You have just completed your undergraduate degree, and one of your favorite cour
ID: 2768061 • Letter: Y
Question
You have just completed your undergraduate degree, and one of your favorite courses was "Today's Entrepreneurs." In fact, you enjoyed it so much you have decided you want to "be your own boss." While you were in the program, your grandfather died and left you $300,000 to do with as you please. You are not an inventor, and you do not have a trade skill that you can market; however, you have decided that you would like to purchase at least one established franchise in the fast foods area, maybe two (if profitable). The problem is that you have never been one to stay with any project for too long, so you figure that your time frame is three years. After three years you will sell off your investment and go on to something else. You have narrowed your selection down to two choices; (1) Franchise L: Lisa's Soups, Salads, & Stuff and (2) Franchise S: Sam's Fabulous Fried Chicken. The net cash flows shown below include the price you would receive for selling the franchise in Year 3 and the forecast of how each franchise will do over the three-year period.
Franchise L's cash flows will start off slowly but will increase rather quickly as people become more health conscious, while Franchise S's cash flows will start off high but will trail off as other chicken competitors enter the marketplace and as people become more health conscious and avoid fried foods. Franchise L serves breakfast and lunch, while Franchise S serves only dinner, so it is possible for you to invest in both franchises. You see these franchises as perfect complements to one another: you could attract both the lunch and dinner crowds and the health conscious and not so health conscious crowds without the franchises' directly competing against one another. Here are the net cash flows (in thousands of dollars):
Expected
net cash flows
Year
Franchise S
Franchise L
0
($100)
($100)
1
70
10
2
50
60
3
20
80
Depreciation, salvage values, net working capital requirements, and tax effects are all included in these cash flows.
You also have made subjective risk assessments of each franchise, and concluded that both franchises have risk characteristics that require a return of 10 percent. You must now determine whether one or both of the projects should be accepted.
In order to do so please answer the following questions fully. Make sure to show a time line, the formula to be used, the steps taken to solve the problem (calculator or excel) and the final numerical answer when appropriate.
Questions:
Define the term net present value (NPV).
What is each franchise's NPV? Make sure to show the formula, steps and final answer.
Based on your answer which franchise would you select? Why?
Would your answer be different if the projects are independent or mutually exclusive? Why or why not?
Would the NPVs change, and therefore your answer, if the cost of capital changed? Why or why not?
Internal Rate of Return (IRR) – you may use a financial calculator or excel. (Worth 8 points)
What is the logic/idea behind the IRR method?
Calculate the IRR for each project. Make sure to show the formula, calculator or excel steps and final answer.
According to IRR, which franchise should be accepted if they are independent? Mutually exclusive? Why?
Would the franchises' IRRs change if the cost of capital changed? Why or why not?
Define the term modified IRR (MIRR).
Find the MIRRs for Franchise L and S. Make sure to show the formula, steps and final answer.
What are the MIRR's advantages and disadvantages vis-a-vis the regular IRR? What are the MIRR's advantages and disadvantages vis-a-vis the NPV?
What is the rationale for the payback method?
Calculate the payback period for each franchise. Make sure to show the formula, steps and final answer.
Calculate the discounted payback period for each franchise. Make sure to show the formula, steps and final answer.
According to the payback criterion, which franchise or franchises should be accepted if the firm's maximum acceptable payback is 2 years, and if Franchise L and S are independent? If they are mutually exclusive? Why?
What is the difference between the regular and discounted payback periods? Make sure to mention the advantage and disadvantage of each.
Based on the results obtained and everything that you have described above, which franchise would you ultimately choose if the projects are mutually exclusive? Explain in detail your decision and why you chose the model you did to make your final decision.
Expected
net cash flows
Year
Franchise S
Franchise L
0
($100)
($100)
1
70
10
2
50
60
3
20
80
Explanation / Answer
Net Present Value (NPV):
Net present value (NPV) of a project is the potential change in an investor's wealth caused by that project while time value of money is being accounted for. It equals the present value of net cash inflows generated by a project less the initial investment on the project. It is one of the most reliable measures used in capital budgeting because it accounts for time value of money by using discounted cash flows in the calculation.
NPV = Initial cash outflow + Periodical cash flows / (1+i) n
NPV of franchise S:
NPV = -$100 + $70 / (1+0.1) 1 + $50 / (1+0.1) 2 + $20 / (1+0.1) 3
NPV = $19.98
NPV of franchise L:
NPV = -$100 + $10 / (1+0.1) 1 + $60 / (1+0.1) 2 + $800 / (1+0.1) 3
NPV = $18.78
Since the NPV of Franchise S is more positive value than Franchise L, it is advisable to accept Franchise S.
Internal Rate of Return (IRR):
Internal rate of return (IRR) is the discount rate at which the net present value of an investment becomes zero. In other words, IRR is the discount rate which equates the present value of the future cash flows of an investment with the initial investment. It is one of the several measures used for investment appraisal.
IRR of franchise S:
$19.98 = -$100 + $70 / (1+i) 1 + $50 / (1+i) 2 + $20 / (1+i) 3
IRR = 24%
IRR of franchise L:
$18.78 = -$100 + $10 / (1+i) 1 + $60 / (1+i) 2 + $800 / (1+i) 3
IRR = 18%
Using excel formula IRR
Calculation of NPV of Franchise S
Year
Cash flow
PVF @ 10%
Discounted cash flow
0
-100
1
-100
1
70
0.909091
63.63636
2
50
0.826446
41.32231
3
20
0.751315
15.0263
NPV
19.98497
IRR
24%
Calculation of NPV of Franchise L
Year
Cash flow
PVF @ 10%
Discounted cash flow
0
-100
1
-100
1
10
0.909091
9.090909
2
60
0.826446
49.58678
3
80
0.751315
60.10518
NPV
18.78287
irr
18%
Since the IRR of franchise S is more when compared to franchise L, though both franchise are having IRR more than desired rate of 10%
Payback Period:
Payback period is the time in which the initial cash outflow of an investment is expected to be recovered from the cash inflows generated by the investment. It is one of the simplest investment appraisal techniques.
Payback Period = A + B / C
In the above formula,
A is the last period with a negative cumulative cash flow;
B is the absolute value of cumulative cash flow at the end of the period A;
C is the total cash flow during the period after A
Accept the project only if its payback period is LESS than the target payback period.
Calculation of Payback of Franchise S
Year
Cash flow
Cumulative Cash flow
0
-100
-100
1
70
-30
2
50
20
3
20
40
Payback period (1year + 30/50)
1.6
Calculation of NPV of Franchise L
Year
Cash flow
Cumulative Cash flow
0
-100
-100
1
10
-90
2
60
-30
3
80
50
Payback period (2year + 30/80)
2.375
Discounted Payback Period:
One of the major disadvantages of simple payback period is that it ignores the time value of money. To counter this limitation, an alternative procedure called discounted payback period may be followed, which accounts for time value of money by discounting the cash inflows of the project
Payback Period = A + B / C
In the above formula,
A is the last period with a negative cumulative cash flow;
B is the absolute value of cumulative cash flow at the end of the period A;
C is the total cash flow during the period after A
Accept the project only if it’s payback period is LESS than the target payback period.
Calculation of Discounted Payback of Franchise S
Year
Cash flow
PVF @ 10%
Discounted cash flow
Cumulative Cash flow
0
-100
1
-100
-100
1
70
0.909091
63.63636
-36.3636
2
50
0.826446
41.32231
4.958678
3
20
0.751315
15.0263
19.98497
Discounted payback period (1 year + 36.3636 / 41.32231)
1.88
Calculation of Discounted Payback of Franchise L
Year
Cash flow
PVF @ 10%
Discounted cash flow
Cumulative Cash flow
0
-100
1
-100
-100
1
10
0.909091
9.090909
-90.9091
2
60
0.826446
49.58678
-41.3223
3
80
0.751315
60.10518
18.78287
Discounted payback period (2 year + 41.3223 / 60.105
2.6875
Calculation of NPV of Franchise S
Year
Cash flow
PVF @ 10%
Discounted cash flow
0
-100
1
-100
1
70
0.909091
63.63636
2
50
0.826446
41.32231
3
20
0.751315
15.0263
NPV
19.98497
IRR
24%
Calculation of NPV of Franchise L
Year
Cash flow
PVF @ 10%
Discounted cash flow
0
-100
1
-100
1
10
0.909091
9.090909
2
60
0.826446
49.58678
3
80
0.751315
60.10518
NPV
18.78287
irr
18%
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