Question

Investment Timing Option: Decision-Tree Analysis

Kim Hotels is interested in developing a new hotel in Seoul. The company estimates that the hotel would require an initial investment of $17 million. Kim expects the hotel will produce positive cash flows of $3 million a year at the end of each of the next 20 years. The project's cost of capital is 14%.

1. What is the project's net present value? Do not round intermediate calculations. Enter your answer in millions. For example, an answer of $1.23 million should be entered as 1.23, not 1,230,000. Round your answer to two decimal places.

   $    million

2. Kim expects the cash flows to be $3 million a year, but it recognizes that the cash flows could actually be much higher or lower, depending on whether the Korean government imposes a large hotel tax. One year from now, Kim will know whether the tax will be imposed. There is a 50% chance that the tax will be imposed, in which case the yearly cash flows will be only $2.1 million. At the same time, there is a 50% chance that the tax will not be imposed, in which case the yearly cash flows will be $3.9 million. Kim is deciding whether to proceed with the hotel today or to wait a year to find out whether the tax will be imposed. If Kim waits a year, the initial investment will remain at $17 million. Assume that all cash flows are discounted at 14%. Use decision-tree analysis to determine whether Kim should proceed with the project today or wait a year before deciding.

Answer 1

a) Initial investment = $17m; n = 20 years; Cash flow (C) = $3m; r = .14

Present value = (C*(1-(1/(1+r)^n))/r

Present value = (3*(1-1/1.14^20))/.14

Present value = $19.87m

Initial investment = $17m

Hence, NPV = -17+19.87 = $2.87m

b) Both the scenarios have 50% probability of happening.

Case I: Using the similar formula in case 1 with cashflows (C) of $2.1m per year

Present value = $13.91m

NPV 1 = -17+13.91 = -$3.09m

Case II: Using the similar formula in case 2 with cashflows (C) of $3.9m per year

Present value = $25.83m

NPV 2 = -17+25.83 = $8.83m

Since, both these cases have 50% probability of happening, in case of uncertainty, NPV will be:

NPV = 0.5*NPV1 + 0.5*NPV2

NPV = 0.5*(-3.09) + 0.5*8.83

NPV = $2.87m

Hence, NPV in both the scenarios with certainty as well uncertainty are same which suggest that Kim should not wait for a year and shall proceed with the project today.