THUMBS UP WILL BE GIVEN IF ALL OF THE QUESTIONS ARE ANSWERED CORRECTLY AND ALL S
ID: 1170736 • Letter: T
Question
THUMBS UP WILL BE GIVEN IF ALL OF THE QUESTIONS ARE ANSWERED CORRECTLY AND ALL STEPS ARE SHOWN
James Polk Hospital has currently unused space in its lobby. In three years, the space will be required for a planned expansion, but the hospital is considering uses of the space until then. The hospital has decided that it wants to purchase at least one and maybe two fast food franchises, to take advantage of the high volume of patients and visitors that walk through the lobby all day long. The hospital plans to purchase the franchise(s), operate them for three years, and then close them down. The hospital has narrowed its selection down to two choices:
Franchise L: Lisa's Soups, Salads, and Stuff
Franchise S: Sam's Wonderful Fried Chicken
The net cash flows shown below include the costs of closing down the franchises in Year 3 and the forecast of how each franchise will do over the three-year period. Franchise L serves breakfast and lunch, while Franchise S serves only dinner, so it is possible for the hospital to invest in both franchises. The hospital believes these franchises are perfect complements to one another: The hospital could attract both the breakfast/lunch and dinner crowds and both the health-conscious and not-so-health-conscious crowds without the franchises directly competing against one another. The corporate cost of capital is 10 percent.
Net cash flows
Year
Franchise S
Franchise L
0
-$100
-$100
1
$70
$10
2
$50
$60
3
$20
$80
a. Calculate each franchise's payback period, net present value (NPV), internal rate of return (IRR), and modified internal rate of return (MIRR).
b. Graph the NPV of each franchise at different values of the corporate cost of capital from 0 to 24 percent in 2 percent increments.
- How sensitive are the franchise NPVs to the corporate cost of capital?
- Why do the franchise NPVs differ in their sensitivity to the corporate cost of capital?
- At what cost of capital does each franchise intersect the X-axis? What are these values?
c. Which project or projects should be accepted if they are independent? Which project should be accepted if they are mutually exclusive?
d. Suppose the hospital could sell off the equipment for each franchise at the end of any year. Use NPV to determine the optimal economic life of each franchise when the salvage values are as follows:
Salvage value
Year
Franchise S
Franchise L
0
$100
$100
1
$60
$70
2
$20
$30
3
$0
$0
Net cash flows
Year
Franchise S
Franchise L
0
-$100
-$100
1
$70
$10
2
$50
$60
3
$20
$80
Explanation / Answer
$19
With increase in cost of capital
capital the NPV for both franchise reduces the NPV of franchise S is more than than NPV of franchise at 2% cost of capital as cost of capital increases the NPV of Franchise S reduces as compared with franchise L
At cost of capital of 8% the NPV of both the franchise intersect at X axis.
If the projects are independent than both the projects can be accepted since both have positive NPV, if they are mutually exclusive than Fanchise S should be accepted since it has more NPV
Payback Period Year 0 1 2 3 Casflow Franchise S ($100) $70 $50 $20 Cumulative cashflow ($100) ($30) $20 $40 Casflow Franchise L ($100) $10 $60 $80 Cumulative cashflow ($100) ($90) ($30) $50 Payback period for Franchise S 1 yr + (30/50) 1.6 Yrs Payback period for Franchise L 2 yr + 30/80 2.375 Yrs Net Present Value Year Franchise S Present value at r=10 = cashinflow/(1.10^n) Franchise L Present value at r=10 = cashinflow/(1.10^n) 0 ($100) ($100) ($100) ($100) 1 $70 $63.64 $10 $9.09 2 $50 $41.32 $60 $49.59 3 $20 $15.03 $80 $60.11 Net Present Value $20$19
IRR If we assume IRR is 12% Year Discounted factor Franchise S Present value at r=10 = cashinflow/(1.10^n) Franchise L Present value at r=10 = cashinflow/(1.10^n) 0 ($100) ($100) ($100) ($100) 1 0.892857143 $70 $62.50 $10 $8.93 2 0.797193878 $50 $39.86 $60 $47.83 3 0.711780248 $20 $14.24 $80 $56.94 $17 $14 If we assume IRR is 14% Year Discounted factor Franchise S Present value at r=10 = cashinflow/(1.10^n) Franchise L Present value at r=10 = cashinflow/(1.10^n) 0 ($100) ($100) ($100) ($100) 1 0.877192982 $70 $61.40 $10 $8.77 2 0.769467528 $50 $38.47 $60 $46.17 3 0.674971516 $20 $13.50 $80 $54.00 $13 $9 If we assume IRR is 16% Year Discounted factor Franchise S Present value at r=10 = cashinflow/(1.10^n) Franchise L Present value at r=10 = cashinflow/(1.10^n) 0 ($100) ($100) ($100) ($100) 1 0.862068966 $70 $60.34 $10 $8.62 2 0.743162901 $50 $37.16 $60 $44.59 3 0.640657674 $20 $12.81 $80 $51.25 $10 $4 If we assume IRR is 18% Year Discounted factor Franchise S Present value at r=10 = cashinflow/(1.10^n) Franchise L Present value at r=10 = cashinflow/(1.10^n) 0 ($100) ($100) ($100) ($100) 1 0.847457627 $70 $59.32 $10 $8.47 2 0.71818443 $50 $35.91 $60 $43.09 3 0.608630873 $20 $12.17 $80 $48.69 $7 $0 In case of Franchise L, the IRR is 18% If we assume IRR is 20% To be ignored Year Discounted factor Franchise S Present value at r=10 = cashinflow/(1.10^n) Franchise L Present value at r=10 = cashinflow/(1.10^n) 0 ($100) ($100) ($100) ($100) 1 0.833333333 $70 $58.33 $10 $8.33 2 0.694444444 $50 $34.72 $60 $41.67 3 0.578703704 $20 $11.57 $80 $46.30 $5 ($4) If we assume IRR is 22% To be ignored Year Discounted factor Franchise S Present value at r=10 = cashinflow/(1.10^n) Franchise L Present value at r=10 = cashinflow/(1.10^n) 0 ($100) ($100) ($100) ($100) 1 0.819672131 $70 $57.38 $10 $8.20 2 0.671862403 $50 $33.59 $60 $40.31 3 0.550706887 $20 $11.01 $80 $44.06 $2 ($7) If we assume IRR is 23.50% To be ignored Year Discounted factor Franchise S Present value at r=10 = cashinflow/(1.10^n) Franchise L Present value at r=10 = cashinflow/(1.10^n) 0 ($100) ($100) ($100) ($100) 1 0.809716599 $70 $56.68 $10 $8.10 2 0.655640971 $50 $32.78 $60 $39.34 3 0.530883377 $20 $10.62 $80 $42.47 $0 ($10) The IRR for franchise L is 23.50% Modified Internal rate of return MIRR for Franchise L In case of MIRR the positive cashflow would be reinvested at the cost of capital of 10% IRR = 23.50% MIRR = Geometric mean of Terminal value of cash inflows/present value of cash outflow - 1 Terminal Value of cash inflow Year Franchise S Terminal Value Terminal Value 1 $70 $70*(1.1^1) 77 2 $50 $50*(1.1^2) 60.5 3 $20 $20*(1.1^3) 26.62 164.12 MIRR = ($164.12/$100)^1/3 - 1 Solving for above will give 17.96% MIRR for Franchise S Year Franchise L Terminal Value Terminal Value 1 $10 $10*(1.1^1) 11.00 2 $60 $60*(1.1^2) 72.60 3 $80 $80*(1.1^3) 106.48 190.08 MIRR = ($190.08/$100)^1/3 - 1With increase in cost of capital
In order to plot the NPV of franchises in the graph first we have to calculate NPV at different cost of capital Year Discounted factor @ 2% Discounted factor @ 4% Discounted factor @ 6% Discounted factor @ 8% Discounted factor @ 24% Franchise S Present value of Franchise S at r=2 Franchise L Present value of Franchise L at r=2 Present value of Franchise S at r=4 Present value of Franchise L at r=4 Present value of Franchise S at r=6 Present value of Franchise L at r=6 Present value of Franchise S at r=8 Present value of Franchise L at r=8 Present value of Franchise S at r=24 Present value of Franchise L at r=24 0 ($100) ($100) ($100) ($100) ($100) ($100) ($100) ($100) ($100) ($100) ($100) ($100) 1 0.98039 0.96154 0.94340 0.92593 0.80645 $70 $68.63 $10 $9.80 67.30769 9.615385 66.03774 9.433962 64.81481 9.259259 56.45161 8.064516 2 0.96117 0.92456 0.89000 0.85734 0.65036 $50 $48.06 $60 $57.67 46.22781 55.47337 44.49982 53.39979 42.86694 51.44033 32.51821 39.02185 3 0.94232 0.88900 0.83962 0.79383 0.52449 $20 $18.85 $80 $75.39 17.77993 71.11971 16.79239 67.16954 15.87664 63.50658 10.48975 41.95898 Net Present Value $36 $43 $31 $36 $27 $30 $24 $24 ($1) ($11) Cost of Capital(%) NPV of Franchise L NPV of Franchise S 2 $36 $43capital the NPV for both franchise reduces the NPV of franchise S is more than than NPV of franchise at 2% cost of capital as cost of capital increases the NPV of Franchise S reduces as compared with franchise L
At cost of capital of 8% the NPV of both the franchise intersect at X axis.
4 $31 $36If the projects are independent than both the projects can be accepted since both have positive NPV, if they are mutually exclusive than Fanchise S should be accepted since it has more NPV
If Franchise is sold at Yr 1 than NPV would be Year Fanchise S Present value Fanchise L Present value 0 ($100) ($100) ($100) ($100) 1 $130 $118.18 $80 $72.73 NPV $18 ($27) If Franchise is sold at Yr 2 than NPV would be Year Fanchise S Present value Fanchise L Present value 0 ($100) ($100) ($100) ($100) 1 $70 $63.64 $10 $9.09 2 $70 $57.85 $90 $74.38 NPV ($36) ($91) If Franchise is sold at Yr 3 than NPV would be Year Fanchise S Present value Fanchise L Present value 0 ($100) ($100) ($100) ($100) 1 $70 $63.64 $10 $9.09 2 $50 $41.32 $60 $49.59 3 $20 $15.03 $80 $60.11 NPV $20 $19 The econmic life of the franchise should be 3 yrs which give the effective NPV for both franchise 6 $27 $30 8 $24 $24 10 $20 $19 12 $17 $14 14 $13 $9 16 $10 $4 18 $7 $0 20 $5 ($4) 22 $2 ($7) 24 ($1) ($11)Related Questions
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