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Solution 14.13

Evaluate and comment on the above project using the following methods:

Net present value.
Internal rate of return.

The initial step in this question is to calculate the capital and operating cash flows. Regarding the capital cash flows the consultancy costs are irrelevant to the decision they have already being paid. All increases in working capital will be liquidated in the final year.
Regarding the operating cash flows depreciation is excluded or added back and the profit lost in other areas due to the decision to upgrade is a relevant cost and must be deducted in calculating the operating cash flows. The calculation of the operating cash flows are as follows.

(A) Cash flows / year	1	2	3	4	5
Sales revenue	1,800	1,900	2,100	2,250	2,350
Less: Variable costs	720	830	900	930	980
Cash contribution	1,080	1,070	1,200	1,320	1,370
Less: Hotel fixed overheads	790	810	825	835	850
Operating accounting profit	290	260	375	485	520
Add: Depreciation	650	650	650	650	650
Operating cash flows from hotel	940	910	1,025	1,135	1,170
Less: Other profits lost	-35	-40	-45	-45	-45
Relevant oper. cash flows	905	870	980	1,090	1,125

Opening working capital	90	95	105	113	118
(Incr)/decr in working capital	-90	-5	-10	-8	-5
Recovery of work cap end yr 5					118

Calculation of NPV

			NPV Method
Yr	Investment	(Incr)/Decr	Operating	Net	11%	Present Value
		working capital	Cash Flow	Cash Flow	Disc	Net Csh Flows
	€	€	€	€		€
0	-3,750	-90		-3,840	1.000	-3,840
1		-5	905	900	0.901	811
2		-10	870	860	0.812	698
3		-8	980	973	0.731	711
4		-5	1,090	1,085	0.659	715
5	500	118	1,125	1,743	0.593	1,034
	-3,250	0	4,970	1,720	NPV	129

Calculation of IRR
The NPV of the project is a positive value based on a discount factor of 11%. To calculate the IRR one must calculate a negative NPV using a higher discount factor.

	Calculation IRR
		13%	Present Value
Year	Net Cash Flow	Disc	Net Cash Flows

0	-3840	1.000	-3,840
1	900	0.885	796
2	860	0.783	674
3	973	0.693	674
4	1,085	0.613	665
5	1,743	0.543	946
		NPV	-85

The IRR is calculated as (11) + ( 129 x 2) = 12.2%
129 + 85

How sensitive is the project to the assumptions regarding selling prices and customer numbers?

This part of the question asks how sensitive the NPV of the project is to changes in selling price and sales volume. With regard to selling price if we calculate the present value of sales then we can assess how much sales must fall for the NPV to be zero.
In a similar way changes to sales volume will affect sales and variable costs. Thus we should calculate the prevent value of contribution and assess how much contribution must fall for the NPV to be zero.

(B)		Selling Prices					Sales Volume
Year	11%	Revenue	Present Value				Contribution	Present Value
	Disc		Revenue					Contribution
		€	€				€	€
1	0.901	1,800	1,622				1,080	973
2	0.812	1,900	1,542				1,070	868
3	0.731	2,100	1,536				1,200	877
4	0.659	2,250	1,482				1,320	870
5	0.593	2,350	1,395				1,370	813
		10,400	7,576				6,040	4,401
NPV of project			129					129
% decrease for before NPV zero				(129/7576)	1.7%	(129/4401)			2.9%

One can see that the NPV of the project is more sensitive to sales price than sales volume and that only a decrease in price of 1.7% will ensure the project does not give a positive NPV. Sales volume only needs to fall by 2.9% from its forecast level for the project not to have a positive NPV. Thus the project is very sensitive to changes in both selling price and sales volume and would be considered to have a high level of operating risk or gearing.

Advise whether or not the company should upgrade its fixed assets.

Overall the project give a positive NPV of €129,000 representing 3% of the initial outlay of €3,840,000. The project also offers an IRR of 12.2% compared to the cost of capital of 11%. These factors indicate acceptance of the project. However the viability of the project is very sensitive to the assumptions about selling prices and sales volume. A reduction in selling price of 1.7% would bring the NPV of the project down to zero. Customer numbers would only need to fall by 2.9% to bring the NPV of the project down to zero. In view of growing competition and overcapacity in the market at present this gives too little leeway and thus on balance the project should be rejected. However further investigation of forecast customer numbers prices and costs is desirable.