Question

An existing online book retailer is considering whether to open a brick and mortar bookshop. The project is assumed to last for four years. Projected revenues and costs from the online retailer’s existing operations in each of years 1-4 are £1m and £400k, respectively. It is however estimated that the opening of the bookshop would boost both revenues and costs by 50% in each of years 1-4. The bookshop launch requires an initial investment of £400k in year 0, none of which will be recovered at the end of the project. The bookshop’s operations require an inventory of £50k in year 0, £100k in year 1, £150k in year 2, and £200k in year 3. The inventory is expected to be entirely sold in year 4. Assume that both the project and the retailer are fully financed through equity and that the retailer’s shares have a beta equal to 2. The risk free rate is 4%, the market risk premium is 3% and there are no taxes.

a. Determine the net present value of the project.

b. Assume now that the project requires the conversion of an existing property, currently owned by the retailer and valued at £1m. If rented out, the property would generate a rental income of £100k in each of years 1-4. The market value of the property is expected to stay constant during the next 4 years. Determine the net present value of the project (if necessary, you can make assumptions on what the firm would do with the property – rent out/sell - if the project were not undertaken).

c. Suppose you were told that the online retailer had a debt to equity ratio equal to one. Assuming that the beta of debt is equal to zero and that the project is still 100% equity financed, what would be the appropriate discount rate for the project?

Answer 1

a)		0	1	2	3	4
	Increase in revenues		500000	500000	500000	500000
	Increase in costs		200000	200000	200000	200000
	Increase in NOPAT		300000	300000	300000	300000
	Capital expenditure	400000				0
	Increase in NWC	50000	50000	50000	50000	-200000
	FCF	-450000	250000	250000	250000	500000
	PVIF at 10% (4+2*3)	1	0.90909	0.82645	0.75131	0.68301
	PV at 10%	-450000	227273	206612	187829	341507
	NPV	513220
b)	Assumption: The property would be rented out.
	Increase in revenues		500000	500000	500000	500000
	Increase in costs		200000	200000	200000	200000
	Loss of rental income		100000	100000	100000	100000
	Increase in NOPAT		200000	200000	200000	200000
	Capital expenditure	400000				0
	Increase in NWC	50000	50000	50000	50000	-200000
	FCF	-450000	150000	150000	150000	400000
	PVIF at 10% (4+2*3)	1	0.90909	0.82645	0.75131	0.68301
	PV at 10%	-450000	136364	123967	112697	273205
	NPV	196233
c)	Discount rate = Levered beta = Unlevered Beta x (1 + ((1 – Tax Rate) x (Debt/Equity)))
	= 2+(1+0*1) = 10%. The discount rate is same, as the tax rate is NIL and D/E = 1