Question

Lapos operates a chain of sandwich shops. The company is considering two possible expansion plans. Plan A would open 8 smaller shops at a cost of $8,400,000. Expected annual net cash inflows are $1,550,000 with 0 residual value at the end of 10 years. Under plan B, Lapos would open 3 shops at a cost of $ 8,250,000. This plan is expected to generate net cash inflows of $1,080,000 per year for 10 years, the estimated useful life of the properties. Estimated residual value for Plan B is $980,000.Lapos uses straight-line depreciation and requires an annual return of 8%.

1) Compute the ROR, the NPV, and the profitability index of these two plans. What are the strengths and weaknesses of these capital budgeting models?

2) Which expansion plan should lapos choose? Why?

3) Estimate Plan A's IRR. How does the IRR compare with the company's required rate of return?

Answer 1

Computation of NPV, ROR and Profitability Index:

We use 'Rate Table For the Present Value of an Ordinary Annuity of 1' and look for 8% under 10 years.

Option A.

Year	Cashflow	Discount Factor @8%	Discounted Cashflows
1-10	1550000	6.7101	10,400,655
		So, Present Value of Inflows	10,400,655
		Less: Initial Capital Outlay	8,400,000
		So, NPV	2,000,655

ROR = (Present Value of Inflows - Initial outlay) / Initial outlay *100

Ie., ROR = (10400655-8400000)/8400000*100 = 23.82%

Profitability Index = PV of Inflows/Initial Outlay

Ie., Profitability Index = 10400655/8400000 = 1.24

Option B.

Year	Cashflow	Discount Factor @8%	Discounted Cashflows
1-10	1080000	6.7101	7246908
10 (Residual Value)	980000	0.4632	453936
		PV of Cash Inflows	7700844
		Less: Initial Capital Outlay	8250000
		NPV	-549156

ROR => (7700844 - 8250000) / 8250000 * 100 = -6.65% (ie negative)

Profitability Index => 7700844/8250000 = 0.93

Strengths of using these capital budgeting models is that,

• We can realise if the outcome of the project yields positive results ie using NPV.
• Secondly, impact of present values of Inflows over that of outlay can help in decision making based on Profitability Index
• Facilitates comparison between different sets of alternatives.

The weakness of this type of model is that the decision is made on future set of numbers which may be influenced by several factors and hence a mere estimate and not accurate.

2. Hence since Plan A having higher NPV, higher Profitability Index and ROR should be chosen against Plan B.

3. IRR of Plan A: Given NPV is at 8%. Hence we chose 15% so that we get negative NPV in order to compute the value of IRR:

Year	Cashflow	Discount Factor @ 15%	Discounted Cashflows
1-10	1550000	5.0188	7779140
		Less: Initial Capital Outlay	8400000
		NPV	-620860

IRR = Lower discount Rate + ((NPV @ lower rate) / (NPV at lower rate - NPV at higher rate) * (higher rate - lower rate)

Ie. IRR = 8% + ((2000655) / (2000655 - (-620860)) * (15-8) => 13.04%.

The IRR is higher than the company’s required rate of return. Hence this yields positive NPV and Profitability scores. IRR works like a level above which the NPV goes negative with Profitability Index falling below 1. Hence IRR works as a cushion below which rates falling under yield positive NPV and profits for the given amount of data.