Question

You are advising an entrepreneur who is considering investing in a project that involves setting up a coffee shop and selling it at the end of the year. The project requires an initial investment of £800,000 today (at date 0) and is expected to generate a single cash flow at the end of the year (at date 1). The size of the cash flow at date 1 depends on the state of the economy, and the entrepreneur expects the cash flow at date 1 to be either £2 million or £1.5 million with equal probability. The cost of capital of the project is 10%, and the risk-free interest rate is 2%. Suppose the entrepreneur lives in a world with perfect capital markets.

i)Find the net present value for this project, and advise the entrepreneur whether (and why) she should invest in the project or not.

ii)Instead of investing her own funds to set up the coffee shop, the entrepreneur wonders whether she could simply sell the project to investors today (at date 0). What would be the market value of the project today (i.e., the market value of the unlevered equity of an all-equity firm at date 0)?

iii)As an alternative to financing the project entirely with equity, the entrepreneur is considering financing part of the initial investment using debt. Suppose she finances £400,000 using risk-free debt, and the remaining £400,000 using equity.

Show the cash flows at date 1 to the shareholders of the levered firm (i.e., the holders of the ‘levered equity’), and to the holders of the debt.

iv)Quantify the returns to shareholders of the all-equity financed project in part (b) and the returns to shareholders of the partly debt-financed project in part (c). How and why do these returns differ?

Please, type it, as it is hard to understand handwriting.

Answer 1

i)

Cash Outlay at Date 0	£          800,000.00
Cash Inflow at Date 1	£       1,750,000.00	(2,000,000*50%)+(1,500,000*50%)
Cash Inflow at Date 0	£       1,590,909.09	(1,750,000/1.1)
Net Cash Inflow at Date 0 or the Net Present Value	£          790,909.09
Cost of Capital	10%

ii) Instead of investing her own funds to set up the coffee shop, the entrepreneur wonders whether she could simply sell the project to investors today (at date 0). The market value of the project today (i.e., the market value of the unlevered equity of an all-equity firm at date 0) will be Initial Investment + NPV = 800,000 + 790,909 = 15,90,909

iv) The returns differ because the equity's cost is 10% and debt cost is only 2% there is savings of 8%(tax ignored) in levered return

Particulars	Amount	Cost	Prop	Weighted Cost
Equity	£          400,000.00	10%	0.5	5%
Debt	£          400,000.00	2%	0.5	1%
			Total	6%

Cash Outlay at Date 0	£          800,000.00
Cash Inflow at Date 1	£       1,750,000.00
Cash Inflow at Date 0	£       1,650,943.40
Net Cash Inflow at Date 0 or the Net Present Value	£          850,943.40