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 $20 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 13%. a. What is the project's net present value? A negative value should be entered with a negative sign. Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places. million b. 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 $1.8 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 $4.2 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 $20 million. Assume that all cash flows are discounted at 13%. Use decision-tree analysis to determine whether Kim should proceed with the project today or wait a year before deciding. -Select-

Answer 1

1. Initial cost= $20 million

Expected cash flow = $3 million

Tenor = 20 years

Net Present Value = Total Cash Inflows PV from Investments – Cost of Investments

So we need to find the present value of the 20 years cash flow

Present Value of periodic payment= P* (1- (1+r)^-n)/r

P = 3 million

R= 13%

N= 20

PV= 3(1-(1+0.13)^-20)/ 0.13

= 3*0.913/0.13

= 21.074

So NPV= 21.074-20

= 1.07 million

2. In case of probability, we need to find the adjusted cash flow.

probability	cash flow	adjusted cash flow ( probability * cash flow)
0.5	1.8	0.90
0.5	4.2	2.10
	total	3.00

So the adjusted cash flow $3 million per year

Present Value of periodic payment= P* (1- (1+r)^-n)/r

P = 3 million

R= 13%

N= 19

PV= 3(1-(1+0.13)^-20)/ 0.13

= 3*0.913/0.13

= 21.074

But the value of PV is at the end of 1 yr , we need to find the PV of today

PV= Future Value / (1 + interest rate%)^n

PV= 21.074/(1.13)

= 18.65

So NPV= 18.65-20

= -1.35 million.

As we can see that if they wait for 1 yr the NPV turns negative.

So it is not a good decision to wait and they should invest toady.