Question

1. Investment Timing Option: Decision-Tree Analysis

The Karns Oil Company is deciding whether to drill for oil on a tract of land that the company owns. The company estimates the project would cost $5 million today. Karns estimates that, once drilled, the oil will generate positive net cash flows of $2.5 million a year at the end of each of the next 4 years. Although the company is fairly confident about its cash flow forecast, in 2 years it will have more information about the local geology and about the price of oil. Karns estimates that if it waits 2 years then the project would cost $7.5 million. Moreover, if it waits 2 years, then there is a 90% chance that the net cash flows would be $2.65 million a year for 4 years and a 10% chance that they would be $1.35 million a year for 4 years. Assume all cash flows are discounted at 10%.

a) If the company chooses to drill today, 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) Using decision-tree analysis, does it make sense to wait 2 years before deciding whether to drill?
-Select-Yes, it makes sense to wait two years to drill. OR No, it makes sense to drill today.Item 2

2. Investment Timing Option: Option Analysis

The Karns Oil Company is deciding whether to drill for oil on a tract of land that the company owns. The company estimates the project would cost $8 million today. Karns estimates that, once drilled, the oil will generate positive net cash flows of $4 million a year at the end of each of the next 4 years. Although the company is fairly confident about its cash flow forecast, in 2 years it will have more information about the local geology and about the price of oil. Karns estimates that if it waits 2 years then the project would cost $9 million. Moreover, if it waits 2 years, then there is a 90% chance that the net cash flows would be $4.2 million a year for 4 years and a 10% chance that they would be $2.2 million a year for 4 years. Assume all cash flows are discounted at 10%. Use the Black-Scholes model to estimate the value of the option. Assume the variance of the project's rate of return is 0.111 and that the risk-free rate is 5%. Do not round intermediate calculations. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Round your answer to three decimal places.

$   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

1)

Project life: 4 Years

Discounted Rate : 10%

Initial outlay = $5 million

Net cash inflows = $2.5 million

a)

Year	Cash flows	PV of cash flows (in $ million)
1	2.5/(1+0.1)^1	2.27
2	2.5/(1+0.1)^2	2.07
3	2.5/(1+0.1)^3	1.88
4	2.5/(1+0.1)^4	1.71
	Total	7.92

NPV = -5.00 + 7.92 = $2.92 millions

b)

10% Probability (Low)
Year	Cash flows	PV of cash flows (in $ million)
1	1.35/(1+0.1)^1	1.23
2	1.35/(1+0.1)^2	1.12
3	1.35/(1+0.1)^3	1.01
4	1.35/(1+0.1)^4	0.92
	Total	4.28

90% Probability (High)
Year	Cash flows	PV of cash flows (in $ million)
1	2.65/(1+0.1)^1	2.41
2	2.65/(1+0.1)^2	2.19
3	2.65/(1+0.1)^3	1.99
4	2.65/(1+0.1)^4	1.81
	Total	8.40

10% Probability Cash Flows Scenario = (-5.00+4,28) = -$0.72 million

90% Probability Cash Flows Scenario = (-5.00+8.40) = $3.40 million

Expected NPV = 0.1 x (-0.72) + 0.9 x (3.40) = $2.99 million

If the cash flows are only $1.35 million, the NPV of the project is negative and, thus, would not be undertaken. The value of the option of waiting for two years is evaluated as 0.1 x (0) + 0.9 x (3.4) = $3.06 million.

Since the NPV of waiting two years is more than going ahead and commencing the project today, hence it makes to wait two years to drill

2)

Option 1 (100% probability)

C0 = Cost in Year 0 = $8.00 million

CF = Cash Flow per year = $4.00 million for Years 1, 2, 3, 4

DR = Discount Rate = 10%

Year	Cash flows	PV of cash flows (in $ million)
1	4.00/(1+0.1)^1	3.64
2	4.00/(1+0.1)^2	3.31
3	4.00/(1+0.1)^3	3.01
4	4.00/(1+0.1)^4	2.73
	Total	12.68

NPV = -8.00+12.68 = $4.68 million

Option 2 (wait 2 years with 90% Probability)

C0 = Cost in Year 0 = $9.00 million

CF = Cash Flow per year = $4.20 million for Years 1, 2, 3, 4

DR = Discount Rate = 10%

Year	Cash flows	PV of cash flows (in $ million)
1	4.20/(1+0.1)^1	3.82
2	4.20/(1+0.1)^2	3.47
3	4.20/(1+0.1)^3	3.16
4	4.20/(1+0.1)^4	2.87
	Total	13.31

NPV = -9.00+13.31 = $4.31 millions and with 90% probability the revised NPV is $3.88 million

Option 2 (wait 2 years with 10% probability)

C0 = Cost in Year 0 = $9.00 million

CF = Cash Flow per year = $2.20 million for Years 1, 2, 3, 4

DR = Discount Rate = 10%

Year	Cash flows	PV of cash flows (in million)
1	2.20/(1+0.1)^1	2.00
2	2.20/(1+0.1)^2	1.82
3	2.20/(1+0.1)^3	1.65
4	2.20/(1+0.1)^4	1.50
	Total	6.97

NPV = -9.00+6.97 = -$2.03 millions and with 10% probability the revised NPV is -$0.20 million

Option 2 NPV = $3.88 - $0.20 = $3.68 million

Black-Scholes Model:

Spot Price = Option 1 = $4.68

Strike Price = Option 2 = $3.68

t = Time to Expiration = 2 years between Option 1 and Option 2

v = Volatility = Variance of the project's rate of return = 11.10%

r = Risk Free Interest Rate = 5%

Use the Black-Sholes caculator at https://goodcalculators.com/black-scholes-calculator/

Call Price = Value of the Option = $1.35 million