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 $18 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%.

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 $2.2 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 $3.8 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 $18 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.

Answer 1

Year	Calculation= (Cash inflow/ (1+ discount rate)^n)	Present Value Cash flow ( in million)
1	3/(1+0.13)^1	$2.655
2	$3/(1+0.13)^2	$2.349
3	$3/(1+0.13)^3	$2.079
4	$3/(1+0.13)^4	$1.839
5	$3/(1+0.13)^5	1.628
6	$3/(1+0.13)^6	1.441
7	$3/(1+0.13)^7	1.275
8	$3/(1+0.13)^8	1.128
9	$3/(1+0.13)^9	0.998
10	$3/(1+0.13)^10	0.883
11	$3/(1+0.13)^11	0.782
12	$3/(1+0.13)^12	0.692
13	$3/(1+0.13)^13	0.612
14	$3/(1+0.13)^14	0.542
15	$3/(1+0.13)^15	0.479
16	$3/(1+0.13)^16	0.424
17	$3/(1+0.13)^17	0.375
18	$3/(1+0.13)^18	0.332
19	$3/(1+0.13)^19	0.294
20	$3/(1+0.13)^20	0.260
	Total Cumulative Cashflow	$21.064
	Less: Investment	$18
	NPV	$3.064

Q2 there are two cases:

Ans:

Tax Imposed with Probability of 50%	Tax not Imposed
Year	Cash inflow/(1+discount rate)^n Cashflow = $2.2million Discount rate =13%	PV Cashflow	Cashflow/ (1+discount rate)^n Cashflow=$3.8million	PV Cashflow
1	$2.2/(1+0.13)^1	$1.947	$3.8/(1+0.13)^1	$3.363
2	$2.2/(1+0.13)^2	$1.723	$3.8/(1+0.13)^2	$2.976
3	$2.2/(1+0.13)^3	$1.525	$3.8/(1+0.13)^3	$2.634
4	$2.2/(1+0.13)^4	$1.349	$3.8/(1+0.13)^4	$2.331
5	$2.2/(1+0.13)^5	$1.194	$3.8/(1+0.13)^5	$2.062
6	$2.2/(1+0.13)^6	$1.057	$3.8/(1+0.13)^6	$1.825
7	$2.2/(1+0.13)^7	$0.935	$3.8/(1+0.13)^7	$1.615
8	$2.2/(1+0.13)^8	$0.828	$3.8/(1+0.13)^8	$1.429
9	$2.2/(1+0.13)^9	$0.732	$3.8/(1+0.13)^9	$1.265
10	$2.2/(1+0.13)^10	$0.648	$3.8/(1+0.13)^10	$1.119
11	$2.2/(1+0.13)^11	$0.574	$3.8/(1+0.13)^11	$0.991
12	$2.2/(1+0.13)^12	$0.449	$3.8/(1+0.13)^12	$0.877
13	$2.2/(1+0.13)^13	$0.397	$3.8/(1+0.13)^13	$0.776
14	$2.2/(1+0.13)^14	$0.352	$3.8/(1+0.13)^14	$0.687
15	$2.2/(1+0.13)^15	$0.311	$3.8/(1+0.13)^15	$0.608
16	$2.2./(1+0.13)^16	$0.275	$3.8/(1+0.13)^16	$0.538
17	$2.2/(1+0.13)^17	$0.244	$3.8/(1+0.13)^17	$0.476
18	$2.2/(1+0.13)^18	$0.216	$3.8/(1+0.13)^18	$0.421
19	$2.2/(1+0.13)^19	$0.191	$3.8/(1+0.13)^19	$0.373
20	$2.2/(1+0.13)^20	$0.397	$3.8/(1+0.13)^20	$0.330
	Cumulative Present Value Cashflow	$15.45		$26.697
	Less: Investment	$20		($20)
	NPV	($4.55)		$6.697
	Tax imposed NPV @ year 1	($4.55)/(1+0.13)^1 =($4.027)		$6.697/(1+0.13)^1 = $5.920

Decision Tree

New Hotel Project in Seoul	Imposed Tax with 50% probability	Investment	$20million
cash flow	$15.45
NPV	($15.45-$20)/(1+0.13)^1 =-$4.027
No Tax imposed with Probability 50%	investment	$20million
Cashflow	$26.697
NPV @ Year1	($26.697-$20)/(1+0.13)^1 =$5.920

Expected NPV = 0.50× $(-4.027)+ 0.50×$5.920

= 0.947

If the tax is imposed, the NPV of the Project is negative hence rejected

Option for waiting 1year

= 0.50×($0)+0.50×$5.920 = $2.96million

The NPV of waiting 1year ($2.96million) is greater than going today with NPV ($0.947million) hence waiting for 1year and then proceed is much wise decision.