Question

1. 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 $23 million. Kim expects the hotel will produce positive cash flows of $3.68 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? Negative value, if any, should be indicated by a minus sign. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answer to two decimal places.
$     million

b) Kim expects the cash flows to be $3.68 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 $2.3 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 $5.06 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 $23 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-It makes sense to proceed with the project today OR It makes sense to wait a year before deciding.

2. Investment Timing Option: Option 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%.

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 $20 million. Assume that all cash flows are discounted at 13%. Use the Black-Scholes model to estimate the value of the option. Assume that the variance of the project's rate of return is 0.0687 and that the risk-free rate is 5%. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answer to three decimal places.

Use computer software packages, such as Minitab or Excel, to solve this problem.

$   million

{I tried looking at other similar problems on here and replacing them with my numbers but i keep getting the wrong answer. Please help.}

Answer 1

Answer to question 1.

Facts

Initial Investment = - $23 mn

Expected Annual Cash-flow = $3.68 mn (end of each year)

Tenure = 20 years

Project’s cost of capital = 13%

Answer (a).

Project’s Net Present Value

Net present value of a project is the present value of the future cash flows discounted at a specified rate adjusted with initial investment.

Present Value of all the annual cash flows (assuming the salvage value is 0)

Excel formula “=PV(13%,20,3.68,0)” Answer is “$25.8510858073 mn”

(Note: You can also individually discount the cash flows and add them up)

So, Net Present Value = Present value of future cash flows – Initial investment

NPV = 25.8510858073 – 23

NPV = $2.85 mn

Answer (b).

Case 1: Kim waits for a year and Tax is imposed

Annual cash flow = $2.3 mn

Tenure = 19 years

Initial investment (Same)

Excel Formula: “=PV(13%,19,2.3,0)” Answer is “$15.9573 mn”

Net Present Value = Present value of future cash flows – Initial investment

NPV = 15.9573 – 23

NPV = - 7.0246 mn $

Case 2: Kim waits and Tax is not imposed

Annual cash flow = $5.06 mn

Tenure = 19 years

Initial investment (Same)

Excel Formula: “=PV(13%,19,5.06,0)” Answer is “$35.1061 mn”

Net Present Value = Present value of future cash flows – Initial investment

NPV = 35.1061 – 23

NPV = 12.1061 mn $

Present value (today) for the Case where Kim waits for a year would be:

{(0.5*Case 1) + (0.5*Case2)}/(1.13)

= ((0.5*-7.0246)+(0.5*12.1061))/1.13

= $2.2484 mn

(Note the value is T=1 and we need to discount it thus we divide it by 1.13)

Thus if Kim does not wait, the expected NPV is $2.85 and if he waits then the expected NPV is $2.2484 mn. So after the decision tree analysis, Kim should not wait and It makes sense to proceed with the project today.

Answer to Question 2

For pricing an option in Black scholes model we need to have 5 parameters:

Current price (S)

Exercise price (E)

Variance (v)

Risk free rate (rf)

Time (t)

Computation of Current price in BSM (S)

Expected Annual Cash-flow = $3 mn (end of each year)

Tenure = 20 years

Project’s cost of capital = 13%

Project’s Net Present Value

Present Value of all the annual cash flows (assuming the salvage value is 0)

Excel formula “=PV(13%,20,3,0)” Answer is “$20.81390785 mn” (This is the Current price in the input of BSM model)

Strike price (E) is the cost of starting the project (which is fixed and doesn’t change) = $20 mn

Variance is 6.87% (given)

Time is 1 year (Till when we have the option to start a project)

Rf is 5% (given)

Now putting these inputs in the BSM model in Excel we get the price of the call option as $1.85 mn

(Note: There are open source BSM calculators available for excel, when you give these parameters, you’ll get the above answer)