, you are evaluating two mutually exclusive projects with the following net cash flows:

Yr   Cash Flow X   Cash Flow Y
0    -100,000       -100,000
1   50,000       10,000
2   40,000       30,000
3   30,000       40,000
4   10,000       60,000

If Denver’s cost of capital is 15 percent, which project would you choose?
NPV X    = -100,000 + (50,000/1.15) + (40,000/1.15²) + (30,000/1.15³) + (10,000/1.5^4)
= -50,803.31
NPV Y   = -100,000 + (10,000/1.15) + (30,000/1.15²) + (40,000/1.15³) + (60,000/1.5^4)
= -56,998.65

5. Two projects being considered are mutually exclusive and have the following projected cash flows: If the required rate of return on these projects is 10 percent, which would be chosen and why?
Answer: A. Project B because it has the higher NPV.

NPV A    = -50,000 + (15,625/1.10) + (15,625/1.10²) + (15,625/1.10³) + (15,625/1.10^4)
= -470.85
NPV B   = -50,000 + (0/1.10) + (0/1.10²) + (0/1.10³) + (99,500/1.10^4)
= -0.735
IRR A   = 9.56%
IRR B   = 18.77%

6. The capital budgeting director of Sparrow Corporation is evaluating a project that costs \$200,000, is expected to last for 10 years and produce after-tax cash flows, including depreciation, of \$44,503 per year.  If the firm’s cost of capital is 14 percent and its tax rate is 40 percent, what is the project’s IRR?

7. An insurance firm agrees to pay you \$3,310 at the end of 20 years if you pay premiums of \$100 per year at the end of each year for 20 years.  Find the internal rate of return to the nearest whole percentage point.

IRR=0+(-100/(1+IRR))+(-100/(1+IRR)^2 )+ … +((-100+3310)/(1+IRR)^20 )

8. A company is analyzing two mutually exclusive projects, S and L, whose cash flows are shown below:

Years        0      1   2   3
|      |   |   |

S      -1,100   1,000    350   50
L      -1,100   0   300   1,500

The company’s cost of capital is 12 percent, and it can obtain an unlimited amount of capital at that cost.  What is the regular IRR (not MIRR) of the better project, that is, the project that the company should choose if it wants to maximize its stock price?

NPV Project S= -1100+1000/(1+12%)^1 +350/(1+12%)^2 +50/(1+12%)^3 =107.46

NPV Project L= -1100+0/(1+12%)^1 +300/(1+12%)^2 +1500/(1+12%)^3 =206.83

IRR Project L=19.075%

9. 9   Your company is choosing between the following non-repeatable, equally risky, mutually exclusive projects with the cash flows shown below. Your cost of capital is 10 percent.  How much value will your firm sacrifice if it selects the project with the higher IRR?

Project S:     0         1         2         3
|         |         |         |
-1,000     500       500       500

Project L:     0         1         2         3         4         5
|         |         |         |         |         |
-2,000   668.76  668.76   668.76  668.76    668.76

IRR Project S = 23.375%
IRR Project L = 20.00%
We choose project S – IRR project S is higher than IRR project L
NPV Project S= -1000+500/((1+10%)^1)+500/(1+10%)^2 +500/(10+10%)^3 =243.43
NPV Project L= -2000+668.76/(1+10%)^1 +668.76/(1+10%)^2   668.76/(1+10%)^3   668.76/(1+10%)^4   668.76/(1+10%)^5 =535.13

How much value will your firm sacrifice if it selects the project with the higher IRR
= NPV Project S – NPV Project L
= 535.13 – 243.43 = 291.7

10.Green Grocers is deciding among two mutually exclusive projects.  The two projects have the following cash flows:

Project A              Project B
Year      Cash Flow      Cash Flow
0       -\$50,000       -\$30,000
1         10,000          6,000
2         15,000         12,000
3         40,000         18,000
4         20,000         12,000

The company’s weighted average cost of capital is 10 percent (WACC = 10%). What is the net present value (NPV) of the project with the highest internal rate of return (IRR)?

IRR Project A = 21.38%
IRR Project B = 19.28%
NPV Project A= -50000+10000/1.1+15000/〖1.1〗^2 +40000/〖1.1〗^3 +20000/〖1.1〗^4 =15,200.46

11.Projects X and Y have the following expected net cash flows:

Project X   Project Y
Year   Cash Flow   Cash Flow
0   -\$500,000   -\$500,000
1     250,000     350,000
2     250,000     350,000
3     250,000

Assume that both projects have a 10 percent cost of capital.  What is the net present value (NPV) of the project that has the highest IRR?

IRR Project A = 23.38%
IRR Project B = 25.69%
NPV Project B= -500,000+350,000/1.1+350,000/〖1.1〗^2 =107,438

12. Company C is considering two mutually exclusive projects, Project A and Project B.  The projects are equally risky and have the following cash flows:

Project A   Project B
Year   Cash Flow   Cash Flow
0     -\$300     -\$300
1       140       500
2       360       150
3       400       100

At what cost of capital would the two projects have the same net present value (NPV)?

X = Cost of capital
NPV Project A=NPV Project B
-300+ 140/(1+X)^1 +360/(1+X)^2 +400/(1+X)^3 = -300+ 500/(1+X)^1 +150/(1+X)^2 +100/(1+X)^3
-300+300+ 140/(1+X)^1 +360/(1+X)^2 +400/(1+X)^3 - 500/(1+X)^1 -150/(1+X)^2 -100/(1+X)^3   =0
-360/(1+X)^1 +210/(1+X)^2 +300/(1+X)^3 =0
Using Excel – X = 25%

#### yhayduch

• Sr. Member
• Posts: 4
##### Homework #3 Capital Budgeting and Investment Return Calculation
« Reply #2 on: January 20, 2010, 10:54:26 pm »
Question #1

The right answer is that all else equal, a project’s NPV increases as the cost of capital declines.
For instance: NPV = -100 + 50/1.15

Question #4

NPV: PV – Required Investment
co + (C1/1+r) + (C2/1+r)^2 + (C3/1+r)^3….

NPV Project X = -100000 + (50000/1.15) + (40000/1.15^2) + (30000/1,15^3) + (10000/1.15^4) = -832.97

NPV Project Y = -100000 + (10000/1.15) + (30000/1.15^2) + (40000/1.15^3) + (60000/1.15^4) = -8014,19

Answer a, Neither of the Projects

Question #5

NPV Project A = -50000 + (15625/1.1) + (15625/1.1^2) + (15625/1,1^3) + (15625/1.1^4) + (15625/1.1^5) = 9.231

NPV Project B = -50000 + 0 + 0 + 0 + 0 + (99500/1.1^5) = 11.781

Answer a, Project B because it has the higher NPV

Question #9

NPV Project S = - 1000 + (500/1.1) + (500/1.1^2) + (500/1,1^3) = 243.43

NPV Project L = - 2000 + (668.76/1.1) + (668.76/1.1^2) + (668.76/1.1^3) + (668.76/1.1^4) + (668.76/1.1^5) = 535.13

\$ 535.13 – \$ 243.43 = \$ 291.70

Question #11

NPV Project X = -500000 + (250000/1.1) + (250000/1.1^2) + (250000/1.1^3) = \$ 121,713.00

NPV Project Y = -500000 + (350000/1.1) + (350000/1.1^2) = \$ 107,438.02

Question #12

Get ∆ of cash flows
Get IRR = 25%
At 25% both projects will have the same NPV

#### mpeiris

• Silver Member
• Posts: 5
##### Re: Homework 3
« Reply #3 on: January 24, 2010, 01:00:01 am »
Capital Budgeting & Investment Return Calculation
Q1: Ranking Methods
A1: B | With the increase of the positive cash inflows the NPV decreases and therefore the cost of capital decreases. The IRR is not influenced by the cost of capital.

Q2:  Ranking Conflicts
A2: A

Q3: NPV Profiles
A3: B | Project A has larger cash flows in the later years

Q4: NPV
A4: A | Assume Project X and Y are mutually exclusive
Year   0   1   2   3   4
Cash Flow X   -\$100 000   50 000   40 000   30 000   10 000
Cash Flow Z   -\$100 000   10 000   30 000   40 000   60 000

Cost of Capital: i=15%
Project X: NPV= -\$100000 + (50000/1.15) + (40 000/1.15²) + (30 000/1.15³) + (10 000/1.154)
= - 100000+ 43478.26 + 30245.75 + 19725.45 + 5717.53 = -8330
Project Y: NPV=-\$100000+ (10 000/1.15) + (30 000/1.15²) + (40 000/1.15³) + (60 000/1.154)
= - 100000+ 8695.65+ 22684.31 + 26300.65+ 34305.19= -8014.20
Both NPV’s are negative; therefore neither project should be conducted

Q5: NPV
A5: A | Assume Project A and B are mutually exclusive
Same procedure as in question 4
Decide for the Project with the highest NPV, which in this case is Project B

Q6: IRR
A6: C | Tax Rate and Cost of Capital are not relevant.
Cash flows: -\$200 000 + \$44503…after 10 years..+\$44503
IRR?  NPV=0=-\$200 000 + \$44503/1.1 + \$44503/1.1²…after 10 years..+\$44503/1.110
Use financial calculator: 18%

Q7: IRR
A7: C | IRR=0+(-100/(1+IRR))+(-100/(1+IRR)² )+ … +((-100+3310)/(1+IRR)20 )
IRR=5%

Q8: IRR and mutually exclusive projects
A8: D | Assume the Projects S and L are mutually exclusive
Step 1: Calculate the NPV of both projects S and L
NPV Project S= -1100+1000/(1+12%)^1 +350/(1+12%)^2 +50/(1+12%)^3 =107.46

NPV Project L= -1100+0/(1+12%)^1 +300/(1+12%)^2 +1500/(1+12%)^3 =206.83
Choose L as it has the higher NPV. Calculate IRR.
IRR=19.075%

Q9: IRR and NPV
A9: B | Step 1:  calculate the IRR of Project S and L
IRR Project S = 23.375%
IRR Project L = 20.00%
Choose S because IRR is higher.
Step 2: Calculate the NPV of Project S and L
NPV Project S= -1000+500/((1+10%)^1)+500/(1+10%)^2 +500/(10+10%)^3 =243.43
NPV Project L= -2000+668.76/(1+10%)^1 +668.76/(1+10%)^2   668.76/(1+10%)^3   668.76/(1+10%)^4   668.76/(1+10%)^5 =535.13
NPV Project S – NPV Project L=243.43-535.13=291.7

Q10: NPV and IRR
A10: E | IRR Project A = 21.38%
IRR Project B = 19.28%
NPV Project A= -50000+10000/1.1+15000/1.1^2 +40000/1.1^3 +20000/1.1^4 =15,200.46

Q11: NPV and IRR
A11: D | IRR Project A = 23.38%  IRR Project B = 25.69%
NPV Project B= -500,000+350,000/1.1+350,000/1.1^2 =107,438

Q12: Crossover rates
A12: D |
Calculate ∆ of cash flows A and B
Year  Cash FlowA Cash FlowB A - B
0     -\$300     -\$300      \$0
1       140       500    -360
2       360       150     210
3       400       100     300
i = 25%

#### Anastasia Nerlikh

• Silver Member
• Posts: 5
##### Re: Homework 3
« Reply #4 on: January 24, 2010, 12:19:03 pm »
Q.4

Year   Cash Flow X   Cash Flow Y
0  -100,000      -100,000

1   50,000          10,000
2   40,000          30,000
3   30,000          40,000
4   10,000          60,000

Cost of capital is 15%

1.Solving for Project X:

0: -100000
1:50000/1.15=43,478.26
2:40000/1.15^2=30,245
3:3000/1.15^3=19,736,8
4:10000/1.15^4=5,717.55

NPV of X = 43,478.26+30,245+19,736,8+5,717.55-100000=-824.

2.Solving for Project Y:

0:-100000
1:10000/1.15=8,695.6
2:30000/1.15^2=22,684.3
3:4000/1.15^3=26,315.8
4:60000/1.15^4=34,305

NPV of Y=8,695.6+22,684.3+26,315.8+34,305-100000= -8000.

Answer a:neither project,since both of them have negative NPV.

Q.5

Year   Cash Flow A   Cash Flow B
0  -50,000         -50,000

1   15,625               0
2   15,625               0
3   15,625               0
4   15,625               0
5   15,625        99,500

Cost of capital 10%

1.Solving for A:
0:-50000
1:15,625/1.1=14,204.5
2:15,625/1.1^2=12,913.2
3:15,625/1.1^3=11,739.3
4:15,625/1.1^4=10,672.08
5:15,625/1.1^5=9,701.9

NPV of A=14,204.5+12,913.2+11,739.3+10,672.08+9,701.9-50000=9,230.9

2.Solving for Project B:

0:-50000
1:0
2:0
3:0
4:0
5:99,500/1.1^5=61,781

NPV of B=61,781-50000=11,781

11,781>9,701.9

Answer a:we choose Project B,because its NPV is higher than of Project A.

• Sr. Member
• Posts: 4
##### Re: Homework 3
« Reply #5 on: January 24, 2010, 02:41:15 pm »
4.

Year       CF X             CF Y
0 -100,000        -100,000
1   50,000          10,000
2   40,000          30,000
3   30,000          40,000
4   10,000          60,000

Project X: NPV= -\$1000,00 + (50,000/1.15) + (40,000/1.15^2) + (30,000/1.15^3) + (10,000/1.15^4)= -832.97
Project Y: NPV= -\$100,000  + (10,000/1.15) + (30,000/1.15^2) + (40,000/1.15^3) + (60,000/1.15^4)= -8014.20

a. Neither of the projects, as both have a negative NPV!

5.

NPV A = -50,000 + (15,625/1.1) + (15,625/1.1^2) + (15,625/1,1^3) + (15,625/1.1^4) + (15,625/1.1^5) = 9,231.04

NPV B = -50,000 + 0 + 0 + 0 + 0 + (99,500/1.1^5) = 11,781.67

ANSWER: a.Project B, because it has the higher NPV.

6. 0 = -20,000 + (44,503/(1+r)^1 (...) 44,503/(1+r)^10
Solved with Excel: IRR = 18%

7. 0 = (-100/(1+IRR)^1 (...) + (-100+3,310)/(1+IRR)^20
Solved with Excel: IRR = 5%

9.
NPV S = - 1000 + (500/1.1) + (500/1.1^2) + (500/1,1^3) = 243.43

NPV L = - 2000 + (668.76/1.1) + (668.76/1.1^2) + (668.76/1.1^3) + (668.76/1.1^4) + (668.76/1.1^5) = 535.13

535.13 – 243.43 = \$ 291.70, answer b.

10.
Calculate IRR with Excel:
IRR: Project A = 21.38%
IRR: Project B = 19.28%
NPV: Project A= -50000+10000/1.1+15000/(1.1)^2 +40000/(1.1)^3 +20000/(1.1)^4 =15,200.46

11.

Calculate IRR with Excel:
IRR: Project A = 23.38%
IRR: Project B = 25.69%
NPV Project B= -500,000 + 350,000/1.1+350,000/(1.1)^2 = 107,438

12.

CF A - CF B to get the following CFs: 0 ; -360; 210; 300
Using Excel to calculate IRR of these CFs: At 25% both projects have the same NPV

#### gieremie

• Member
• Posts: 2
##### Re: Homework 3
« Reply #6 on: January 24, 2010, 10:53:49 pm »
4. As the director of capital budgeting for Denver Corporation, you are evaluating two mutually
exclusive projects with the following net cash flows: If Denver’s cost of capital is 15 percent, which project would you choose?
Project X       Project Z
Year     Cash Flow     Cash Flow
0       -\$100,000     -\$100,000
1          50,000        10,000
2          40,000        30,000
3          30,000        40,000
4          10,000        60,000

NPV: Co + (C1/1+r) + (C2/1+r)^2 + (C3/1+r)^3+(Cn/1+r)^n

NPV Project X = -100000 + (50000/1.15) + (40000/1.15^2) + (30000/1,15^3) + (10000/1.15^4) = - \$832.97

NPV Project Y = -100000 + (10000/1.15) + (30000/1.15^2) + (40000/1.15^3) + (60000/1.15^4) = -\$8014.19

The correct answer is A. (any of the projects can be taken).
5. Two projects being considered are mutually exclusive and have the following projected cash flows:
Project A       Project B
Year     Cash Flow     Cash Flow
0              -\$50,000      -\$50,000
1            15,625             0
2            15,625             0
3            15,625             0
4            15,625             0
5            15,625        99,500

If the required rate of return on these projects is 10 percent, which would be chosen and why?
NPV: Co + (C1/1+r) + (C2/1+r)^2 + (C3/1+r)^3+(Cn/1+r)^n
NPV Project A = -50000 + (15625/1.1) + (15625/1.1^2) + (15625/1,1^3) + (15625/1.1^4) + (15625/1.1^5) = 9.231
NPV Project B = -50000 + 0 + 0 + 0 + 0 + (99500/1.1^5) = 11.781

The correct answer is A, Project B, with a higher NPV.
8. There are two projects Project s and Project L with follow cash flows.
Project S       Project L
Year     Cash Flow     Cash Flow
0          -\$1100             -\$1100
1            1000                 0
2            350                   300
3            50                    1500
We have to select the project with highest positive NPV
Opportunity Cost of Capital is: r=12%
So, NPV Project S = -1100 + (1000/1.12) + (350/1.12^2) + (50/1,12^3) = 107.46
NPV Project L = -1100 + 0 + (300/1.12^2) + (1500/1.12^3) = 206.83
We have to select project L, because NPV is higher 107.46<206.83
And IRR we calculate with financial calculator or Excel and have 19 %.

#### bbulir

• Silver Member
• Posts: 5
##### Re: Homework 3
« Reply #7 on: January 28, 2010, 04:53:28 pm »
1)   Ranking methods
The NPV of a project increases as the cost of capital declines. The IRR is not influenced by the cost of capital.

2)   Ranking conflicts

The NPV method accepts all investments with a NPV>0, while the IRR method indicates reinvestment at IRR=0.

3)   NPV profiles

Project A has larger cash flows in the later years, due to lower interest rates and higher NPV.

4)   NPV Denver Corporation

Project X: NPV= -1000,000\$ + (50,000/1.15) + (40,000/1.152) + (30,000/1.153) +
(10,000/1.154)= -832.97\$

Project Y: NPV= -100,000\$  + (10,000/1.15) + (30,000/1.152) + (40,000/1.153) +
(60,000/1.154)= -8014.20\$

As both NPV’s  are negative, none of the projects  should be conducted by Denver Corp.

5)   NPV
See 4) for procedure
Project A = -50,000 + (15,625/1.1) + (15,625/1.12) + (15,625/1,13) + (15,625/1.14) + (15,625/1.15) = 9,231.04\$

Project B = -50,000 + (99,500/1.15) = 11,781.67

As Project B’s NPV is above Project A’s, the company will launch Project B.

6)   IRR

NPV=0
0 = -200,000 + (44,503/(1+r)...after  10 years…+ 44,503/(1+r)10
Solved with Excel: IRR = 18%

7)   IRR
NPV=0
0 = (-100/(1+IRR))+(-100/(1+IRR)² )+... + (-100+3,310)/(1+IRR)20
Solved with Excel: IRR = 5%

IRR and mutually exclusive projects S and L

NPV Project S= -1100+1000/(1+12%) +350/(1+12%)2 +50/(1+12%)3 =107.46\$

NPV Project L= -1100+0/(1+12%) +300/(1+12%)2 +1500/(1+12%)3 =206.83\$

Because Project L has the higher NPV, the company will launch it. IRR=19.075%

9)   NPV and IRR

NPV S = - 1000 + (500/1.1) + (500/1.12) + (500/1,13) = 243.43\$

NPV L = - 2000 + (668.76/1.1) + (668.76/1.12) + (668.76/1.13) + (668.76/1.14) + (668.76/1.15) = 535.13\$

535.13 – 243.43 = 291.70\$, as the amount of money, that the company would sacrifice, deciding on basis of IRR.

10)   NPV and IRR

Project B IRR: = 19.28%
Project A IRR: = 21.38%
Project A NPV: = -50000+10000/1.1+15000/(1.1)2 +40000/(1.1)3 +20000/(1.1)4 = 15,200\$

11)   NPV and IRR

Project X IRR: = 23.38%
Project Y IRR: = 25.69%
Project Y NPV: = -500,000 + 350,000/1.1+350,000/(1.1)2 = 107,438\$

12)   Crossover Rate

Calculating CF-∆ of Projects A and B
Year  CF A    CF B  ∆ A - B
0     -300        -300        0
1       140             500 -360
2       360            150  210
3       400            100  300
IRR = 25%
At 25% Cost of Capital, both projects will have the same NPV.