Question

 

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

Answer 1

a.	Calculation of payback period
	Franchise S
	Year	Cash Inflow	Cumulative cash inflow
	1	70	70
	2	50	120
	3	20	140
		Payback period = Years before full recovery + (unrecovered cost / cash flow duriung the year)
			= 1 + (100-70 / 50)
			1.6
	Franchise L
	Year	Cash Inflow	Cumulative cash inflow
	1	10	10
	2	60	70
	3	80	150
		Payback period = Years before full recovery + (unrecovered cost / cash flow duriung the year)
			= 2 + (100-70 / 80)
			2.375
	Calculation of Net Present Value (NPV)
	Franchise S
	Year	Cash Inflow	PVF @ 10%	PV
	1	70	0.909	63.63636
	2	50	0.826	41.32231
	3	20	0.751	15.0263
		Present Value of cash inflow		119.985
		Less: Cash outflow		-100
				19.98497
	Franchise L
	Year	Cash Inflow	PVF @ 10%	PV
	1	10	0.909	9.090909
	2	60	0.826	49.58678
	3	80	0.751	60.10518
		Present Value of cash inflow		118.7829
		Less: Cash outflow		-100
				18.78287
	Calculation of IRR
	Franchise S
	Let r = 10%
	Year	Cash Inflow	PVF @ 10%	PV
	1	70	0.909	63.63636
	2	50	0.826	41.32231
	3	20	0.751	15.0263
		Present Value of cash inflow		119.985
		Less: Cash outflow		-100
				19.98497
	Let r = 30%
	Year	Cash Inflow	PVF @ 30%	PV
	1	70	0.769	53.84615
	2	50	0.592	29.5858
	3	20	0.455	9.103323
		Present Value of cash inflow		92.53528
		Less: Cash outflow		-100
				-7.46472
	IRR = L + (NPV (L) / NPV (l) - NPV (h)) * (H-L)
	24.5611609
	Franchise L
	Let r = 10%
	Year	Cash Inflow	PVF @ 10%	PV
	1	10	0.909	9.090909
	2	60	0.826	49.58678
	3	80	0.751	60.10518
		Present Value of cash inflow		118.7829
		Less: Cash outflow		-100
				18.78287
	Let r = 30%
	Year	Cash Inflow	PVF @ 30%	PV
	1	10	0.769	7.692308
	2	60	0.592	35.50296
	3	80	0.455	36.41329
		Present Value of cash inflow		79.60856
		Less: Cash outflow		-100
				-20.3914
	IRR = L + (NPV (L) / NPV (l) - NPV (h)) * (H-L)
	19.58938071
	Calculation of MIRR
	Franchise S
	70 * 1.1*1.1		Year 1 cashflows re invested for 2 years
	84.7
	50*1.1		Year 2 cashflows re invested for 1 year
	55
	20		Year 3 cashflows cannot be re invested
	Total = 84.7+55+20
	Terminal value = 159.7
	MIRR = (159.7/100)cube root - 1
	1.168
	Franchise L
	10 * 1.1*1.1		Year 1 cashflows re invested for 2 years
	12.1
	60*1.1		Year 2 cashflows re invested for 1 year
	66
	80		Year 3 cashflows cannot be re invested
	Total = 12.1+66+80
	Terminal value = 158.1
	MIRR = (158.1/100)cube root - 1
	1.165