Question

You have just graduated from the MBA program of a large university, 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 master’s program, your grandfather died and left you $1.5 million 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 3 years. After 3 years you will 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 3-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 whereas 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):

Franchise L:

Year	Group 2
0	-300
1	30
2	200
3	240

Franchise S:

Year	Group 2
0	-300
1	210
2	150
3	30

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 12.5%. You must now determine whether one or both of the franchises should be accepted.

a.         (1) Define the term net present value (NPV). What is each franchise’s NPV?

(2) According to NPV, which franchise or franchises should be accepted if they are independent? Mutually exclusive?

(3) Would the NPVs change if the cost of capital changed to 10%?

b.         (1) Define the term internal rate of return (IRR). What is each franchise’s IRR?

(2) What is the logic behind the IRR method? According to IRR, which franchises should be accepted if they are independent? Mutually exclusive?

(3) Would the franchises’ IRRs change if the cost of capital changed to 10%?

c.         (1) Draw NPV profiles for Franchises L and S. At what discount rate do the profiles cross?

(2) Look at your NPV profile graph without referring to the actual NPVs and IRRs. Which franchise or franchises should be accepted if they are independent? Mutually exclusive? Explain. Are your answers correct at any cost of capital less than 23.6%?

d.         Define the term modified IRR (MIRR). Find the MIRRs for Franchises L and S.

e.         What does the profitability index (PI) measure? What are the PIs of Franchises S and L?

f.          (1) What is the payback period? Find the paybacks for Franchises L and S.

(2) According to the payback criterion, which franchise or franchises should be accepted if the firm’s maximum acceptable payback is 2 years and if Franchises L and S are independent? If they are mutually exclusive?

(3) What is the discounted payback periods for Franchise L and S?

g.         In an unrelated analysis, you have the opportunity to choose between the following two mutually exclusive projects, Project T (which lasts for 2 years) and Project F (which lasts for 4 years):

Expected Net Cash Flows:

Project T:

Year	Group 2
0	-250000
1	160,000
2	160,000

Project F:

Year	Group 2
0	-250,000
1	87,500
2	87,500
3	87,500
4	87,500

The projects provide a necessary service, so whichever one is selected is expected to be repeated into the foreseeable future. Both projects have a 10% cost of capital.

(1) What is each project’s initial NPV without replication?

(2) What is each project’s equivalent annual annuity?

(3) Apply the replacement chain approach to determine the projects’ extended NPVs. Which project should be chosen?

(4) Assume that the cost to replicate Project T in 2 years will increase by 5% due to inflation. How should the analysis be handled now, and which project should be chosen?

Answer 1

(a) Net Present Value is the present value of cash inflows over and above the present value of total investment. It is used to determine the financial viability of a project.

N. P. V. of Franchise L:

Year	Cash inflows	Present value interest factor at 12.5%	Present Values
1	30	1/(1+0.125)1 = 0.8889	30 * 0.8889 = 26.67
2	200	0.7901	158.02
3	240	0.7023	168.56

*Present Value Interest Factor of r% for n periods = 1/(1+r)ⁿ

N.P.V. = Present value of cash inflows - Initial investment

= (26.67 + 158.02 + 168.56) - 300

Therefore, N.P.V. of Franchise L = 53.25

N. P. V. of Franchise S:

Year	Cash inflows	Present value interest factor at 12.5%	Present Values
1	210	1/(1+0.125)1 = 0.8889	210 * 0.8889 = 186.67
2	150	0.7901	118.52
3	30	0.7023	21.07

N.P.V. = Present value of cash inflows - Initial investment

= (186.67 + 118.52 + 21.07) - 300

Therefore, N.P.V. of Franchise S = 26.26

• According to N.P.V., both franchises could be accepted as they both have positive net present values if they are independent.
• If both the franchises are mutually exclusive, then Franchise L shall be accepted as it has higher N.P.V.

If cost of capital came down to 10% then N.P.V. will change:

N. P. V. of Franchise L:

Year	Cash inflows	Present value interest factor at 10%	Present Values
1	30	1/(1+0.10)1 = 0.9091	30 * 0.9091 = 27.27
2	200	0.8264	165.28
3	240	0.7513	180.31

*Present Value Interest Factor of r% for n periods = 1/(1+r)ⁿ

N.P.V. = Present value of cash inflows - Initial investment

= (27.27 + 165.28 + 180.31) - 300

Therefore, N.P.V. of Franchise L = 72.86

N. P. V. of Franchise S:

Year	Cash inflows	Present value interest factor at 10%	Present Values
1	210	1/(1+0.10)1 = 0.9091	210 * 0.9091 = 190.91
2	150	0.8264	123.96
3	30	0.7513	22.54

N.P.V. = Present value of cash inflows - Initial investment

= (190.91 + 123.96 + 22.54) - 300

Therefore, N.P.V. of Franchise S = 37.41

(b) Internal rate of return is the return or discounting rate at which present value of cash inflows equals the present value of cash out flows of a project. This is usually found by trial and error method

I.R.R. of Franchise L:

Lets take 20% and 21% as discounting factors:

Year	Cash flows	Present value interest factor at 20%	Present values	Present value interest factor at 21%	Present values
1	30	0.8333	25	0.8264	24.79
2	200	0.6944	138.89	0.683	136.60
3	240	0.5787	138.89	0.5645	135.47
		Total	302.78		296.87

Internal rate of return = Lower rate + Proportionate rate

= 20% + [(302.78-300)/(302.78-296.87)]

Therefore, Internal rate of return = 20.47%

I.R.R. of Franchise S:

Lets take 19% and 20% as discounting factors:

Year	Cash flows	Present value interest factor at 19%	Present values	Present value interest factor at 20%	Present values
1	210	0.8403	176.47	0.8333	175
2	150	0.7062	105.92	0.6944	104.17
3	30	0.5934	17.80	0.5787	17.36
		Total	300.19		296.53

Internal rate of return = Lower rate + Proportionate rate

= 19% + [(300.19 - 300) / (300.19 - 296.53)]

Therefore, Internal rate of return = 20.05%

Logic behind internal rate of return is to determine the rate at which it covers its initial investment.

If the projects are independent of each other, then both projects shall be accepted as they are above the required rate of return of 12.5%.

If the projects are mutually exclusive, then project with higher I.R.R. shall be accepted i.e. Franchise L.