Question

. The following situation will be used in questions 3, 4 and 5. A hotel is projected to have $ 55 mi in total revenues during the following year. Total expenses are projected to be $ 40 mi. 3% of the total revenue is allocated as capital reserves. In the next four years, the annual growth rates in total revenues and total expenses will be (2%, 3%, 4%, 3%) and (4%, 7%, 4%, 3%) respectively. In the following years, revenues and total expenses will stabilize at a constant rate of 2.5%. The market discount rate on such assets is estimated at 9%. Going out cap rate is 7.5%. Cost of sales is usually 3%. Assume no additional costs (brokerage etc.) at the time of the purchase. Your investment horizon is 5 years. What is the estimated hotel value today? a) $ 154,961,520 b) $ 224,901,389 c) $ 162,515,008 d) $ 48,477,484 On the basis of the data provided at question 3, what is your expected IRR if you invest $ 150 mi in this hotel today?

a) 11.02%

b) -16.96%

c) 9.83%

d) -23.89%

Answer 1

Solution

The answer to the first part is d i.e. $48,477,484.

The working is given in the below table (figures in million dollars):

Year --->	Formula	1	2	3	4	5	6	7	…….
Growth rate (Revenue)			1.02	1.03	1.04	1.03	1.025	1.025	…….
Revenue	Prev year rev * Growth rate	55.00	56.10	57.78	60.09	61.90	63.44	65.03	…….
Growth rate (Expenses)			1.04	1.07	1.04	1.03	1.025	1.025	…….
Expenses	Prev year exp * Growth rate	(40.00)	(41.60)	(44.51)	(46.29)	(47.68)	(48.87)	(50.10)	…….
Net income	Revenue - Expenses	15.00	14.50	13.27	13.80	14.22	14.57	14.94	…….
Cost of sales (% of revenue)	Revenue*3%	(1.65)	(1.68)	(1.73)	(1.80)	(1.86)	(1.90)	(1.95)	…….
Net income (after selling cost)	Net income - Cost of sales	13.35	12.82	11.54	12.00	12.36	12.67	12.98	…….
Discount rate	1.09n where n is the year	1.0900	1.1881	1.2950	1.4116	1.5386	1.6771	1.8280	…….
Present Value	Net income / Discount rate	12.25	10.79	8.91	8.50	8.03	NA	NA	NA
Total Present value of first 5 years						48.48

For the second part we need to find out the IRR or what rate increases the Present Value to the investment $150 million. This cannot be higher than 9% as any IRR higher than 9% will bring the NPV to below $48.48 Thus options a and c is ruled out and we will only focus on the other two ones b and d.

Applying these discount rates to the cash flows for the 5 years we get

Year --->	Formula	1	2	3	4	5
At -16.96% discount rates are	=(1-0.1696)^n	0.8304	0.6896	0.5726	0.4755	0.3949
Present Value	Net income / Discount rate	16.08	18.59	20.15	25.23	31.30
Total Present values of the 5 years						111.35
At -23.89% discount rates are	=(1-0.2389)^n	0.7611	0.5793	0.4409	0.3356	0.2554
Present Value	Net income / Discount rate	17.54	22.13	26.17	35.76	48.39
Total Present values of the 5 years						149.99

Thus the IRR for an investment of $150 million is option d or -23.89% as we can see above that it discounts the cash flows to $149.99 approx.